Table 1 Computed values of functions with the proposed CRNs compared to their exact values.

From: Computing Mathematical Functions using DNA via Fractional Coding

Function

x = 0

x = 0.1

x = 0.2

x = 0.3

x = 0.4

x = 0.5

x = 0.6

x = 0.7

x = 0.8

x = 0.9

x = 1

MSE

e − x

computed

0.9568

0.8770

0.7975

0.7228

0.6609

0.5951

0.5295

0.4772

0.4300

0.3872

0.3482

5.02 × 10−4

exact

1

0.9048

0.8187

0.7408

0.6703

0.6065

0.5488

0.4966

0.4493

0.4066

0.3679

sin(x)

computed

0

0.1045

0.2062

0.3043

0.3970

0.4833

0.5570

0.6261

0.6844

0.7460

0.7967

4.63×10−4

exact

0

0.0998

0.1986

0.2955

0.3894

0.4794

0.5646

0.64421

0.7173

0.7833

0.8414

cos(x)

computed

0.9728

0.9757

0.9641

0.9407

0.9129

0.8671

0.8071

0.7461

0.6778

0.6029

0.5221

3.16 × 10−4

exact

1

0.9950

0.9800

0.9553

0.9210

0.8775

0.8253

0.7648

0.6967

0.6216

0.5403

log(1 + x)

computed

0.0090

0.0985

0.1868

0.2675

0.3410

0.4075

0.4660

0.5212

0.5707

0.6217

0.6699

1.8 × 10−4

exact

0

0.0953

0.1823

0.2623

0.3364

0.4054

0.4700

0.5306

0.5877

0.6418

0.6931

tanh(x)

computed

0

0.0935

0.1883

0.2823

0.3701

0.4574

0.5277

0.5826

0.6246

0.6682

0.7038

7.35 × 10−4

exact

0

0.0996

0.1973

0.2913

0.3799

0.4621

0.5370

0.6043

0.6640

0.7162

0.7615

sigmoid(x)

computed

0.5196

0.5453

0.5657

0.5878

0.6068

0.6212

0.6366

0.6570

0.6721

0.6906

0.7084

2.5 × 10−4

exact

0.5000

0.5250

0.5498

0.5744

0.5987

0.6225

0.6457

0.6682

0.6900

0.7109

0.7311

\(\frac{sin(\pi x)}{\pi }\)

computed

0

0.0984

0.1871

0.2574

0.3023

0.3176

0.3016

0.2565

0.1931

0.1329

0.0899

8.48 × 10−4

exact

0

0.0984

0.1871

0.2576

0.3027

0.3183

0.3027

0.2575

0.1871

0.0984

0

\(\frac{cos(\pi x)}{5.9348}\)

computed

0.1685

0.1602

0.1363

0.0991

0.0527

0.0030

−0.0429

−0.07729

−0.0921

−0.0852

−0.0673

1.67 × 10−3

exact

0.1685

0.1603

0.1363

0.0990

0.0521

0

−0.0521

−0.0990

−0.1363

−0.1603

−0.1685

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