Diagrams.Tangent:$catParam from diagrams-lib-1.3.0.3, D

Average Error: 0.1 → 0.1

Time: 2.7s

Precision: 64

Math

\[3 \cdot \left(\left(\left(x \cdot 3\right) \cdot x - x \cdot 4\right) + 1\right)\]

↓

\[x \cdot \left(x \cdot 9 - 12\right) + 3\]

C

double f(double x) {
        double r658510 = 3.0;
        double r658511 = x;
        double r658512 = r658511 * r658510;
        double r658513 = r658512 * r658511;
        double r658514 = 4.0;
        double r658515 = r658511 * r658514;
        double r658516 = r658513 - r658515;
        double r658517 = 1.0;
        double r658518 = r658516 + r658517;
        double r658519 = r658510 * r658518;
        return r658519;
}

↓

double f(double x) {
        double r658520 = x;
        double r658521 = 9.0;
        double r658522 = r658520 * r658521;
        double r658523 = 12.0;
        double r658524 = r658522 - r658523;
        double r658525 = r658520 * r658524;
        double r658526 = 3.0;
        double r658527 = r658525 + r658526;
        return r658527;
}

Error

Bits error versus x

Target

Original	0.1
Target	0.1
Herbie	0.1

\[3 + \left(\left(9 \cdot x\right) \cdot x - 12 \cdot x\right)\]

Derivation

1. Initial program 0.1

   \[3 \cdot \left(\left(\left(x \cdot 3\right) \cdot x - x \cdot 4\right) + 1\right)\]

2. Taylor expanded around 0 0.1

   \[\leadsto \color{blue}{\left(9 \cdot {x}^{2} + 3\right) - 12 \cdot x}\]

3. Taylor expanded around 0 0.1

   \[\leadsto \color{blue}{\left(9 \cdot {x}^{2} + 3\right) - 12 \cdot x}\]

4. Simplified 0.1

   \[\leadsto \color{blue}{x \cdot \left(x \cdot 9 - 12\right) + 3}\]

5. Final simplification 0.1

   \[\leadsto x \cdot \left(x \cdot 9 - 12\right) + 3\]

Reproduce

herbie shell --seed 2019354 
(FPCore (x)
  :name "Diagrams.Tangent:$catParam from diagrams-lib-1.3.0.3, D"
  :precision binary64

  :herbie-target
  (+ 3 (- (* (* 9 x) x) (* 12 x)))

  (* 3 (+ (- (* (* x 3) x) (* x 4)) 1)))