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

Average Error: 0.1 → 0.1

Time: 10.5s

Precision: 64

Math

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

↓

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

C

double f(double x) {
        double r506429 = 3.0;
        double r506430 = x;
        double r506431 = r506430 * r506429;
        double r506432 = r506431 * r506430;
        double r506433 = 4.0;
        double r506434 = r506430 * r506433;
        double r506435 = r506432 - r506434;
        double r506436 = 1.0;
        double r506437 = r506435 + r506436;
        double r506438 = r506429 * r506437;
        return r506438;
}

↓

double f(double x) {
        double r506439 = 3.0;
        double r506440 = x;
        double r506441 = 9.0;
        double r506442 = r506441 * r506440;
        double r506443 = 12.0;
        double r506444 = r506442 - r506443;
        double r506445 = r506440 * r506444;
        double r506446 = r506439 + r506445;
        return r506446;
}

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. Simplified 0.1

   \[\leadsto \color{blue}{3 \cdot \left(1 + x \cdot \left(x \cdot 3 - 4\right)\right)}\]

3. Taylor expanded around 0 0.1

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

4. Simplified 0.1

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

5. Final simplification 0.1

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

Reproduce

herbie shell --seed 2019305 
(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)))