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

Average Error: 0.3 → 0.2

Time: 3.7s

Precision: 64

Math

\[\left(3 \cdot \left(2 - x \cdot 3\right)\right) \cdot x\]

↓

\[x \cdot \left(6 - x \cdot 9\right)\]

C

double f(double x) {
        double r2840 = 3.0;
        double r2841 = 2.0;
        double r2842 = x;
        double r2843 = r2842 * r2840;
        double r2844 = r2841 - r2843;
        double r2845 = r2840 * r2844;
        double r2846 = r2845 * r2842;
        return r2846;
}

↓

double f(double x) {
        double r2847 = x;
        double r2848 = 6.0;
        double r2849 = 9.0;
        double r2850 = r2847 * r2849;
        double r2851 = r2848 - r2850;
        double r2852 = r2847 * r2851;
        return r2852;
}

Error

Bits error versus x

Target

Original	0.3
Target	0.2
Herbie	0.2

\[6 \cdot x - 9 \cdot \left(x \cdot x\right)\]

Derivation

1. Initial program 0.3

   \[\left(3 \cdot \left(2 - x \cdot 3\right)\right) \cdot x\]
2. Using strategy rm

3. Applied associate-*l* 0.3

   \[\leadsto \color{blue}{3 \cdot \left(\left(2 - x \cdot 3\right) \cdot x\right)}\]
4. Using strategy rm

5. Applied add-cube-cbrt 0.3

   \[\leadsto \color{blue}{\left(\left(\sqrt[3]{3} \cdot \sqrt[3]{3}\right) \cdot \sqrt[3]{3}\right)} \cdot \left(\left(2 - x \cdot 3\right) \cdot x\right)\]

6. Applied associate-*l* 0.5

   \[\leadsto \color{blue}{\left(\sqrt[3]{3} \cdot \sqrt[3]{3}\right) \cdot \left(\sqrt[3]{3} \cdot \left(\left(2 - x \cdot 3\right) \cdot x\right)\right)}\]

7. Taylor expanded around 0 0.2

   \[\leadsto \color{blue}{6 \cdot x - 9 \cdot {x}^{2}}\]

8. Simplified 0.2

   \[\leadsto \color{blue}{x \cdot \left(6 - x \cdot 9\right)}\]

9. Final simplification 0.2

   \[\leadsto x \cdot \left(6 - x \cdot 9\right)\]

Reproduce

herbie shell --seed 2020025 +o rules:numerics
(FPCore (x)
  :name "Diagrams.Tangent:$catParam from diagrams-lib-1.3.0.3, E"
  :precision binary64

  :herbie-target
  (- (* 6 x) (* 9 (* x x)))

  (* (* 3 (- 2 (* x 3))) x))