Average Error: 0.2 → 0.2
Time: 9.8s
Precision: 64
\[\left(3 \cdot \left(2 - x \cdot 3\right)\right) \cdot x\]
↓
\[\left(6 - x \cdot 9\right) \cdot x\]
\left(3 \cdot \left(2 - x \cdot 3\right)\right) \cdot x
↓
\left(6 - x \cdot 9\right) \cdot x
double f(double x) {
        double r30085846 = 3.0;
        double r30085847 = 2.0;
        double r30085848 = x;
        double r30085849 = r30085848 * r30085846;
        double r30085850 = r30085847 - r30085849;
        double r30085851 = r30085846 * r30085850;
        double r30085852 = r30085851 * r30085848;
        return r30085852;
}
↓
double f(double x) {
        double r30085853 = 6.0;
        double r30085854 = x;
        double r30085855 = 9.0;
        double r30085856 = r30085854 * r30085855;
        double r30085857 = r30085853 - r30085856;
        double r30085858 = r30085857 * r30085854;
        return r30085858;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.2
Target0.2
Herbie0.2
\[6 \cdot x - 9 \cdot \left(x \cdot x\right)\]

Derivation

  1. Initial program 0.2

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

  2. Taylor expanded around 0 0.2

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

  3. Final simplification0.2

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

Reproduce

herbie shell --seed 2019171 +o rules:numerics
(FPCore (x)
  :name "Diagrams.Tangent:$catParam from diagrams-lib-1.3.0.3, E"

  :herbie-target
  (- (* 6.0 x) (* 9.0 (* x x)))

  (* (* 3.0 (- 2.0 (* x 3.0))) x))