Average Error: 0.3 → 0.2
Time: 2.7s
Precision: 64
\[\left(3 \cdot \left(2 - x \cdot 3\right)\right) \cdot x\]
↓
\[\left(6 - 9 \cdot x\right) \cdot x\]
\left(3 \cdot \left(2 - x \cdot 3\right)\right) \cdot x
↓
\left(6 - 9 \cdot x\right) \cdot x
double f(double x) {
        double r705870 = 3.0;
        double r705871 = 2.0;
        double r705872 = x;
        double r705873 = r705872 * r705870;
        double r705874 = r705871 - r705873;
        double r705875 = r705870 * r705874;
        double r705876 = r705875 * r705872;
        return r705876;
}
↓
double f(double x) {
        double r705877 = 6.0;
        double r705878 = 9.0;
        double r705879 = x;
        double r705880 = r705878 * r705879;
        double r705881 = r705877 - r705880;
        double r705882 = r705881 * r705879;
        return r705882;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.3
Target0.2
Herbie0.2
\[6 \cdot x - 9 \cdot \left(x \cdot x\right)\]

Derivation

  1. Initial program 0.3

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

  2. Taylor expanded around 0 0.2

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

  3. Final simplification0.2

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

Reproduce

herbie shell --seed 2020036 +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))