Average Error: 0.2 → 0.2
Time: 2.6s
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 r677898 = 3.0;
        double r677899 = 2.0;
        double r677900 = x;
        double r677901 = r677900 * r677898;
        double r677902 = r677899 - r677901;
        double r677903 = r677898 * r677902;
        double r677904 = r677903 * r677900;
        return r677904;
}
↓
double f(double x) {
        double r677905 = 6.0;
        double r677906 = 9.0;
        double r677907 = x;
        double r677908 = r677906 * r677907;
        double r677909 = r677905 - r677908;
        double r677910 = r677909 * r677907;
        return r677910;
}

Error

Bits error versus x

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Results

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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

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

Reproduce

herbie shell --seed 2020065 +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))