Average Error: 0.3 → 0.2
Time: 28.8s
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 r32360894 = 3.0;
        double r32360895 = 2.0;
        double r32360896 = x;
        double r32360897 = r32360896 * r32360894;
        double r32360898 = r32360895 - r32360897;
        double r32360899 = r32360894 * r32360898;
        double r32360900 = r32360899 * r32360896;
        return r32360900;
}
↓
double f(double x) {
        double r32360901 = 6.0;
        double r32360902 = x;
        double r32360903 = 9.0;
        double r32360904 = r32360902 * r32360903;
        double r32360905 = r32360901 - r32360904;
        double r32360906 = r32360905 * r32360902;
        return r32360906;
}

Error

Bits error versus x

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Results

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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. 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. Taylor expanded around 0 0.2

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

  5. Simplified0.2

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

  6. Final simplification0.2

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

Reproduce

herbie shell --seed 2019200 +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))