Average Error: 0.2 → 0.2
Time: 17.1s
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 r35260191 = 3.0;
        double r35260192 = 2.0;
        double r35260193 = x;
        double r35260194 = r35260193 * r35260191;
        double r35260195 = r35260192 - r35260194;
        double r35260196 = r35260191 * r35260195;
        double r35260197 = r35260196 * r35260193;
        return r35260197;
}
↓
double f(double x) {
        double r35260198 = 6.0;
        double r35260199 = x;
        double r35260200 = 9.0;
        double r35260201 = r35260199 * r35260200;
        double r35260202 = r35260198 - r35260201;
        double r35260203 = r35260202 * r35260199;
        return r35260203;
}

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

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

  3. Simplified0.2

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

  4. Final simplification0.2

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

Reproduce

herbie shell --seed 2019170 +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))