Average Error: 0.2 → 0.2
Time: 15.2s
Precision: 64
\[\left(3 \cdot \left(2 - x \cdot 3\right)\right) \cdot x\]
↓
\[x \cdot \left(6 - x \cdot 9\right)\]
\left(3 \cdot \left(2 - x \cdot 3\right)\right) \cdot x
↓
x \cdot \left(6 - x \cdot 9\right)
double f(double x) {
        double r544767 = 3.0;
        double r544768 = 2.0;
        double r544769 = x;
        double r544770 = r544769 * r544767;
        double r544771 = r544768 - r544770;
        double r544772 = r544767 * r544771;
        double r544773 = r544772 * r544769;
        return r544773;
}
↓
double f(double x) {
        double r544774 = x;
        double r544775 = 6.0;
        double r544776 = 9.0;
        double r544777 = r544774 * r544776;
        double r544778 = r544775 - r544777;
        double r544779 = r544774 * r544778;
        return r544779;
}

Error

Bits error versus x

Try it out

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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

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

  3. Simplified0.2

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

  4. Final simplification0.2

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

Reproduce

herbie shell --seed 2019199 
(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))