Average Error: 0.3 → 0.2
Time: 2.7s
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 r634230 = 3.0;
        double r634231 = 2.0;
        double r634232 = x;
        double r634233 = r634232 * r634230;
        double r634234 = r634231 - r634233;
        double r634235 = r634230 * r634234;
        double r634236 = r634235 * r634232;
        return r634236;
}
↓
double f(double x) {
        double r634237 = x;
        double r634238 = 6.0;
        double r634239 = 9.0;
        double r634240 = r634237 * r634239;
        double r634241 = r634238 - r634240;
        double r634242 = r634237 * r634241;
        return r634242;
}

Error

Bits error versus x

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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. Using strategy rm

  3. Applied associate-*l*0.2

    \[\leadsto \color{blue}{3 \cdot \left(\left(2 - x \cdot 3\right) \cdot x\right)}\]

  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

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

Reproduce

herbie shell --seed 2020062 +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))