Average Error: 0.2 → 0.1
Time: 3.1s
Precision: 64
\[\left(x \cdot x\right) \cdot \left(3 - x \cdot 2\right)\]
↓
\[\left(x \cdot x\right) \cdot 3 + \left(-2 \cdot {x}^{3}\right)\]
\left(x \cdot x\right) \cdot \left(3 - x \cdot 2\right)
↓
\left(x \cdot x\right) \cdot 3 + \left(-2 \cdot {x}^{3}\right)
double f(double x) {
        double r1047115 = x;
        double r1047116 = r1047115 * r1047115;
        double r1047117 = 3.0;
        double r1047118 = 2.0;
        double r1047119 = r1047115 * r1047118;
        double r1047120 = r1047117 - r1047119;
        double r1047121 = r1047116 * r1047120;
        return r1047121;
}
↓
double f(double x) {
        double r1047122 = x;
        double r1047123 = r1047122 * r1047122;
        double r1047124 = 3.0;
        double r1047125 = r1047123 * r1047124;
        double r1047126 = 2.0;
        double r1047127 = 3.0;
        double r1047128 = pow(r1047122, r1047127);
        double r1047129 = r1047126 * r1047128;
        double r1047130 = -r1047129;
        double r1047131 = r1047125 + r1047130;
        return r1047131;
}

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.2
Target0.2
Herbie0.1
\[x \cdot \left(x \cdot \left(3 - x \cdot 2\right)\right)\]

Derivation

  1. Initial program 0.2

    \[\left(x \cdot x\right) \cdot \left(3 - x \cdot 2\right)\]
  2. Using strategy rm

  3. Applied sub-neg0.2

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

  4. Applied distribute-lft-in0.2

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

  5. Simplified0.1

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

  6. Final simplification0.1

    \[\leadsto \left(x \cdot x\right) \cdot 3 + \left(-2 \cdot {x}^{3}\right)\]

Reproduce

herbie shell --seed 2020025 +o rules:numerics
(FPCore (x)
  :name "Data.Spline.Key:interpolateKeys from smoothie-0.4.0.2"
  :precision binary64

  :herbie-target
  (* x (* x (- 3 (* x 2))))

  (* (* x x) (- 3 (* x 2))))