Average Error: 0.2 → 0.1
Time: 2.4s
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 r686186 = x;
        double r686187 = r686186 * r686186;
        double r686188 = 3.0;
        double r686189 = 2.0;
        double r686190 = r686186 * r686189;
        double r686191 = r686188 - r686190;
        double r686192 = r686187 * r686191;
        return r686192;
}
↓
double f(double x) {
        double r686193 = x;
        double r686194 = r686193 * r686193;
        double r686195 = 3.0;
        double r686196 = r686194 * r686195;
        double r686197 = 2.0;
        double r686198 = 3.0;
        double r686199 = pow(r686193, r686198);
        double r686200 = r686197 * r686199;
        double r686201 = -r686200;
        double r686202 = r686196 + r686201;
        return r686202;
}

Error

Bits error versus x

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Your Program's Arguments

Results

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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 2020003 
(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))))