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 r692401 = x;
        double r692402 = r692401 * r692401;
        double r692403 = 3.0;
        double r692404 = 2.0;
        double r692405 = r692401 * r692404;
        double r692406 = r692403 - r692405;
        double r692407 = r692402 * r692406;
        return r692407;
}
↓
double f(double x) {
        double r692408 = x;
        double r692409 = r692408 * r692408;
        double r692410 = 3.0;
        double r692411 = r692409 * r692410;
        double r692412 = 2.0;
        double r692413 = 3.0;
        double r692414 = pow(r692408, r692413);
        double r692415 = r692412 * r692414;
        double r692416 = -r692415;
        double r692417 = r692411 + r692416;
        return r692417;
}

Error

Bits error versus x

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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 2020002 
(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))))