Average Error: 0.2 → 0.2
Time: 12.0s
Precision: 64
\[\left(x \cdot x\right) \cdot \left(3 - x \cdot 2\right)\]
↓
\[\left(x \cdot x\right) \cdot \left(3 - x \cdot 2\right)\]
\left(x \cdot x\right) \cdot \left(3 - x \cdot 2\right)
↓
\left(x \cdot x\right) \cdot \left(3 - x \cdot 2\right)
double f(double x) {
        double r537390 = x;
        double r537391 = r537390 * r537390;
        double r537392 = 3.0;
        double r537393 = 2.0;
        double r537394 = r537390 * r537393;
        double r537395 = r537392 - r537394;
        double r537396 = r537391 * r537395;
        return r537396;
}
↓
double f(double x) {
        double r537397 = x;
        double r537398 = r537397 * r537397;
        double r537399 = 3.0;
        double r537400 = 2.0;
        double r537401 = r537397 * r537400;
        double r537402 = r537399 - r537401;
        double r537403 = r537398 * r537402;
        return r537403;
}

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

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. Using strategy rm

  7. Applied associate-*l*0.1

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

  8. Final simplification0.2

    \[\leadsto \left(x \cdot x\right) \cdot \left(3 - x \cdot 2\right)\]

Reproduce

herbie shell --seed 2019303 
(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))))