Average Error: 0.2 → 0.1
Time: 15.4s
Precision: 64
\[\left(x \cdot x\right) \cdot \left(3 - x \cdot 2\right)\]
↓
\[x \cdot \left(x \cdot 3\right) + \left(-2 \cdot {x}^{3}\right)\]
\left(x \cdot x\right) \cdot \left(3 - x \cdot 2\right)
↓
x \cdot \left(x \cdot 3\right) + \left(-2 \cdot {x}^{3}\right)
double f(double x) {
        double r620338 = x;
        double r620339 = r620338 * r620338;
        double r620340 = 3.0;
        double r620341 = 2.0;
        double r620342 = r620338 * r620341;
        double r620343 = r620340 - r620342;
        double r620344 = r620339 * r620343;
        return r620344;
}
↓
double f(double x) {
        double r620345 = x;
        double r620346 = 3.0;
        double r620347 = r620345 * r620346;
        double r620348 = r620345 * r620347;
        double r620349 = 2.0;
        double r620350 = 3.0;
        double r620351 = pow(r620345, r620350);
        double r620352 = r620349 * r620351;
        double r620353 = -r620352;
        double r620354 = r620348 + r620353;
        return r620354;
}

Error

Bits error versus x

Try it out

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. 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 simplification0.1

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

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))))