Average Error: 0.2 → 0.1
Time: 31.9s
Precision: 64
\[\left(x \cdot x\right) \cdot \left(3 - x \cdot 2\right)\]
↓
\[x \cdot \left(3 \cdot x\right) + \left(-2 \cdot {x}^{3}\right)\]
\left(x \cdot x\right) \cdot \left(3 - x \cdot 2\right)
↓
x \cdot \left(3 \cdot x\right) + \left(-2 \cdot {x}^{3}\right)
double f(double x) {
        double r898382 = x;
        double r898383 = r898382 * r898382;
        double r898384 = 3.0;
        double r898385 = 2.0;
        double r898386 = r898382 * r898385;
        double r898387 = r898384 - r898386;
        double r898388 = r898383 * r898387;
        return r898388;
}
↓
double f(double x) {
        double r898389 = x;
        double r898390 = 3.0;
        double r898391 = r898390 * r898389;
        double r898392 = r898389 * r898391;
        double r898393 = 2.0;
        double r898394 = 3.0;
        double r898395 = pow(r898389, r898394);
        double r898396 = r898393 * r898395;
        double r898397 = -r898396;
        double r898398 = r898392 + r898397;
        return r898398;
}

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 associate-*l*0.2

    \[\leadsto \color{blue}{x \cdot \left(x \cdot \left(3 - x \cdot 2\right)\right)}\]
  4. Using strategy rm

  5. Applied sub-neg0.2

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

  6. Applied distribute-lft-in0.2

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

  7. Applied distribute-lft-in0.2

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

  8. Simplified0.2

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

  9. Simplified0.1

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

  10. Final simplification0.1

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

Reproduce

herbie shell --seed 2020045 
(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))))