Average Error: 62.0 → 52.0
Time: 2.8s
Precision: 64
\[x = 10864 \land y = 18817\]
\[9 \cdot {x}^{4} - \left(y \cdot y\right) \cdot \left(y \cdot y - 2\right)\]
↓
\[\sqrt[3]{{\left(9 \cdot {x}^{4} - {y}^{4}\right)}^{3}} - \left(y \cdot y\right) \cdot \left(-2\right)\]
9 \cdot {x}^{4} - \left(y \cdot y\right) \cdot \left(y \cdot y - 2\right)
↓
\sqrt[3]{{\left(9 \cdot {x}^{4} - {y}^{4}\right)}^{3}} - \left(y \cdot y\right) \cdot \left(-2\right)
double f(double x, double y) {
        double r55053 = 9.0;
        double r55054 = x;
        double r55055 = 4.0;
        double r55056 = pow(r55054, r55055);
        double r55057 = r55053 * r55056;
        double r55058 = y;
        double r55059 = r55058 * r55058;
        double r55060 = 2.0;
        double r55061 = r55059 - r55060;
        double r55062 = r55059 * r55061;
        double r55063 = r55057 - r55062;
        return r55063;
}
↓
double f(double x, double y) {
        double r55064 = 9.0;
        double r55065 = x;
        double r55066 = 4.0;
        double r55067 = pow(r55065, r55066);
        double r55068 = r55064 * r55067;
        double r55069 = y;
        double r55070 = 4.0;
        double r55071 = pow(r55069, r55070);
        double r55072 = r55068 - r55071;
        double r55073 = 3.0;
        double r55074 = pow(r55072, r55073);
        double r55075 = cbrt(r55074);
        double r55076 = r55069 * r55069;
        double r55077 = 2.0;
        double r55078 = -r55077;
        double r55079 = r55076 * r55078;
        double r55080 = r55075 - r55079;
        return r55080;
}

Error

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 62.0

    \[9 \cdot {x}^{4} - \left(y \cdot y\right) \cdot \left(y \cdot y - 2\right)\]
  2. Using strategy rm

  3. Applied sub-neg62.0

    \[\leadsto 9 \cdot {x}^{4} - \left(y \cdot y\right) \cdot \color{blue}{\left(y \cdot y + \left(-2\right)\right)}\]

  4. Applied distribute-lft-in62.0

    \[\leadsto 9 \cdot {x}^{4} - \color{blue}{\left(\left(y \cdot y\right) \cdot \left(y \cdot y\right) + \left(y \cdot y\right) \cdot \left(-2\right)\right)}\]

  5. Applied associate--r+52.0

    \[\leadsto \color{blue}{\left(9 \cdot {x}^{4} - \left(y \cdot y\right) \cdot \left(y \cdot y\right)\right) - \left(y \cdot y\right) \cdot \left(-2\right)}\]

  6. Simplified52.0

    \[\leadsto \color{blue}{\left(9 \cdot {x}^{4} + \left(-{y}^{4}\right)\right)} - \left(y \cdot y\right) \cdot \left(-2\right)\]
  7. Using strategy rm

  8. Applied add-cbrt-cube52.0

    \[\leadsto \color{blue}{\sqrt[3]{\left(\left(9 \cdot {x}^{4} + \left(-{y}^{4}\right)\right) \cdot \left(9 \cdot {x}^{4} + \left(-{y}^{4}\right)\right)\right) \cdot \left(9 \cdot {x}^{4} + \left(-{y}^{4}\right)\right)}} - \left(y \cdot y\right) \cdot \left(-2\right)\]

  9. Simplified52.0

    \[\leadsto \sqrt[3]{\color{blue}{{\left(9 \cdot {x}^{4} - {y}^{4}\right)}^{3}}} - \left(y \cdot y\right) \cdot \left(-2\right)\]

  10. Final simplification52.0

    \[\leadsto \sqrt[3]{{\left(9 \cdot {x}^{4} - {y}^{4}\right)}^{3}} - \left(y \cdot y\right) \cdot \left(-2\right)\]

Reproduce

herbie shell --seed 2020064 
(FPCore (x y)
  :name "From Rump in a 1983 paper, rewritten"
  :precision binary64
  :pre (and (== x 10864) (== y 18817))
  (- (* 9 (pow x 4)) (* (* y y) (- (* y y) 2))))