Average Error: 62.0 → 52.0
Time: 2.6s
Precision: 64
\[x = 10864 \land y = 18817\]
\[9 \cdot {x}^{4} - \left(y \cdot y\right) \cdot \left(y \cdot y - 2\right)\]
↓
\[\sqrt[3]{{\left(9 \cdot {x}^{4} - {y}^{4}\right)}^{3}} - \left(-2\right) \cdot \left(y \cdot y\right)\]
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(-2\right) \cdot \left(y \cdot y\right)
double f(double x, double y) {
        double r51744 = 9.0;
        double r51745 = x;
        double r51746 = 4.0;
        double r51747 = pow(r51745, r51746);
        double r51748 = r51744 * r51747;
        double r51749 = y;
        double r51750 = r51749 * r51749;
        double r51751 = 2.0;
        double r51752 = r51750 - r51751;
        double r51753 = r51750 * r51752;
        double r51754 = r51748 - r51753;
        return r51754;
}
↓
double f(double x, double y) {
        double r51755 = 9.0;
        double r51756 = x;
        double r51757 = 4.0;
        double r51758 = pow(r51756, r51757);
        double r51759 = r51755 * r51758;
        double r51760 = y;
        double r51761 = 4.0;
        double r51762 = pow(r51760, r51761);
        double r51763 = r51759 - r51762;
        double r51764 = 3.0;
        double r51765 = pow(r51763, r51764);
        double r51766 = cbrt(r51765);
        double r51767 = 2.0;
        double r51768 = -r51767;
        double r51769 = r51760 * r51760;
        double r51770 = r51768 * r51769;
        double r51771 = r51766 - r51770;
        return r51771;
}

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-rgt-in62.0

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

  5. Applied associate--r+52.0

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

  6. Simplified52.0

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

  8. Applied add-cbrt-cube52.0

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

  9. Simplified52.0

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

  10. Final simplification52.0

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

Reproduce

herbie shell --seed 2020039 
(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))))