Average Error: 62.0 → 62.0
Time: 5.0s
Precision: 64
\[x = 10864 \land y = 18817\]
\[9 \cdot {x}^{4} - \left(y \cdot y\right) \cdot \left(y \cdot y - 2\right)\]
↓
\[9 \cdot {x}^{4} - \left({y}^{4} - 2 \cdot \left(y \cdot y\right)\right)\]
9 \cdot {x}^{4} - \left(y \cdot y\right) \cdot \left(y \cdot y - 2\right)
↓
9 \cdot {x}^{4} - \left({y}^{4} - 2 \cdot \left(y \cdot y\right)\right)
double f(double x, double y) {
        double r53822 = 9.0;
        double r53823 = x;
        double r53824 = 4.0;
        double r53825 = pow(r53823, r53824);
        double r53826 = r53822 * r53825;
        double r53827 = y;
        double r53828 = r53827 * r53827;
        double r53829 = 2.0;
        double r53830 = r53828 - r53829;
        double r53831 = r53828 * r53830;
        double r53832 = r53826 - r53831;
        return r53832;
}
↓
double f(double x, double y) {
        double r53833 = 9.0;
        double r53834 = x;
        double r53835 = 4.0;
        double r53836 = pow(r53834, r53835);
        double r53837 = r53833 * r53836;
        double r53838 = y;
        double r53839 = 4.0;
        double r53840 = pow(r53838, r53839);
        double r53841 = 2.0;
        double r53842 = r53838 * r53838;
        double r53843 = r53841 * r53842;
        double r53844 = r53840 - r53843;
        double r53845 = r53837 - r53844;
        return r53845;
}

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 simplification62.0

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

Reproduce

herbie shell --seed 2019308 
(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))))