Average Error: 52.0 → 52.0
Time: 7.6s
Precision: 64
\[x = 10864 \land y = 18817\]
\[\left(9 \cdot {x}^{4} - {y}^{4}\right) + 2 \cdot \left(y \cdot y\right)\]
↓
\[2 \cdot \left(y \cdot y\right) + \sqrt[3]{{\left({x}^{4} \cdot 9 - {y}^{4}\right)}^{3}}\]
\left(9 \cdot {x}^{4} - {y}^{4}\right) + 2 \cdot \left(y \cdot y\right)
↓
2 \cdot \left(y \cdot y\right) + \sqrt[3]{{\left({x}^{4} \cdot 9 - {y}^{4}\right)}^{3}}
double f(double x, double y) {
        double r44089 = 9.0;
        double r44090 = x;
        double r44091 = 4.0;
        double r44092 = pow(r44090, r44091);
        double r44093 = r44089 * r44092;
        double r44094 = y;
        double r44095 = pow(r44094, r44091);
        double r44096 = r44093 - r44095;
        double r44097 = 2.0;
        double r44098 = r44094 * r44094;
        double r44099 = r44097 * r44098;
        double r44100 = r44096 + r44099;
        return r44100;
}
↓
double f(double x, double y) {
        double r44101 = 2.0;
        double r44102 = y;
        double r44103 = r44102 * r44102;
        double r44104 = r44101 * r44103;
        double r44105 = x;
        double r44106 = 4.0;
        double r44107 = pow(r44105, r44106);
        double r44108 = 9.0;
        double r44109 = r44107 * r44108;
        double r44110 = pow(r44102, r44106);
        double r44111 = r44109 - r44110;
        double r44112 = 3.0;
        double r44113 = pow(r44111, r44112);
        double r44114 = cbrt(r44113);
        double r44115 = r44104 + r44114;
        return r44115;
}

Error

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Your Program's Arguments

Results

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Derivation

  1. Initial program 52.0

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

  3. Applied add-cbrt-cube52.0

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

  4. Simplified52.0

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

  5. Final simplification52.0

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

Reproduce

herbie shell --seed 2019194 
(FPCore (x y)
  :name "From Rump in a 1983 paper"
  :pre (and (== x 10864.0) (== y 18817.0))
  (+ (- (* 9.0 (pow x 4.0)) (pow y 4.0)) (* 2.0 (* y y))))