Average Error: 52.0 → 52.0
Time: 10.3s
Precision: 64
\[x = 10864 \land y = 18817\]
\[\left(9 \cdot {x}^{4} - {y}^{4}\right) + 2 \cdot \left(y \cdot y\right)\]
↓
\[2 \cdot \left(y \cdot y\right) + \sqrt[3]{\left({x}^{4} \cdot 9 - {y}^{4}\right) \cdot \left(\left({x}^{4} \cdot 9 - {y}^{4}\right) \cdot \left({x}^{4} \cdot 9 - {y}^{4}\right)\right)}\]
\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) \cdot \left(\left({x}^{4} \cdot 9 - {y}^{4}\right) \cdot \left({x}^{4} \cdot 9 - {y}^{4}\right)\right)}
double f(double x, double y) {
        double r3870053 = 9.0;
        double r3870054 = x;
        double r3870055 = 4.0;
        double r3870056 = pow(r3870054, r3870055);
        double r3870057 = r3870053 * r3870056;
        double r3870058 = y;
        double r3870059 = pow(r3870058, r3870055);
        double r3870060 = r3870057 - r3870059;
        double r3870061 = 2.0;
        double r3870062 = r3870058 * r3870058;
        double r3870063 = r3870061 * r3870062;
        double r3870064 = r3870060 + r3870063;
        return r3870064;
}
↓
double f(double x, double y) {
        double r3870065 = 2.0;
        double r3870066 = y;
        double r3870067 = r3870066 * r3870066;
        double r3870068 = r3870065 * r3870067;
        double r3870069 = x;
        double r3870070 = 4.0;
        double r3870071 = pow(r3870069, r3870070);
        double r3870072 = 9.0;
        double r3870073 = r3870071 * r3870072;
        double r3870074 = pow(r3870066, r3870070);
        double r3870075 = r3870073 - r3870074;
        double r3870076 = r3870075 * r3870075;
        double r3870077 = r3870075 * r3870076;
        double r3870078 = cbrt(r3870077);
        double r3870079 = r3870068 + r3870078;
        return r3870079;
}

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. Final simplification52.0

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

Reproduce

herbie shell --seed 2019174 
(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))))