Average Error: 52.0 → 52.0
Time: 13.5s
Precision: 64
\[x = 10864 \land y = 18817\]
\[\left(9 \cdot {x}^{4} - {y}^{4}\right) + 2 \cdot \left(y \cdot y\right)\]
↓
\[\sqrt[3]{{\left(9 \cdot {x}^{4} - {y}^{4}\right)}^{3}} + 2 \cdot \left(y \cdot y\right)\]
\left(9 \cdot {x}^{4} - {y}^{4}\right) + 2 \cdot \left(y \cdot y\right)
↓
\sqrt[3]{{\left(9 \cdot {x}^{4} - {y}^{4}\right)}^{3}} + 2 \cdot \left(y \cdot y\right)
double f(double x, double y) {
        double r42094 = 9.0;
        double r42095 = x;
        double r42096 = 4.0;
        double r42097 = pow(r42095, r42096);
        double r42098 = r42094 * r42097;
        double r42099 = y;
        double r42100 = pow(r42099, r42096);
        double r42101 = r42098 - r42100;
        double r42102 = 2.0;
        double r42103 = r42099 * r42099;
        double r42104 = r42102 * r42103;
        double r42105 = r42101 + r42104;
        return r42105;
}
↓
double f(double x, double y) {
        double r42106 = 9.0;
        double r42107 = x;
        double r42108 = 4.0;
        double r42109 = pow(r42107, r42108);
        double r42110 = r42106 * r42109;
        double r42111 = y;
        double r42112 = pow(r42111, r42108);
        double r42113 = r42110 - r42112;
        double r42114 = 3.0;
        double r42115 = pow(r42113, r42114);
        double r42116 = cbrt(r42115);
        double r42117 = 2.0;
        double r42118 = r42111 * r42111;
        double r42119 = r42117 * r42118;
        double r42120 = r42116 + r42119;
        return r42120;
}

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

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

  5. Final simplification52.0

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

Reproduce

herbie shell --seed 2019304 
(FPCore (x y)
  :name "From Rump in a 1983 paper"
  :precision binary64
  :pre (and (== x 10864) (== y 18817))
  (+ (- (* 9 (pow x 4)) (pow y 4)) (* 2 (* y y))))