Average Error: 52.0 → 52.0
Time: 2.5s
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 r39070 = 9.0;
        double r39071 = x;
        double r39072 = 4.0;
        double r39073 = pow(r39071, r39072);
        double r39074 = r39070 * r39073;
        double r39075 = y;
        double r39076 = pow(r39075, r39072);
        double r39077 = r39074 - r39076;
        double r39078 = 2.0;
        double r39079 = r39075 * r39075;
        double r39080 = r39078 * r39079;
        double r39081 = r39077 + r39080;
        return r39081;
}
↓
double f(double x, double y) {
        double r39082 = 9.0;
        double r39083 = x;
        double r39084 = 4.0;
        double r39085 = pow(r39083, r39084);
        double r39086 = r39082 * r39085;
        double r39087 = y;
        double r39088 = pow(r39087, r39084);
        double r39089 = r39086 - r39088;
        double r39090 = 3.0;
        double r39091 = pow(r39089, r39090);
        double r39092 = cbrt(r39091);
        double r39093 = 2.0;
        double r39094 = r39087 * r39087;
        double r39095 = r39093 * r39094;
        double r39096 = r39092 + r39095;
        return r39096;
}

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 2020060 
(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))))