Average Error: 52.0 → 52.0
Time: 2.4s
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 r69055 = 9.0;
        double r69056 = x;
        double r69057 = 4.0;
        double r69058 = pow(r69056, r69057);
        double r69059 = r69055 * r69058;
        double r69060 = y;
        double r69061 = pow(r69060, r69057);
        double r69062 = r69059 - r69061;
        double r69063 = 2.0;
        double r69064 = r69060 * r69060;
        double r69065 = r69063 * r69064;
        double r69066 = r69062 + r69065;
        return r69066;
}
↓
double f(double x, double y) {
        double r69067 = 9.0;
        double r69068 = x;
        double r69069 = 4.0;
        double r69070 = pow(r69068, r69069);
        double r69071 = r69067 * r69070;
        double r69072 = y;
        double r69073 = pow(r69072, r69069);
        double r69074 = r69071 - r69073;
        double r69075 = 3.0;
        double r69076 = pow(r69074, r69075);
        double r69077 = cbrt(r69076);
        double r69078 = 2.0;
        double r69079 = r69072 * r69072;
        double r69080 = r69078 * r69079;
        double r69081 = r69077 + r69080;
        return r69081;
}

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 2020027 
(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))))