Average Error: 52.0 → 52.0
Time: 2.8s
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 r98070 = 9.0;
        double r98071 = x;
        double r98072 = 4.0;
        double r98073 = pow(r98071, r98072);
        double r98074 = r98070 * r98073;
        double r98075 = y;
        double r98076 = pow(r98075, r98072);
        double r98077 = r98074 - r98076;
        double r98078 = 2.0;
        double r98079 = r98075 * r98075;
        double r98080 = r98078 * r98079;
        double r98081 = r98077 + r98080;
        return r98081;
}
↓
double f(double x, double y) {
        double r98082 = 9.0;
        double r98083 = x;
        double r98084 = 4.0;
        double r98085 = pow(r98083, r98084);
        double r98086 = r98082 * r98085;
        double r98087 = y;
        double r98088 = pow(r98087, r98084);
        double r98089 = r98086 - r98088;
        double r98090 = 3.0;
        double r98091 = pow(r98089, r98090);
        double r98092 = cbrt(r98091);
        double r98093 = 2.0;
        double r98094 = r98087 * r98087;
        double r98095 = r98093 * r98094;
        double r98096 = r98092 + r98095;
        return r98096;
}

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 2020033 
(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))))