Average Error: 52.0 → 52.0
Time: 13.1s
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 r39181 = 9.0;
        double r39182 = x;
        double r39183 = 4.0;
        double r39184 = pow(r39182, r39183);
        double r39185 = r39181 * r39184;
        double r39186 = y;
        double r39187 = pow(r39186, r39183);
        double r39188 = r39185 - r39187;
        double r39189 = 2.0;
        double r39190 = r39186 * r39186;
        double r39191 = r39189 * r39190;
        double r39192 = r39188 + r39191;
        return r39192;
}
↓
double f(double x, double y) {
        double r39193 = 9.0;
        double r39194 = x;
        double r39195 = 4.0;
        double r39196 = pow(r39194, r39195);
        double r39197 = r39193 * r39196;
        double r39198 = y;
        double r39199 = pow(r39198, r39195);
        double r39200 = r39197 - r39199;
        double r39201 = 3.0;
        double r39202 = pow(r39200, r39201);
        double r39203 = cbrt(r39202);
        double r39204 = 2.0;
        double r39205 = r39198 * r39198;
        double r39206 = r39204 * r39205;
        double r39207 = r39203 + r39206;
        return r39207;
}

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 2019322 
(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))))