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 r85239 = 9.0;
        double r85240 = x;
        double r85241 = 4.0;
        double r85242 = pow(r85240, r85241);
        double r85243 = r85239 * r85242;
        double r85244 = y;
        double r85245 = pow(r85244, r85241);
        double r85246 = r85243 - r85245;
        double r85247 = 2.0;
        double r85248 = r85244 * r85244;
        double r85249 = r85247 * r85248;
        double r85250 = r85246 + r85249;
        return r85250;
}
↓
double f(double x, double y) {
        double r85251 = 9.0;
        double r85252 = x;
        double r85253 = 4.0;
        double r85254 = pow(r85252, r85253);
        double r85255 = r85251 * r85254;
        double r85256 = y;
        double r85257 = pow(r85256, r85253);
        double r85258 = r85255 - r85257;
        double r85259 = 3.0;
        double r85260 = pow(r85258, r85259);
        double r85261 = cbrt(r85260);
        double r85262 = 2.0;
        double r85263 = r85256 * r85256;
        double r85264 = r85262 * r85263;
        double r85265 = r85261 + r85264;
        return r85265;
}

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 2020001 
(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))))