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 r62182 = 9.0;
        double r62183 = x;
        double r62184 = 4.0;
        double r62185 = pow(r62183, r62184);
        double r62186 = r62182 * r62185;
        double r62187 = y;
        double r62188 = pow(r62187, r62184);
        double r62189 = r62186 - r62188;
        double r62190 = 2.0;
        double r62191 = r62187 * r62187;
        double r62192 = r62190 * r62191;
        double r62193 = r62189 + r62192;
        return r62193;
}
↓
double f(double x, double y) {
        double r62194 = 9.0;
        double r62195 = x;
        double r62196 = 4.0;
        double r62197 = pow(r62195, r62196);
        double r62198 = r62194 * r62197;
        double r62199 = y;
        double r62200 = pow(r62199, r62196);
        double r62201 = r62198 - r62200;
        double r62202 = 3.0;
        double r62203 = pow(r62201, r62202);
        double r62204 = cbrt(r62203);
        double r62205 = 2.0;
        double r62206 = r62199 * r62199;
        double r62207 = r62205 * r62206;
        double r62208 = r62204 + r62207;
        return r62208;
}

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 2020039 
(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))))