Average Error: 52.0 → 52.0
Time: 3.2s
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 r57207 = 9.0;
        double r57208 = x;
        double r57209 = 4.0;
        double r57210 = pow(r57208, r57209);
        double r57211 = r57207 * r57210;
        double r57212 = y;
        double r57213 = pow(r57212, r57209);
        double r57214 = r57211 - r57213;
        double r57215 = 2.0;
        double r57216 = r57212 * r57212;
        double r57217 = r57215 * r57216;
        double r57218 = r57214 + r57217;
        return r57218;
}
↓
double f(double x, double y) {
        double r57219 = 9.0;
        double r57220 = x;
        double r57221 = 4.0;
        double r57222 = pow(r57220, r57221);
        double r57223 = r57219 * r57222;
        double r57224 = y;
        double r57225 = pow(r57224, r57221);
        double r57226 = r57223 - r57225;
        double r57227 = 3.0;
        double r57228 = pow(r57226, r57227);
        double r57229 = cbrt(r57228);
        double r57230 = 2.0;
        double r57231 = r57224 * r57224;
        double r57232 = r57230 * r57231;
        double r57233 = r57229 + r57232;
        return r57233;
}

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 2019318 
(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))))