Average Error: 52.0 → 52.0
Time: 9.9s
Precision: 64
\[x = 10864 \land y = 18817\]
\[\left(9 \cdot {x}^{4} - {y}^{4}\right) + 2 \cdot \left(y \cdot y\right)\]
↓
\[2 \cdot \left(y \cdot y\right) + \left(9 \cdot {x}^{4} - {y}^{4}\right)\]
\left(9 \cdot {x}^{4} - {y}^{4}\right) + 2 \cdot \left(y \cdot y\right)
↓
2 \cdot \left(y \cdot y\right) + \left(9 \cdot {x}^{4} - {y}^{4}\right)
double f(double x, double y) {
        double r57463 = 9.0;
        double r57464 = x;
        double r57465 = 4.0;
        double r57466 = pow(r57464, r57465);
        double r57467 = r57463 * r57466;
        double r57468 = y;
        double r57469 = pow(r57468, r57465);
        double r57470 = r57467 - r57469;
        double r57471 = 2.0;
        double r57472 = r57468 * r57468;
        double r57473 = r57471 * r57472;
        double r57474 = r57470 + r57473;
        return r57474;
}
↓
double f(double x, double y) {
        double r57475 = 2.0;
        double r57476 = y;
        double r57477 = r57476 * r57476;
        double r57478 = r57475 * r57477;
        double r57479 = 9.0;
        double r57480 = x;
        double r57481 = 4.0;
        double r57482 = pow(r57480, r57481);
        double r57483 = r57479 * r57482;
        double r57484 = pow(r57476, r57481);
        double r57485 = r57483 - r57484;
        double r57486 = r57478 + r57485;
        return r57486;
}

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

    \[\leadsto 2 \cdot \left(y \cdot y\right) + \left(9 \cdot {x}^{4} - {y}^{4}\right)\]

Reproduce

herbie shell --seed 2019298 
(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))))