Average Error: 52.0 → 52.0
Time: 4.3s
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 r40397 = 9.0;
        double r40398 = x;
        double r40399 = 4.0;
        double r40400 = pow(r40398, r40399);
        double r40401 = r40397 * r40400;
        double r40402 = y;
        double r40403 = pow(r40402, r40399);
        double r40404 = r40401 - r40403;
        double r40405 = 2.0;
        double r40406 = r40402 * r40402;
        double r40407 = r40405 * r40406;
        double r40408 = r40404 + r40407;
        return r40408;
}
↓
double f(double x, double y) {
        double r40409 = 2.0;
        double r40410 = y;
        double r40411 = r40410 * r40410;
        double r40412 = r40409 * r40411;
        double r40413 = 9.0;
        double r40414 = x;
        double r40415 = 4.0;
        double r40416 = pow(r40414, r40415);
        double r40417 = r40413 * r40416;
        double r40418 = pow(r40410, r40415);
        double r40419 = r40417 - r40418;
        double r40420 = r40412 + r40419;
        return r40420;
}

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 2019308 
(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))))