Average Error: 52.0 → 52.0
Time: 13.6s
Precision: 64
\[x = 10864 \land y = 18817\]
\[\left(9 \cdot {x}^{4} - {y}^{4}\right) + 2 \cdot \left(y \cdot y\right)\]
↓
\[2 \cdot \left(y \cdot y\right) + \sqrt[3]{\left({x}^{4} \cdot 9 - {y}^{4}\right) \cdot \left(\left({x}^{4} \cdot 9 - {y}^{4}\right) \cdot \left({x}^{4} \cdot 9 - {y}^{4}\right)\right)}\]
\left(9 \cdot {x}^{4} - {y}^{4}\right) + 2 \cdot \left(y \cdot y\right)
↓
2 \cdot \left(y \cdot y\right) + \sqrt[3]{\left({x}^{4} \cdot 9 - {y}^{4}\right) \cdot \left(\left({x}^{4} \cdot 9 - {y}^{4}\right) \cdot \left({x}^{4} \cdot 9 - {y}^{4}\right)\right)}
double f(double x, double y) {
        double r3237415 = 9.0;
        double r3237416 = x;
        double r3237417 = 4.0;
        double r3237418 = pow(r3237416, r3237417);
        double r3237419 = r3237415 * r3237418;
        double r3237420 = y;
        double r3237421 = pow(r3237420, r3237417);
        double r3237422 = r3237419 - r3237421;
        double r3237423 = 2.0;
        double r3237424 = r3237420 * r3237420;
        double r3237425 = r3237423 * r3237424;
        double r3237426 = r3237422 + r3237425;
        return r3237426;
}
↓
double f(double x, double y) {
        double r3237427 = 2.0;
        double r3237428 = y;
        double r3237429 = r3237428 * r3237428;
        double r3237430 = r3237427 * r3237429;
        double r3237431 = x;
        double r3237432 = 4.0;
        double r3237433 = pow(r3237431, r3237432);
        double r3237434 = 9.0;
        double r3237435 = r3237433 * r3237434;
        double r3237436 = pow(r3237428, r3237432);
        double r3237437 = r3237435 - r3237436;
        double r3237438 = r3237437 * r3237437;
        double r3237439 = r3237437 * r3237438;
        double r3237440 = cbrt(r3237439);
        double r3237441 = r3237430 + r3237440;
        return r3237441;
}

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. Final simplification52.0

    \[\leadsto 2 \cdot \left(y \cdot y\right) + \sqrt[3]{\left({x}^{4} \cdot 9 - {y}^{4}\right) \cdot \left(\left({x}^{4} \cdot 9 - {y}^{4}\right) \cdot \left({x}^{4} \cdot 9 - {y}^{4}\right)\right)}\]

Reproduce

herbie shell --seed 2019171 
(FPCore (x y)
  :name "From Rump in a 1983 paper"
  :pre (and (== x 10864.0) (== y 18817.0))
  (+ (- (* 9.0 (pow x 4.0)) (pow y 4.0)) (* 2.0 (* y y))))