Average Error: 52.0 → 52.0
Time: 7.1s
Precision: 64
\[x = 10864 \land y = 18817\]
\[\left(9 \cdot {x}^{4} - {y}^{4}\right) + 2 \cdot \left(y \cdot y\right)\]
↓
\[2 \cdot \left(y \cdot y\right) + \sqrt[3]{{\left(\mathsf{fma}\left(9, {x}^{4}, -{y}^{4}\right)\right)}^{3}}\]
\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(\mathsf{fma}\left(9, {x}^{4}, -{y}^{4}\right)\right)}^{3}}
double f(double x, double y) {
        double r57587 = 9.0;
        double r57588 = x;
        double r57589 = 4.0;
        double r57590 = pow(r57588, r57589);
        double r57591 = r57587 * r57590;
        double r57592 = y;
        double r57593 = pow(r57592, r57589);
        double r57594 = r57591 - r57593;
        double r57595 = 2.0;
        double r57596 = r57592 * r57592;
        double r57597 = r57595 * r57596;
        double r57598 = r57594 + r57597;
        return r57598;
}
↓
double f(double x, double y) {
        double r57599 = 2.0;
        double r57600 = y;
        double r57601 = r57600 * r57600;
        double r57602 = r57599 * r57601;
        double r57603 = 9.0;
        double r57604 = x;
        double r57605 = 4.0;
        double r57606 = pow(r57604, r57605);
        double r57607 = pow(r57600, r57605);
        double r57608 = -r57607;
        double r57609 = fma(r57603, r57606, r57608);
        double r57610 = 3.0;
        double r57611 = pow(r57609, r57610);
        double r57612 = cbrt(r57611);
        double r57613 = r57602 + r57612;
        return r57613;
}

Error

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

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

  5. Final simplification52.0

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

Reproduce

herbie shell --seed 2019174 +o rules:numerics
(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))))