Average Error: 52.0 → 52.0
Time: 8.0s
Precision: 64
\[x = 10864 \land y = 18817\]
\[\left(9 \cdot {x}^{4} - {y}^{4}\right) + 2 \cdot \left(y \cdot y\right)\]
↓
\[\mathsf{fma}\left(2 \cdot y, y, \sqrt[3]{{\left(\mathsf{fma}\left(9, {x}^{4}, -{y}^{4}\right)\right)}^{3}}\right)\]
\left(9 \cdot {x}^{4} - {y}^{4}\right) + 2 \cdot \left(y \cdot y\right)
↓
\mathsf{fma}\left(2 \cdot y, y, \sqrt[3]{{\left(\mathsf{fma}\left(9, {x}^{4}, -{y}^{4}\right)\right)}^{3}}\right)
double f(double x, double y) {
        double r35557 = 9.0;
        double r35558 = x;
        double r35559 = 4.0;
        double r35560 = pow(r35558, r35559);
        double r35561 = r35557 * r35560;
        double r35562 = y;
        double r35563 = pow(r35562, r35559);
        double r35564 = r35561 - r35563;
        double r35565 = 2.0;
        double r35566 = r35562 * r35562;
        double r35567 = r35565 * r35566;
        double r35568 = r35564 + r35567;
        return r35568;
}
↓
double f(double x, double y) {
        double r35569 = 2.0;
        double r35570 = y;
        double r35571 = r35569 * r35570;
        double r35572 = 9.0;
        double r35573 = x;
        double r35574 = 4.0;
        double r35575 = pow(r35573, r35574);
        double r35576 = pow(r35570, r35574);
        double r35577 = -r35576;
        double r35578 = fma(r35572, r35575, r35577);
        double r35579 = 3.0;
        double r35580 = pow(r35578, r35579);
        double r35581 = cbrt(r35580);
        double r35582 = fma(r35571, r35570, r35581);
        return r35582;
}

Error

Derivation

  1. Initial program 52.0

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

  2. Simplified52.0

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

  4. Applied add-cbrt-cube52.0

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

  5. Simplified52.0

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

  6. Final simplification52.0

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

Reproduce

herbie shell --seed 2019194 +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))))