Average Error: 52.0 → 52.0
Time: 7.6s
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 r29197 = 9.0;
        double r29198 = x;
        double r29199 = 4.0;
        double r29200 = pow(r29198, r29199);
        double r29201 = r29197 * r29200;
        double r29202 = y;
        double r29203 = pow(r29202, r29199);
        double r29204 = r29201 - r29203;
        double r29205 = 2.0;
        double r29206 = r29202 * r29202;
        double r29207 = r29205 * r29206;
        double r29208 = r29204 + r29207;
        return r29208;
}
↓
double f(double x, double y) {
        double r29209 = 2.0;
        double r29210 = y;
        double r29211 = r29209 * r29210;
        double r29212 = 9.0;
        double r29213 = x;
        double r29214 = 4.0;
        double r29215 = pow(r29213, r29214);
        double r29216 = pow(r29210, r29214);
        double r29217 = -r29216;
        double r29218 = fma(r29212, r29215, r29217);
        double r29219 = 3.0;
        double r29220 = pow(r29218, r29219);
        double r29221 = cbrt(r29220);
        double r29222 = fma(r29211, r29210, r29221);
        return r29222;
}

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

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

  4. Applied add-cbrt-cube52.0

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

  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 2019195 +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))))