Average Error: 52.0 → 52.0
Time: 11.3s
Precision: 64
\[x = 10864 \land y = 18817\]
\[\left(9 \cdot {x}^{4} - {y}^{4}\right) + 2 \cdot \left(y \cdot y\right)\]
↓
\[\sqrt[3]{{\left(\mathsf{fma}\left({x}^{4}, 9, -{y}^{4}\right)\right)}^{3}} + 2 \cdot \left(y \cdot y\right)\]
\left(9 \cdot {x}^{4} - {y}^{4}\right) + 2 \cdot \left(y \cdot y\right)
↓
\sqrt[3]{{\left(\mathsf{fma}\left({x}^{4}, 9, -{y}^{4}\right)\right)}^{3}} + 2 \cdot \left(y \cdot y\right)
double f(double x, double y) {
        double r88420 = 9.0;
        double r88421 = x;
        double r88422 = 4.0;
        double r88423 = pow(r88421, r88422);
        double r88424 = r88420 * r88423;
        double r88425 = y;
        double r88426 = pow(r88425, r88422);
        double r88427 = r88424 - r88426;
        double r88428 = 2.0;
        double r88429 = r88425 * r88425;
        double r88430 = r88428 * r88429;
        double r88431 = r88427 + r88430;
        return r88431;
}
↓
double f(double x, double y) {
        double r88432 = x;
        double r88433 = 4.0;
        double r88434 = pow(r88432, r88433);
        double r88435 = 9.0;
        double r88436 = y;
        double r88437 = pow(r88436, r88433);
        double r88438 = -r88437;
        double r88439 = fma(r88434, r88435, r88438);
        double r88440 = 3.0;
        double r88441 = pow(r88439, r88440);
        double r88442 = cbrt(r88441);
        double r88443 = 2.0;
        double r88444 = r88436 * r88436;
        double r88445 = r88443 * r88444;
        double r88446 = r88442 + r88445;
        return r88446;
}

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

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

  5. Final simplification52.0

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

Reproduce

herbie shell --seed 2019303 +o rules:numerics
(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))))