Average Error: 52.0 → 52.0
Time: 6.1s
Precision: 64
\[x = 10864 \land y = 18817\]
\[\left(9 \cdot {x}^{4} - {y}^{4}\right) + 2 \cdot \left(y \cdot y\right)\]
↓
\[\sqrt[3]{{\left(\mathsf{fma}\left(9, {x}^{4}, -{y}^{4}\right)\right)}^{3}} + 2 \cdot \left(y \cdot y\right)\]
\left(9 \cdot {x}^{4} - {y}^{4}\right) + 2 \cdot \left(y \cdot y\right)
↓
\sqrt[3]{{\left(\mathsf{fma}\left(9, {x}^{4}, -{y}^{4}\right)\right)}^{3}} + 2 \cdot \left(y \cdot y\right)
double f(double x, double y) {
        double r77465 = 9.0;
        double r77466 = x;
        double r77467 = 4.0;
        double r77468 = pow(r77466, r77467);
        double r77469 = r77465 * r77468;
        double r77470 = y;
        double r77471 = pow(r77470, r77467);
        double r77472 = r77469 - r77471;
        double r77473 = 2.0;
        double r77474 = r77470 * r77470;
        double r77475 = r77473 * r77474;
        double r77476 = r77472 + r77475;
        return r77476;
}
↓
double f(double x, double y) {
        double r77477 = 9.0;
        double r77478 = x;
        double r77479 = 4.0;
        double r77480 = pow(r77478, r77479);
        double r77481 = y;
        double r77482 = pow(r77481, r77479);
        double r77483 = -r77482;
        double r77484 = fma(r77477, r77480, r77483);
        double r77485 = 3.0;
        double r77486 = pow(r77484, r77485);
        double r77487 = cbrt(r77486);
        double r77488 = 2.0;
        double r77489 = r77481 * r77481;
        double r77490 = r77488 * r77489;
        double r77491 = r77487 + r77490;
        return r77491;
}

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

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

Reproduce

herbie shell --seed 2020047 +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))))