Average Error: 52.0 → 52.0
Time: 20.7s
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 r65341 = 9.0;
        double r65342 = x;
        double r65343 = 4.0;
        double r65344 = pow(r65342, r65343);
        double r65345 = r65341 * r65344;
        double r65346 = y;
        double r65347 = pow(r65346, r65343);
        double r65348 = r65345 - r65347;
        double r65349 = 2.0;
        double r65350 = r65346 * r65346;
        double r65351 = r65349 * r65350;
        double r65352 = r65348 + r65351;
        return r65352;
}
↓
double f(double x, double y) {
        double r65353 = 9.0;
        double r65354 = x;
        double r65355 = 4.0;
        double r65356 = pow(r65354, r65355);
        double r65357 = y;
        double r65358 = pow(r65357, r65355);
        double r65359 = -r65358;
        double r65360 = fma(r65353, r65356, r65359);
        double r65361 = 3.0;
        double r65362 = pow(r65360, r65361);
        double r65363 = cbrt(r65362);
        double r65364 = 2.0;
        double r65365 = r65357 * r65357;
        double r65366 = r65364 * r65365;
        double r65367 = r65363 + r65366;
        return r65367;
}

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 2019323 +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))))