Average Error: 52.0 → 52.0
Time: 11.6s
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 r67610 = 9.0;
        double r67611 = x;
        double r67612 = 4.0;
        double r67613 = pow(r67611, r67612);
        double r67614 = r67610 * r67613;
        double r67615 = y;
        double r67616 = pow(r67615, r67612);
        double r67617 = r67614 - r67616;
        double r67618 = 2.0;
        double r67619 = r67615 * r67615;
        double r67620 = r67618 * r67619;
        double r67621 = r67617 + r67620;
        return r67621;
}
↓
double f(double x, double y) {
        double r67622 = x;
        double r67623 = 4.0;
        double r67624 = pow(r67622, r67623);
        double r67625 = 9.0;
        double r67626 = y;
        double r67627 = pow(r67626, r67623);
        double r67628 = -r67627;
        double r67629 = fma(r67624, r67625, r67628);
        double r67630 = 3.0;
        double r67631 = pow(r67629, r67630);
        double r67632 = cbrt(r67631);
        double r67633 = 2.0;
        double r67634 = r67626 * r67626;
        double r67635 = r67633 * r67634;
        double r67636 = r67632 + r67635;
        return r67636;
}

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 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))))