Average Error: 52.0 → 52.0
Time: 11.9s
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 r69665 = 9.0;
        double r69666 = x;
        double r69667 = 4.0;
        double r69668 = pow(r69666, r69667);
        double r69669 = r69665 * r69668;
        double r69670 = y;
        double r69671 = pow(r69670, r69667);
        double r69672 = r69669 - r69671;
        double r69673 = 2.0;
        double r69674 = r69670 * r69670;
        double r69675 = r69673 * r69674;
        double r69676 = r69672 + r69675;
        return r69676;
}
↓
double f(double x, double y) {
        double r69677 = x;
        double r69678 = 4.0;
        double r69679 = pow(r69677, r69678);
        double r69680 = 9.0;
        double r69681 = y;
        double r69682 = pow(r69681, r69678);
        double r69683 = -r69682;
        double r69684 = fma(r69679, r69680, r69683);
        double r69685 = 3.0;
        double r69686 = pow(r69684, r69685);
        double r69687 = cbrt(r69686);
        double r69688 = 2.0;
        double r69689 = r69681 * r69681;
        double r69690 = r69688 * r69689;
        double r69691 = r69687 + r69690;
        return r69691;
}

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))))