Average Error: 52.0 → 52.0
Time: 11.8s
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 r49132 = 9.0;
        double r49133 = x;
        double r49134 = 4.0;
        double r49135 = pow(r49133, r49134);
        double r49136 = r49132 * r49135;
        double r49137 = y;
        double r49138 = pow(r49137, r49134);
        double r49139 = r49136 - r49138;
        double r49140 = 2.0;
        double r49141 = r49137 * r49137;
        double r49142 = r49140 * r49141;
        double r49143 = r49139 + r49142;
        return r49143;
}
↓
double f(double x, double y) {
        double r49144 = x;
        double r49145 = 4.0;
        double r49146 = pow(r49144, r49145);
        double r49147 = 9.0;
        double r49148 = y;
        double r49149 = pow(r49148, r49145);
        double r49150 = -r49149;
        double r49151 = fma(r49146, r49147, r49150);
        double r49152 = 3.0;
        double r49153 = pow(r49151, r49152);
        double r49154 = cbrt(r49153);
        double r49155 = 2.0;
        double r49156 = r49148 * r49148;
        double r49157 = r49155 * r49156;
        double r49158 = r49154 + r49157;
        return r49158;
}

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 2019304 +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))))