Average Error: 52.0 → 52.0
Time: 11.4s
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 r52100 = 9.0;
        double r52101 = x;
        double r52102 = 4.0;
        double r52103 = pow(r52101, r52102);
        double r52104 = r52100 * r52103;
        double r52105 = y;
        double r52106 = pow(r52105, r52102);
        double r52107 = r52104 - r52106;
        double r52108 = 2.0;
        double r52109 = r52105 * r52105;
        double r52110 = r52108 * r52109;
        double r52111 = r52107 + r52110;
        return r52111;
}
↓
double f(double x, double y) {
        double r52112 = x;
        double r52113 = 4.0;
        double r52114 = pow(r52112, r52113);
        double r52115 = 9.0;
        double r52116 = y;
        double r52117 = pow(r52116, r52113);
        double r52118 = -r52117;
        double r52119 = fma(r52114, r52115, r52118);
        double r52120 = 3.0;
        double r52121 = pow(r52119, r52120);
        double r52122 = cbrt(r52121);
        double r52123 = 2.0;
        double r52124 = r52116 * r52116;
        double r52125 = r52123 * r52124;
        double r52126 = r52122 + r52125;
        return r52126;
}

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 2019325 +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))))