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 r61067 = 9.0;
        double r61068 = x;
        double r61069 = 4.0;
        double r61070 = pow(r61068, r61069);
        double r61071 = r61067 * r61070;
        double r61072 = y;
        double r61073 = pow(r61072, r61069);
        double r61074 = r61071 - r61073;
        double r61075 = 2.0;
        double r61076 = r61072 * r61072;
        double r61077 = r61075 * r61076;
        double r61078 = r61074 + r61077;
        return r61078;
}
↓
double f(double x, double y) {
        double r61079 = x;
        double r61080 = 4.0;
        double r61081 = pow(r61079, r61080);
        double r61082 = 9.0;
        double r61083 = y;
        double r61084 = pow(r61083, r61080);
        double r61085 = -r61084;
        double r61086 = fma(r61081, r61082, r61085);
        double r61087 = 3.0;
        double r61088 = pow(r61086, r61087);
        double r61089 = cbrt(r61088);
        double r61090 = 2.0;
        double r61091 = r61083 * r61083;
        double r61092 = r61090 * r61091;
        double r61093 = r61089 + r61092;
        return r61093;
}

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 2019326 +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))))