Average Error: 52.0 → 52.0
Time: 7.5s
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 r61947 = 9.0;
        double r61948 = x;
        double r61949 = 4.0;
        double r61950 = pow(r61948, r61949);
        double r61951 = r61947 * r61950;
        double r61952 = y;
        double r61953 = pow(r61952, r61949);
        double r61954 = r61951 - r61953;
        double r61955 = 2.0;
        double r61956 = r61952 * r61952;
        double r61957 = r61955 * r61956;
        double r61958 = r61954 + r61957;
        return r61958;
}
↓
double f(double x, double y) {
        double r61959 = x;
        double r61960 = 4.0;
        double r61961 = pow(r61959, r61960);
        double r61962 = 9.0;
        double r61963 = y;
        double r61964 = pow(r61963, r61960);
        double r61965 = -r61964;
        double r61966 = fma(r61961, r61962, r61965);
        double r61967 = 3.0;
        double r61968 = pow(r61966, r61967);
        double r61969 = cbrt(r61968);
        double r61970 = 2.0;
        double r61971 = r61963 * r61963;
        double r61972 = r61970 * r61971;
        double r61973 = r61969 + r61972;
        return r61973;
}

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 2019209 +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))))