Average Error: 52.0 → 52.0
Time: 7.8s
Precision: 64
\[x = 10864 \land y = 18817\]
\[\left(9 \cdot {x}^{4} - {y}^{4}\right) + 2 \cdot \left(y \cdot y\right)\]
↓
\[\mathsf{fma}\left(2 \cdot y, y, \sqrt[3]{{\left(\mathsf{fma}\left(9, {x}^{4}, -{y}^{4}\right)\right)}^{3}}\right)\]
\left(9 \cdot {x}^{4} - {y}^{4}\right) + 2 \cdot \left(y \cdot y\right)
↓
\mathsf{fma}\left(2 \cdot y, y, \sqrt[3]{{\left(\mathsf{fma}\left(9, {x}^{4}, -{y}^{4}\right)\right)}^{3}}\right)
double f(double x, double y) {
        double r36420 = 9.0;
        double r36421 = x;
        double r36422 = 4.0;
        double r36423 = pow(r36421, r36422);
        double r36424 = r36420 * r36423;
        double r36425 = y;
        double r36426 = pow(r36425, r36422);
        double r36427 = r36424 - r36426;
        double r36428 = 2.0;
        double r36429 = r36425 * r36425;
        double r36430 = r36428 * r36429;
        double r36431 = r36427 + r36430;
        return r36431;
}
↓
double f(double x, double y) {
        double r36432 = 2.0;
        double r36433 = y;
        double r36434 = r36432 * r36433;
        double r36435 = 9.0;
        double r36436 = x;
        double r36437 = 4.0;
        double r36438 = pow(r36436, r36437);
        double r36439 = pow(r36433, r36437);
        double r36440 = -r36439;
        double r36441 = fma(r36435, r36438, r36440);
        double r36442 = 3.0;
        double r36443 = pow(r36441, r36442);
        double r36444 = cbrt(r36443);
        double r36445 = fma(r36434, r36433, r36444);
        return r36445;
}

Error

Derivation

  1. Initial program 52.0

    \[\left(9 \cdot {x}^{4} - {y}^{4}\right) + 2 \cdot \left(y \cdot y\right)\]

  2. Simplified52.0

    \[\leadsto \color{blue}{\mathsf{fma}\left(2 \cdot y, y, {x}^{4} \cdot 9 - {y}^{4}\right)}\]
  3. Using strategy rm

  4. Applied add-cbrt-cube52.0

    \[\leadsto \mathsf{fma}\left(2 \cdot y, y, \color{blue}{\sqrt[3]{\left(\left({x}^{4} \cdot 9 - {y}^{4}\right) \cdot \left({x}^{4} \cdot 9 - {y}^{4}\right)\right) \cdot \left({x}^{4} \cdot 9 - {y}^{4}\right)}}\right)\]

  5. Simplified52.0

    \[\leadsto \mathsf{fma}\left(2 \cdot y, y, \sqrt[3]{\color{blue}{{\left(\mathsf{fma}\left(9, {x}^{4}, -{y}^{4}\right)\right)}^{3}}}\right)\]

  6. Final simplification52.0

    \[\leadsto \mathsf{fma}\left(2 \cdot y, y, \sqrt[3]{{\left(\mathsf{fma}\left(9, {x}^{4}, -{y}^{4}\right)\right)}^{3}}\right)\]

Reproduce

herbie shell --seed 2019195 +o rules:numerics
(FPCore (x y)
  :name "From Rump in a 1983 paper"
  :pre (and (== x 10864.0) (== y 18817.0))
  (+ (- (* 9.0 (pow x 4.0)) (pow y 4.0)) (* 2.0 (* y y))))