Average Error: 62.0 → 52.0
Time: 1.9s
Precision: binary64
\[x = 10864 \land y = 18817\]
\[9 \cdot {x}^{4} - \left(y \cdot y\right) \cdot \left(y \cdot y - 2\right) \]
↓
\[\begin{array}{l} t_0 := 9 \cdot {x}^{4} - {y}^{4}\\ \sqrt[3]{t_0 \cdot \left(t_0 \cdot t_0\right)} - -2 \cdot \left(y \cdot y\right) \end{array} \]
9 \cdot {x}^{4} - \left(y \cdot y\right) \cdot \left(y \cdot y - 2\right)
↓
\begin{array}{l}
t_0 := 9 \cdot {x}^{4} - {y}^{4}\\
\sqrt[3]{t_0 \cdot \left(t_0 \cdot t_0\right)} - -2 \cdot \left(y \cdot y\right)
\end{array}

(FPCore (x y)
 :precision binary64
 (- (* 9.0 (pow x 4.0)) (* (* y y) (- (* y y) 2.0))))
↓
(FPCore (x y)
 :precision binary64
 (let* ((t_0 (- (* 9.0 (pow x 4.0)) (pow y 4.0))))
   (- (cbrt (* t_0 (* t_0 t_0))) (* -2.0 (* y y)))))
double code(double x, double y) {
	return (9.0 * pow(x, 4.0)) - ((y * y) * ((y * y) - 2.0));
}
↓
double code(double x, double y) {
	double t_0 = (9.0 * pow(x, 4.0)) - pow(y, 4.0);
	return cbrt(t_0 * (t_0 * t_0)) - (-2.0 * (y * y));
}

Error

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 62.0

    \[9 \cdot {x}^{4} - \left(y \cdot y\right) \cdot \left(y \cdot y - 2\right) \]
  2. Using strategy rm

  3. Applied sub-neg_binary6462.0

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

  4. Applied distribute-rgt-in_binary6462.0

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

  5. Applied associate--r+_binary6452.0

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

  6. Simplified52.0

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

  8. Applied add-cbrt-cube_binary6452.0

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

  9. Final simplification52.0

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

Reproduce

herbie shell --seed 2021196 
(FPCore (x y)
  :name "From Rump in a 1983 paper, rewritten"
  :precision binary64
  :pre (and (== x 10864.0) (== y 18817.0))
  (- (* 9.0 (pow x 4.0)) (* (* y y) (- (* y y) 2.0))))