Average Error: 52.0 → 52.0
Time: 1.7s
Precision: binary64
\[x = 10864 \land y = 18817\]
\[\left(9 \cdot {x}^{4} - {y}^{4}\right) + 2 \cdot \left(y \cdot y\right) \]
↓
\[\begin{array}{l} t_0 := 9 \cdot {x}^{4} - {y}^{4}\\ \sqrt[3]{t_0 \cdot \left(t_0 \cdot t_0\right)} + 2 \cdot \left(y \cdot y\right) \end{array} \]
\left(9 \cdot {x}^{4} - {y}^{4}\right) + 2 \cdot \left(y \cdot y\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)) (pow y 4.0)) (* 2.0 (* y y))))
↓
(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)) - pow(y, 4.0)) + (2.0 * (y * y));
}
↓
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

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Your Program's Arguments

Results

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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-cube_binary6452.0

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

  4. 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 2021190 
(FPCore (x y)
  :name "From Rump in a 1983 paper"
  :precision binary64
  :pre (and (== x 10864.0) (== y 18817.0))
  (+ (- (* 9.0 (pow x 4.0)) (pow y 4.0)) (* 2.0 (* y y))))