Average Error: 52.0 → 0
Time: 1.6s
Precision: binary64
\[x = 10864 \land y = 18817\]
\[\left(9 \cdot {x}^{4} - {y}^{4}\right) + 2 \cdot \left(y \cdot y\right) \]
↓
\[\begin{array}{l} t_0 := \sqrt{9 \cdot {x}^{4}}\\ \left(t_0 + y \cdot y\right) \cdot \left(t_0 - y \cdot y\right) + \left(y \cdot y\right) \cdot 2 \end{array} \]
\left(9 \cdot {x}^{4} - {y}^{4}\right) + 2 \cdot \left(y \cdot y\right)
↓
\begin{array}{l}
t_0 := \sqrt{9 \cdot {x}^{4}}\\
\left(t_0 + y \cdot y\right) \cdot \left(t_0 - y \cdot y\right) + \left(y \cdot y\right) \cdot 2
\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 (sqrt (* 9.0 (pow x 4.0)))))
   (+ (* (+ t_0 (* y y)) (- t_0 (* y y))) (* (* y y) 2.0))))
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 = sqrt(9.0 * pow(x, 4.0));
	return ((t_0 + (y * y)) * (t_0 - (y * y))) + ((y * y) * 2.0);
}

Error

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

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-sqr-sqrt_binary6452.0

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

  4. Applied add-sqr-sqrt_binary6452.0

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

  5. Applied difference-of-squares_binary640

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

  6. Simplified0

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

  7. Simplified0

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

  8. Final simplification0

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

Reproduce

herbie shell --seed 2021211 
(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))))