Average Error: 20.0 → 18.9
Time: 5.9s
Precision: 64
\[2 \cdot \sqrt{\left(x \cdot y + x \cdot z\right) + y \cdot z}\]
↓
\[\begin{array}{l} \mathbf{if}\;\left(x \cdot y + x \cdot z\right) + y \cdot z \le 5.4584483795311187 \cdot 10^{305}:\\ \;\;\;\;2 \cdot \sqrt{\left(x \cdot y + x \cdot z\right) + y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \mathsf{hypot}\left(\sqrt{x \cdot y + x \cdot z}, \sqrt{y} \cdot \sqrt{z}\right)\\ \end{array}\]
2 \cdot \sqrt{\left(x \cdot y + x \cdot z\right) + y \cdot z}
↓
\begin{array}{l}
\mathbf{if}\;\left(x \cdot y + x \cdot z\right) + y \cdot z \le 5.4584483795311187 \cdot 10^{305}:\\
\;\;\;\;2 \cdot \sqrt{\left(x \cdot y + x \cdot z\right) + y \cdot z}\\

\mathbf{else}:\\
\;\;\;\;2 \cdot \mathsf{hypot}\left(\sqrt{x \cdot y + x \cdot z}, \sqrt{y} \cdot \sqrt{z}\right)\\

\end{array}
double code(double x, double y, double z) {
	return ((double) (2.0 * ((double) sqrt(((double) (((double) (((double) (x * y)) + ((double) (x * z)))) + ((double) (y * z))))))));
}
↓
double code(double x, double y, double z) {
	double VAR;
	if ((((double) (((double) (((double) (x * y)) + ((double) (x * z)))) + ((double) (y * z)))) <= 5.458448379531119e+305)) {
		VAR = ((double) (2.0 * ((double) sqrt(((double) (((double) (((double) (x * y)) + ((double) (x * z)))) + ((double) (y * z))))))));
	} else {
		VAR = ((double) (2.0 * ((double) hypot(((double) sqrt(((double) (((double) (x * y)) + ((double) (x * z)))))), ((double) (((double) sqrt(y)) * ((double) sqrt(z))))))));
	}
	return VAR;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original20.0
Target19.2
Herbie18.9
\[\begin{array}{l} \mathbf{if}\;z \lt 7.6369500905736745 \cdot 10^{176}:\\ \;\;\;\;2 \cdot \sqrt{\left(x + y\right) \cdot z + x \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\left(\left(0.25 \cdot \left(\left({y}^{-0.75} \cdot \left({z}^{-0.75} \cdot x\right)\right) \cdot \left(y + z\right)\right) + {z}^{0.25} \cdot {y}^{0.25}\right) \cdot \left(0.25 \cdot \left(\left({y}^{-0.75} \cdot \left({z}^{-0.75} \cdot x\right)\right) \cdot \left(y + z\right)\right) + {z}^{0.25} \cdot {y}^{0.25}\right)\right) \cdot 2\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (+ (+ (* x y) (* x z)) (* y z)) < 5.458448379531119e+305

    1. Initial program 2.4

      \[2 \cdot \sqrt{\left(x \cdot y + x \cdot z\right) + y \cdot z}\]

    if 5.458448379531119e+305 < (+ (+ (* x y) (* x z)) (* y z))

    1. Initial program 63.1

      \[2 \cdot \sqrt{\left(x \cdot y + x \cdot z\right) + y \cdot z}\]
    2. Using strategy rm

    3. Applied add-sqr-sqrt63.6

      \[\leadsto 2 \cdot \sqrt{\left(x \cdot y + x \cdot z\right) + y \cdot \color{blue}{\left(\sqrt{z} \cdot \sqrt{z}\right)}}\]

    4. Applied add-sqr-sqrt63.6

      \[\leadsto 2 \cdot \sqrt{\left(x \cdot y + x \cdot z\right) + \color{blue}{\left(\sqrt{y} \cdot \sqrt{y}\right)} \cdot \left(\sqrt{z} \cdot \sqrt{z}\right)}\]

    5. Applied unswap-sqr63.6

      \[\leadsto 2 \cdot \sqrt{\left(x \cdot y + x \cdot z\right) + \color{blue}{\left(\sqrt{y} \cdot \sqrt{z}\right) \cdot \left(\sqrt{y} \cdot \sqrt{z}\right)}}\]

    6. Applied add-sqr-sqrt63.8

      \[\leadsto 2 \cdot \sqrt{\color{blue}{\sqrt{x \cdot y + x \cdot z} \cdot \sqrt{x \cdot y + x \cdot z}} + \left(\sqrt{y} \cdot \sqrt{z}\right) \cdot \left(\sqrt{y} \cdot \sqrt{z}\right)}\]

    7. Applied hypot-def59.2

      \[\leadsto 2 \cdot \color{blue}{\mathsf{hypot}\left(\sqrt{x \cdot y + x \cdot z}, \sqrt{y} \cdot \sqrt{z}\right)}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification18.9

    \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x \cdot y + x \cdot z\right) + y \cdot z \le 5.4584483795311187 \cdot 10^{305}:\\ \;\;\;\;2 \cdot \sqrt{\left(x \cdot y + x \cdot z\right) + y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \mathsf{hypot}\left(\sqrt{x \cdot y + x \cdot z}, \sqrt{y} \cdot \sqrt{z}\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020114 +o rules:numerics
(FPCore (x y z)
  :name "Diagrams.TwoD.Apollonian:descartes from diagrams-contrib-1.3.0.5"
  :precision binary64

  :herbie-target
  (if (< z 7.636950090573675e+176) (* 2 (sqrt (+ (* (+ x y) z) (* x y)))) (* (* (+ (* 0.25 (* (* (pow y -0.75) (* (pow z -0.75) x)) (+ y z))) (* (pow z 0.25) (pow y 0.25))) (+ (* 0.25 (* (* (pow y -0.75) (* (pow z -0.75) x)) (+ y z))) (* (pow z 0.25) (pow y 0.25)))) 2))

  (* 2 (sqrt (+ (+ (* x y) (* x z)) (* y z)))))