Average Error: 20.5 → 20.8
Time: 3.9s
Precision: binary64
\[2 \cdot \sqrt{\left(x \cdot y + x \cdot z\right) + y \cdot z}\]
↓
\[2 \cdot \sqrt{x \cdot y + \left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) \cdot \left(\sqrt[3]{z} \cdot \left(x + y\right)\right)}\]
2 \cdot \sqrt{\left(x \cdot y + x \cdot z\right) + y \cdot z}
↓
2 \cdot \sqrt{x \cdot y + \left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) \cdot \left(\sqrt[3]{z} \cdot \left(x + y\right)\right)}
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) {
	return ((double) (2.0 * ((double) sqrt(((double) (((double) (x * y)) + ((double) (((double) (((double) cbrt(z)) * ((double) cbrt(z)))) * ((double) (((double) cbrt(z)) * ((double) (x + y))))))))))));
}

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

Original20.5
Target19.7
Herbie20.8
\[\begin{array}{l} \mathbf{if}\;z < 7.636950090573675 \cdot 10^{+176}:\\ \;\;\;\;2 \cdot \sqrt{\left(x + y\right) \cdot z + x \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\left(\left(0.25 \cdot \left(\left({y}^{-0.75} \cdot \left({z}^{-0.75} \cdot x\right)\right) \cdot \left(y + z\right)\right) + {z}^{0.25} \cdot {y}^{0.25}\right) \cdot \left(0.25 \cdot \left(\left({y}^{-0.75} \cdot \left({z}^{-0.75} \cdot x\right)\right) \cdot \left(y + z\right)\right) + {z}^{0.25} \cdot {y}^{0.25}\right)\right) \cdot 2\\ \end{array}\]

Derivation

  1. Initial program 20.5

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

  2. Simplified20.5

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

  4. Applied add-cube-cbrt20.8

    \[\leadsto 2 \cdot \sqrt{x \cdot y + \color{blue}{\left(\left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) \cdot \sqrt[3]{z}\right)} \cdot \left(x + y\right)}\]

  5. Applied associate-*l*20.8

    \[\leadsto 2 \cdot \sqrt{x \cdot y + \color{blue}{\left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) \cdot \left(\sqrt[3]{z} \cdot \left(x + y\right)\right)}}\]

  6. Simplified20.8

    \[\leadsto 2 \cdot \sqrt{x \cdot y + \left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) \cdot \color{blue}{\left(\left(x + y\right) \cdot \sqrt[3]{z}\right)}}\]

  7. Final simplification20.8

    \[\leadsto 2 \cdot \sqrt{x \cdot y + \left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) \cdot \left(\sqrt[3]{z} \cdot \left(x + y\right)\right)}\]

Reproduce

herbie shell --seed 2020196 
(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) (* 2.0 (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)))) 2.0))

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