Average Error: 18.5 → 18.5
Time: 23.3s
Precision: 64
\[2.0 \cdot \sqrt{\left(x \cdot y + x \cdot z\right) + y \cdot z}\]
↓
\[\sqrt{\left(y + z\right) \cdot x + z \cdot y} \cdot 2.0\]
2.0 \cdot \sqrt{\left(x \cdot y + x \cdot z\right) + y \cdot z}
↓
\sqrt{\left(y + z\right) \cdot x + z \cdot y} \cdot 2.0
double f(double x, double y, double z) {
        double r46389350 = 2.0;
        double r46389351 = x;
        double r46389352 = y;
        double r46389353 = r46389351 * r46389352;
        double r46389354 = z;
        double r46389355 = r46389351 * r46389354;
        double r46389356 = r46389353 + r46389355;
        double r46389357 = r46389352 * r46389354;
        double r46389358 = r46389356 + r46389357;
        double r46389359 = sqrt(r46389358);
        double r46389360 = r46389350 * r46389359;
        return r46389360;
}
↓
double f(double x, double y, double z) {
        double r46389361 = y;
        double r46389362 = z;
        double r46389363 = r46389361 + r46389362;
        double r46389364 = x;
        double r46389365 = r46389363 * r46389364;
        double r46389366 = r46389362 * r46389361;
        double r46389367 = r46389365 + r46389366;
        double r46389368 = sqrt(r46389367);
        double r46389369 = 2.0;
        double r46389370 = r46389368 * r46389369;
        return r46389370;
}

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

Original18.5
Target18.0
Herbie18.5
\[\begin{array}{l} \mathbf{if}\;z \lt 7.636950090573675 \cdot 10^{+176}:\\ \;\;\;\;2.0 \cdot \sqrt{\left(x + y\right) \cdot z + x \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\frac{1}{4} \cdot \left(\left({y}^{\frac{-3}{4}} \cdot \left({z}^{\frac{-3}{4}} \cdot x\right)\right) \cdot \left(y + z\right)\right) + {z}^{\frac{1}{4}} \cdot {y}^{\frac{1}{4}}\right) \cdot \left(\frac{1}{4} \cdot \left(\left({y}^{\frac{-3}{4}} \cdot \left({z}^{\frac{-3}{4}} \cdot x\right)\right) \cdot \left(y + z\right)\right) + {z}^{\frac{1}{4}} \cdot {y}^{\frac{1}{4}}\right)\right) \cdot 2.0\\ \end{array}\]

Derivation

  1. Initial program 18.5

    \[2.0 \cdot \sqrt{\left(x \cdot y + x \cdot z\right) + y \cdot z}\]

  2. Simplified18.5

    \[\leadsto \color{blue}{\sqrt{z \cdot y + \left(y + z\right) \cdot x} \cdot 2.0}\]

  3. Final simplification18.5

    \[\leadsto \sqrt{\left(y + z\right) \cdot x + z \cdot y} \cdot 2.0\]

Reproduce

herbie shell --seed 2019158 
(FPCore (x y z)
  :name "Diagrams.TwoD.Apollonian:descartes from diagrams-contrib-1.3.0.5"

  :herbie-target
  (if (< z 7.636950090573675e+176) (* 2.0 (sqrt (+ (* (+ x y) z) (* x y)))) (* (* (+ (* 1/4 (* (* (pow y -3/4) (* (pow z -3/4) x)) (+ y z))) (* (pow z 1/4) (pow y 1/4))) (+ (* 1/4 (* (* (pow y -3/4) (* (pow z -3/4) x)) (+ y z))) (* (pow z 1/4) (pow y 1/4)))) 2.0))

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