Average Error: 19.6 → 19.6
Time: 10.9s
Precision: 64
\[2 \cdot \sqrt{\left(x \cdot y + x \cdot z\right) + y \cdot z}\]
↓
\[\sqrt{z \cdot y + \left(y \cdot x + x \cdot z\right)} \cdot 2\]
2 \cdot \sqrt{\left(x \cdot y + x \cdot z\right) + y \cdot z}
↓
\sqrt{z \cdot y + \left(y \cdot x + x \cdot z\right)} \cdot 2
double f(double x, double y, double z) {
        double r578342 = 2.0;
        double r578343 = x;
        double r578344 = y;
        double r578345 = r578343 * r578344;
        double r578346 = z;
        double r578347 = r578343 * r578346;
        double r578348 = r578345 + r578347;
        double r578349 = r578344 * r578346;
        double r578350 = r578348 + r578349;
        double r578351 = sqrt(r578350);
        double r578352 = r578342 * r578351;
        return r578352;
}
↓
double f(double x, double y, double z) {
        double r578353 = z;
        double r578354 = y;
        double r578355 = r578353 * r578354;
        double r578356 = x;
        double r578357 = r578354 * r578356;
        double r578358 = r578356 * r578353;
        double r578359 = r578357 + r578358;
        double r578360 = r578355 + r578359;
        double r578361 = sqrt(r578360);
        double r578362 = 2.0;
        double r578363 = r578361 * r578362;
        return r578363;
}

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

Original19.6
Target18.7
Herbie19.6
\[\begin{array}{l} \mathbf{if}\;z \lt 7.636950090573674520215292914121377944071 \cdot 10^{176}:\\ \;\;\;\;2 \cdot \sqrt{\left(x + y\right) \cdot z + x \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\left(\left(0.25 \cdot \left(\left({y}^{-0.75} \cdot \left({z}^{-0.75} \cdot x\right)\right) \cdot \left(y + z\right)\right) + {z}^{0.25} \cdot {y}^{0.25}\right) \cdot \left(0.25 \cdot \left(\left({y}^{-0.75} \cdot \left({z}^{-0.75} \cdot x\right)\right) \cdot \left(y + z\right)\right) + {z}^{0.25} \cdot {y}^{0.25}\right)\right) \cdot 2\\ \end{array}\]

Derivation

  1. Initial program 19.6

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

  2. Final simplification19.6

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

Reproduce

herbie shell --seed 2019179 
(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)))) (* (* (+ (* 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)))))