Average Error: 19.5 → 19.5
Time: 16.3s
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 r31134314 = 2.0;
        double r31134315 = x;
        double r31134316 = y;
        double r31134317 = r31134315 * r31134316;
        double r31134318 = z;
        double r31134319 = r31134315 * r31134318;
        double r31134320 = r31134317 + r31134319;
        double r31134321 = r31134316 * r31134318;
        double r31134322 = r31134320 + r31134321;
        double r31134323 = sqrt(r31134322);
        double r31134324 = r31134314 * r31134323;
        return r31134324;
}
↓
double f(double x, double y, double z) {
        double r31134325 = z;
        double r31134326 = y;
        double r31134327 = r31134325 * r31134326;
        double r31134328 = x;
        double r31134329 = r31134326 * r31134328;
        double r31134330 = r31134328 * r31134325;
        double r31134331 = r31134329 + r31134330;
        double r31134332 = r31134327 + r31134331;
        double r31134333 = sqrt(r31134332);
        double r31134334 = 2.0;
        double r31134335 = r31134333 * r31134334;
        return r31134335;
}

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

Original19.5
Target18.5
Herbie19.5
\[\begin{array}{l} \mathbf{if}\;z \lt 7.636950090573674520215292914121377944071 \cdot 10^{176}:\\ \;\;\;\;2 \cdot \sqrt{\left(x + y\right) \cdot z + x \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\left(\left(0.25 \cdot \left(\left({y}^{-0.75} \cdot \left({z}^{-0.75} \cdot x\right)\right) \cdot \left(y + z\right)\right) + {z}^{0.25} \cdot {y}^{0.25}\right) \cdot \left(0.25 \cdot \left(\left({y}^{-0.75} \cdot \left({z}^{-0.75} \cdot x\right)\right) \cdot \left(y + z\right)\right) + {z}^{0.25} \cdot {y}^{0.25}\right)\right) \cdot 2\\ \end{array}\]

Derivation

  1. Initial program 19.5

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

  2. Final simplification19.5

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

Reproduce

herbie shell --seed 2019192 
(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)))))