Average Error: 19.6 → 19.6
Time: 17.2s
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 r454897 = 2.0;
        double r454898 = x;
        double r454899 = y;
        double r454900 = r454898 * r454899;
        double r454901 = z;
        double r454902 = r454898 * r454901;
        double r454903 = r454900 + r454902;
        double r454904 = r454899 * r454901;
        double r454905 = r454903 + r454904;
        double r454906 = sqrt(r454905);
        double r454907 = r454897 * r454906;
        return r454907;
}
↓
double f(double x, double y, double z) {
        double r454908 = z;
        double r454909 = y;
        double r454910 = r454908 * r454909;
        double r454911 = x;
        double r454912 = r454909 * r454911;
        double r454913 = r454911 * r454908;
        double r454914 = r454912 + r454913;
        double r454915 = r454910 + r454914;
        double r454916 = sqrt(r454915);
        double r454917 = 2.0;
        double r454918 = r454916 * r454917;
        return r454918;
}

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 +o rules:numerics
(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)))))