Average Error: 20.8 → 20.8
Time: 8.2s
Precision: 64
\[2 \cdot \sqrt{\left(x \cdot y + x \cdot z\right) + y \cdot z}\]
↓
\[\sqrt{y \cdot z + x \cdot \left(y + z\right)} \cdot 2\]
2 \cdot \sqrt{\left(x \cdot y + x \cdot z\right) + y \cdot z}
↓
\sqrt{y \cdot z + x \cdot \left(y + z\right)} \cdot 2
double f(double x, double y, double z) {
        double r721067 = 2.0;
        double r721068 = x;
        double r721069 = y;
        double r721070 = r721068 * r721069;
        double r721071 = z;
        double r721072 = r721068 * r721071;
        double r721073 = r721070 + r721072;
        double r721074 = r721069 * r721071;
        double r721075 = r721073 + r721074;
        double r721076 = sqrt(r721075);
        double r721077 = r721067 * r721076;
        return r721077;
}
↓
double f(double x, double y, double z) {
        double r721078 = y;
        double r721079 = z;
        double r721080 = r721078 * r721079;
        double r721081 = x;
        double r721082 = r721078 + r721079;
        double r721083 = r721081 * r721082;
        double r721084 = r721080 + r721083;
        double r721085 = sqrt(r721084);
        double r721086 = 2.0;
        double r721087 = r721085 * r721086;
        return r721087;
}

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

Original20.8
Target20.0
Herbie20.8
\[\begin{array}{l} \mathbf{if}\;z \lt 7.6369500905736745 \cdot 10^{176}:\\ \;\;\;\;2 \cdot \sqrt{\left(x + y\right) \cdot z + x \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\left(\left(0.25 \cdot \left(\left({y}^{-0.75} \cdot \left({z}^{-0.75} \cdot x\right)\right) \cdot \left(y + z\right)\right) + {z}^{0.25} \cdot {y}^{0.25}\right) \cdot \left(0.25 \cdot \left(\left({y}^{-0.75} \cdot \left({z}^{-0.75} \cdot x\right)\right) \cdot \left(y + z\right)\right) + {z}^{0.25} \cdot {y}^{0.25}\right)\right) \cdot 2\\ \end{array}\]

Derivation

  1. Initial program 20.8

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

  2. Simplified20.8

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

  3. Final simplification20.8

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

Reproduce

herbie shell --seed 2020047 
(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 (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))

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