Average Error: 20.0 → 20.0
Time: 16.5s
Precision: 64
\[2 \cdot \sqrt{\left(x \cdot y + x \cdot z\right) + y \cdot z}\]
↓
\[\sqrt{\left(y + z\right) \cdot x + z \cdot y} \cdot 2\]
2 \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
double f(double x, double y, double z) {
        double r33086215 = 2.0;
        double r33086216 = x;
        double r33086217 = y;
        double r33086218 = r33086216 * r33086217;
        double r33086219 = z;
        double r33086220 = r33086216 * r33086219;
        double r33086221 = r33086218 + r33086220;
        double r33086222 = r33086217 * r33086219;
        double r33086223 = r33086221 + r33086222;
        double r33086224 = sqrt(r33086223);
        double r33086225 = r33086215 * r33086224;
        return r33086225;
}
↓
double f(double x, double y, double z) {
        double r33086226 = y;
        double r33086227 = z;
        double r33086228 = r33086226 + r33086227;
        double r33086229 = x;
        double r33086230 = r33086228 * r33086229;
        double r33086231 = r33086227 * r33086226;
        double r33086232 = r33086230 + r33086231;
        double r33086233 = sqrt(r33086232);
        double r33086234 = 2.0;
        double r33086235 = r33086233 * r33086234;
        return r33086235;
}

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

Original20.0
Target19.4
Herbie20.0
\[\begin{array}{l} \mathbf{if}\;z \lt 7.636950090573674520215292914121377944071 \cdot 10^{176}:\\ \;\;\;\;2 \cdot \sqrt{\left(x + y\right) \cdot z + x \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\left(\left(0.25 \cdot \left(\left({y}^{-0.75} \cdot \left({z}^{-0.75} \cdot x\right)\right) \cdot \left(y + z\right)\right) + {z}^{0.25} \cdot {y}^{0.25}\right) \cdot \left(0.25 \cdot \left(\left({y}^{-0.75} \cdot \left({z}^{-0.75} \cdot x\right)\right) \cdot \left(y + z\right)\right) + {z}^{0.25} \cdot {y}^{0.25}\right)\right) \cdot 2\\ \end{array}\]

Derivation

  1. Initial program 20.0

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

  2. Simplified20.0

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

  3. Final simplification20.0

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

Reproduce

herbie shell --seed 2019172 
(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)))))