Average Error: 20.1 → 20.1
Time: 21.0s
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 r462248 = 2.0;
        double r462249 = x;
        double r462250 = y;
        double r462251 = r462249 * r462250;
        double r462252 = z;
        double r462253 = r462249 * r462252;
        double r462254 = r462251 + r462253;
        double r462255 = r462250 * r462252;
        double r462256 = r462254 + r462255;
        double r462257 = sqrt(r462256);
        double r462258 = r462248 * r462257;
        return r462258;
}
↓
double f(double x, double y, double z) {
        double r462259 = y;
        double r462260 = z;
        double r462261 = r462259 * r462260;
        double r462262 = x;
        double r462263 = r462259 + r462260;
        double r462264 = r462262 * r462263;
        double r462265 = r462261 + r462264;
        double r462266 = sqrt(r462265);
        double r462267 = 2.0;
        double r462268 = r462266 * r462267;
        return r462268;
}

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

Original20.1
Target19.2
Herbie20.1
\[\begin{array}{l} \mathbf{if}\;z \lt 7.636950090573674520215292914121377944071 \cdot 10^{176}:\\ \;\;\;\;2 \cdot \sqrt{\left(x + y\right) \cdot z + x \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\left(\left(0.25 \cdot \left(\left({y}^{-0.75} \cdot \left({z}^{-0.75} \cdot x\right)\right) \cdot \left(y + z\right)\right) + {z}^{0.25} \cdot {y}^{0.25}\right) \cdot \left(0.25 \cdot \left(\left({y}^{-0.75} \cdot \left({z}^{-0.75} \cdot x\right)\right) \cdot \left(y + z\right)\right) + {z}^{0.25} \cdot {y}^{0.25}\right)\right) \cdot 2\\ \end{array}\]

Derivation

  1. Initial program 20.1

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

  2. Simplified20.1

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

  3. Final simplification20.1

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

Reproduce

herbie shell --seed 2019326 
(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)))))