Average Error: 20.0 → 20.0
Time: 13.2s
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 r496623 = 2.0;
        double r496624 = x;
        double r496625 = y;
        double r496626 = r496624 * r496625;
        double r496627 = z;
        double r496628 = r496624 * r496627;
        double r496629 = r496626 + r496628;
        double r496630 = r496625 * r496627;
        double r496631 = r496629 + r496630;
        double r496632 = sqrt(r496631);
        double r496633 = r496623 * r496632;
        return r496633;
}
↓
double f(double x, double y, double z) {
        double r496634 = y;
        double r496635 = z;
        double r496636 = r496634 * r496635;
        double r496637 = x;
        double r496638 = r496634 + r496635;
        double r496639 = r496637 * r496638;
        double r496640 = r496636 + r496639;
        double r496641 = sqrt(r496640);
        double r496642 = 2.0;
        double r496643 = r496641 * r496642;
        return r496643;
}

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
Target19.2
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

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

  3. Final simplification20.0

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

Reproduce

herbie shell --seed 2019208 
(FPCore (x y z)
  :name "Diagrams.TwoD.Apollonian:descartes from diagrams-contrib-1.3.0.5"
  :precision binary64

  :herbie-target
  (if (< z 7.6369500905736745e176) (* 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)))))