Average Error: 20.2 → 20.2
Time: 16.0s
Precision: 64
\[2 \cdot \sqrt{\left(x \cdot y + x \cdot z\right) + y \cdot z}\]
↓
\[\sqrt{y \cdot \left(z + x\right) + z \cdot x} \cdot 2\]
2 \cdot \sqrt{\left(x \cdot y + x \cdot z\right) + y \cdot z}
↓
\sqrt{y \cdot \left(z + x\right) + z \cdot x} \cdot 2
double f(double x, double y, double z) {
        double r502580 = 2.0;
        double r502581 = x;
        double r502582 = y;
        double r502583 = r502581 * r502582;
        double r502584 = z;
        double r502585 = r502581 * r502584;
        double r502586 = r502583 + r502585;
        double r502587 = r502582 * r502584;
        double r502588 = r502586 + r502587;
        double r502589 = sqrt(r502588);
        double r502590 = r502580 * r502589;
        return r502590;
}
↓
double f(double x, double y, double z) {
        double r502591 = y;
        double r502592 = z;
        double r502593 = x;
        double r502594 = r502592 + r502593;
        double r502595 = r502591 * r502594;
        double r502596 = r502592 * r502593;
        double r502597 = r502595 + r502596;
        double r502598 = sqrt(r502597);
        double r502599 = 2.0;
        double r502600 = r502598 * r502599;
        return r502600;
}

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

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

Derivation

  1. Initial program 20.2

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

  2. Simplified20.2

    \[\leadsto \color{blue}{\sqrt{y \cdot z + x \cdot \left(y + z\right)} \cdot 2}\]
  3. Using strategy rm

  4. Applied distribute-rgt-in20.2

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

  5. Applied associate-+r+20.2

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

  6. Simplified20.2

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

  7. Final simplification20.2

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

Reproduce

herbie shell --seed 2019304 
(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)))))