Average Error: 19.6 → 19.6
Time: 19.3s
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 r35611575 = 2.0;
        double r35611576 = x;
        double r35611577 = y;
        double r35611578 = r35611576 * r35611577;
        double r35611579 = z;
        double r35611580 = r35611576 * r35611579;
        double r35611581 = r35611578 + r35611580;
        double r35611582 = r35611577 * r35611579;
        double r35611583 = r35611581 + r35611582;
        double r35611584 = sqrt(r35611583);
        double r35611585 = r35611575 * r35611584;
        return r35611585;
}
↓
double f(double x, double y, double z) {
        double r35611586 = y;
        double r35611587 = z;
        double r35611588 = r35611586 + r35611587;
        double r35611589 = x;
        double r35611590 = r35611588 * r35611589;
        double r35611591 = r35611587 * r35611586;
        double r35611592 = r35611590 + r35611591;
        double r35611593 = sqrt(r35611592);
        double r35611594 = 2.0;
        double r35611595 = r35611593 * r35611594;
        return r35611595;
}

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

Original19.6
Target19.0
Herbie19.6
\[\begin{array}{l} \mathbf{if}\;z \lt 7.636950090573674520215292914121377944071 \cdot 10^{176}:\\ \;\;\;\;2 \cdot \sqrt{\left(x + y\right) \cdot z + x \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\left(\left(0.25 \cdot \left(\left({y}^{-0.75} \cdot \left({z}^{-0.75} \cdot x\right)\right) \cdot \left(y + z\right)\right) + {z}^{0.25} \cdot {y}^{0.25}\right) \cdot \left(0.25 \cdot \left(\left({y}^{-0.75} \cdot \left({z}^{-0.75} \cdot x\right)\right) \cdot \left(y + z\right)\right) + {z}^{0.25} \cdot {y}^{0.25}\right)\right) \cdot 2\\ \end{array}\]

Derivation

  1. Initial program 19.6

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

  2. Simplified19.6

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

  3. Final simplification19.6

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

Reproduce

herbie shell --seed 2019170 
(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)))))