Average Error: 20.3 → 20.3
Time: 13.2s
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 r411669 = 2.0;
        double r411670 = x;
        double r411671 = y;
        double r411672 = r411670 * r411671;
        double r411673 = z;
        double r411674 = r411670 * r411673;
        double r411675 = r411672 + r411674;
        double r411676 = r411671 * r411673;
        double r411677 = r411675 + r411676;
        double r411678 = sqrt(r411677);
        double r411679 = r411669 * r411678;
        return r411679;
}
↓
double f(double x, double y, double z) {
        double r411680 = y;
        double r411681 = z;
        double r411682 = r411680 + r411681;
        double r411683 = x;
        double r411684 = r411682 * r411683;
        double r411685 = r411681 * r411680;
        double r411686 = r411684 + r411685;
        double r411687 = sqrt(r411686);
        double r411688 = 2.0;
        double r411689 = r411687 * r411688;
        return r411689;
}

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

Original20.3
Target19.3
Herbie20.3
\[\begin{array}{l} \mathbf{if}\;z \lt 7.636950090573674520215292914121377944071 \cdot 10^{176}:\\ \;\;\;\;2 \cdot \sqrt{\left(x + y\right) \cdot z + x \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\left(\left(0.25 \cdot \left(\left({y}^{-0.75} \cdot \left({z}^{-0.75} \cdot x\right)\right) \cdot \left(y + z\right)\right) + {z}^{0.25} \cdot {y}^{0.25}\right) \cdot \left(0.25 \cdot \left(\left({y}^{-0.75} \cdot \left({z}^{-0.75} \cdot x\right)\right) \cdot \left(y + z\right)\right) + {z}^{0.25} \cdot {y}^{0.25}\right)\right) \cdot 2\\ \end{array}\]

Derivation

  1. Initial program 20.3

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

  2. Simplified20.3

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

  3. Final simplification20.3

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

Reproduce

herbie shell --seed 2019196 
(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)))))