Average Error: 20.8 → 20.8
Time: 8.7s
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 r737652 = 2.0;
        double r737653 = x;
        double r737654 = y;
        double r737655 = r737653 * r737654;
        double r737656 = z;
        double r737657 = r737653 * r737656;
        double r737658 = r737655 + r737657;
        double r737659 = r737654 * r737656;
        double r737660 = r737658 + r737659;
        double r737661 = sqrt(r737660);
        double r737662 = r737652 * r737661;
        return r737662;
}
↓
double f(double x, double y, double z) {
        double r737663 = y;
        double r737664 = z;
        double r737665 = r737663 * r737664;
        double r737666 = x;
        double r737667 = r737663 + r737664;
        double r737668 = r737666 * r737667;
        double r737669 = r737665 + r737668;
        double r737670 = sqrt(r737669);
        double r737671 = 2.0;
        double r737672 = r737670 * r737671;
        return r737672;
}

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

Original20.8
Target20.0
Herbie20.8
\[\begin{array}{l} \mathbf{if}\;z \lt 7.6369500905736745 \cdot 10^{176}:\\ \;\;\;\;2 \cdot \sqrt{\left(x + y\right) \cdot z + x \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\left(\left(0.25 \cdot \left(\left({y}^{-0.75} \cdot \left({z}^{-0.75} \cdot x\right)\right) \cdot \left(y + z\right)\right) + {z}^{0.25} \cdot {y}^{0.25}\right) \cdot \left(0.25 \cdot \left(\left({y}^{-0.75} \cdot \left({z}^{-0.75} \cdot x\right)\right) \cdot \left(y + z\right)\right) + {z}^{0.25} \cdot {y}^{0.25}\right)\right) \cdot 2\\ \end{array}\]

Derivation

  1. Initial program 20.8

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

  2. Simplified20.8

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

  3. Final simplification20.8

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

Reproduce

herbie shell --seed 2020047 
(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)))))