Average Error: 19.7 → 19.7
Time: 4.4s
Precision: 64
\[2 \cdot \sqrt{\left(x \cdot y + x \cdot z\right) + y \cdot z}\]
↓
\[2 \cdot \sqrt{x \cdot y + z \cdot \left(x + y\right)}\]
2 \cdot \sqrt{\left(x \cdot y + x \cdot z\right) + y \cdot z}
↓
2 \cdot \sqrt{x \cdot y + z \cdot \left(x + y\right)}
double f(double x, double y, double z) {
        double r785977 = 2.0;
        double r785978 = x;
        double r785979 = y;
        double r785980 = r785978 * r785979;
        double r785981 = z;
        double r785982 = r785978 * r785981;
        double r785983 = r785980 + r785982;
        double r785984 = r785979 * r785981;
        double r785985 = r785983 + r785984;
        double r785986 = sqrt(r785985);
        double r785987 = r785977 * r785986;
        return r785987;
}
↓
double f(double x, double y, double z) {
        double r785988 = 2.0;
        double r785989 = x;
        double r785990 = y;
        double r785991 = r785989 * r785990;
        double r785992 = z;
        double r785993 = r785989 + r785990;
        double r785994 = r785992 * r785993;
        double r785995 = r785991 + r785994;
        double r785996 = sqrt(r785995);
        double r785997 = r785988 * r785996;
        return r785997;
}

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

Original19.7
Target19.3
Herbie19.7
\[\begin{array}{l} \mathbf{if}\;z \lt 7.6369500905736745 \cdot 10^{176}:\\ \;\;\;\;2 \cdot \sqrt{\left(x + y\right) \cdot z + x \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\left(\left(0.25 \cdot \left(\left({y}^{-0.75} \cdot \left({z}^{-0.75} \cdot x\right)\right) \cdot \left(y + z\right)\right) + {z}^{0.25} \cdot {y}^{0.25}\right) \cdot \left(0.25 \cdot \left(\left({y}^{-0.75} \cdot \left({z}^{-0.75} \cdot x\right)\right) \cdot \left(y + z\right)\right) + {z}^{0.25} \cdot {y}^{0.25}\right)\right) \cdot 2\\ \end{array}\]

Derivation

  1. Initial program 19.7

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

  3. Applied associate-+l+19.7

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

  4. Simplified19.7

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

  5. Final simplification19.7

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

Reproduce

herbie shell --seed 2020021 
(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)))))