Average Error: 19.9 → 19.9
Time: 4.0s
Precision: 64
\[2 \cdot \sqrt{\left(x \cdot y + x \cdot z\right) + y \cdot z}\]
↓
\[2 \cdot \sqrt{x \cdot \left(y + z\right) + y \cdot z}\]
2 \cdot \sqrt{\left(x \cdot y + x \cdot z\right) + y \cdot z}
↓
2 \cdot \sqrt{x \cdot \left(y + z\right) + y \cdot z}
double f(double x, double y, double z) {
        double r794859 = 2.0;
        double r794860 = x;
        double r794861 = y;
        double r794862 = r794860 * r794861;
        double r794863 = z;
        double r794864 = r794860 * r794863;
        double r794865 = r794862 + r794864;
        double r794866 = r794861 * r794863;
        double r794867 = r794865 + r794866;
        double r794868 = sqrt(r794867);
        double r794869 = r794859 * r794868;
        return r794869;
}
↓
double f(double x, double y, double z) {
        double r794870 = 2.0;
        double r794871 = x;
        double r794872 = y;
        double r794873 = z;
        double r794874 = r794872 + r794873;
        double r794875 = r794871 * r794874;
        double r794876 = r794872 * r794873;
        double r794877 = r794875 + r794876;
        double r794878 = sqrt(r794877);
        double r794879 = r794870 * r794878;
        return r794879;
}

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

Original19.9
Target19.2
Herbie19.9
\[\begin{array}{l} \mathbf{if}\;z \lt 7.6369500905736745 \cdot 10^{176}:\\ \;\;\;\;2 \cdot \sqrt{\left(x + y\right) \cdot z + x \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\left(\left(0.25 \cdot \left(\left({y}^{-0.75} \cdot \left({z}^{-0.75} \cdot x\right)\right) \cdot \left(y + z\right)\right) + {z}^{0.25} \cdot {y}^{0.25}\right) \cdot \left(0.25 \cdot \left(\left({y}^{-0.75} \cdot \left({z}^{-0.75} \cdot x\right)\right) \cdot \left(y + z\right)\right) + {z}^{0.25} \cdot {y}^{0.25}\right)\right) \cdot 2\\ \end{array}\]

Derivation

  1. Initial program 19.9

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

  3. Applied distribute-lft-out19.9

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

  4. Final simplification19.9

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

Reproduce

herbie shell --seed 2020060 
(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)))))