Average Error: 20.1 → 20.1
Time: 21.6s
Precision: 64
\[2 \cdot \sqrt{\left(x \cdot y + x \cdot z\right) + y \cdot z}\]
↓
\[2 \cdot \sqrt{\left(x \cdot y + x \cdot z\right) + y \cdot z}\]
2 \cdot \sqrt{\left(x \cdot y + x \cdot z\right) + y \cdot z}
↓
2 \cdot \sqrt{\left(x \cdot y + x \cdot z\right) + y \cdot z}
double f(double x, double y, double z) {
        double r340845 = 2.0;
        double r340846 = x;
        double r340847 = y;
        double r340848 = r340846 * r340847;
        double r340849 = z;
        double r340850 = r340846 * r340849;
        double r340851 = r340848 + r340850;
        double r340852 = r340847 * r340849;
        double r340853 = r340851 + r340852;
        double r340854 = sqrt(r340853);
        double r340855 = r340845 * r340854;
        return r340855;
}
↓
double f(double x, double y, double z) {
        double r340856 = 2.0;
        double r340857 = x;
        double r340858 = y;
        double r340859 = r340857 * r340858;
        double r340860 = z;
        double r340861 = r340857 * r340860;
        double r340862 = r340859 + r340861;
        double r340863 = r340858 * r340860;
        double r340864 = r340862 + r340863;
        double r340865 = sqrt(r340864);
        double r340866 = r340856 * r340865;
        return r340866;
}

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

Original20.1
Target19.1
Herbie20.1
\[\begin{array}{l} \mathbf{if}\;z \lt 7.636950090573674520215292914121377944071 \cdot 10^{176}:\\ \;\;\;\;2 \cdot \sqrt{\left(x + y\right) \cdot z + x \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\left(\left(0.25 \cdot \left(\left({y}^{-0.75} \cdot \left({z}^{-0.75} \cdot x\right)\right) \cdot \left(y + z\right)\right) + {z}^{0.25} \cdot {y}^{0.25}\right) \cdot \left(0.25 \cdot \left(\left({y}^{-0.75} \cdot \left({z}^{-0.75} \cdot x\right)\right) \cdot \left(y + z\right)\right) + {z}^{0.25} \cdot {y}^{0.25}\right)\right) \cdot 2\\ \end{array}\]

Derivation

  1. Initial program 20.1

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

  2. Final simplification20.1

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

Reproduce

herbie shell --seed 2019322 +o rules:numerics
(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)))))