Average Error: 20.4 → 20.4
Time: 4.4s
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 r703914 = 2.0;
        double r703915 = x;
        double r703916 = y;
        double r703917 = r703915 * r703916;
        double r703918 = z;
        double r703919 = r703915 * r703918;
        double r703920 = r703917 + r703919;
        double r703921 = r703916 * r703918;
        double r703922 = r703920 + r703921;
        double r703923 = sqrt(r703922);
        double r703924 = r703914 * r703923;
        return r703924;
}
↓
double f(double x, double y, double z) {
        double r703925 = 2.0;
        double r703926 = x;
        double r703927 = y;
        double r703928 = z;
        double r703929 = r703927 + r703928;
        double r703930 = r703926 * r703929;
        double r703931 = r703927 * r703928;
        double r703932 = r703930 + r703931;
        double r703933 = sqrt(r703932);
        double r703934 = r703925 * r703933;
        return r703934;
}

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

Original20.4
Target19.5
Herbie20.4
\[\begin{array}{l} \mathbf{if}\;z \lt 7.6369500905736745 \cdot 10^{176}:\\ \;\;\;\;2 \cdot \sqrt{\left(x + y\right) \cdot z + x \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\left(\left(0.25 \cdot \left(\left({y}^{-0.75} \cdot \left({z}^{-0.75} \cdot x\right)\right) \cdot \left(y + z\right)\right) + {z}^{0.25} \cdot {y}^{0.25}\right) \cdot \left(0.25 \cdot \left(\left({y}^{-0.75} \cdot \left({z}^{-0.75} \cdot x\right)\right) \cdot \left(y + z\right)\right) + {z}^{0.25} \cdot {y}^{0.25}\right)\right) \cdot 2\\ \end{array}\]

Derivation

  1. Initial program 20.4

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

  3. Applied distribute-lft-out20.4

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

  4. Final simplification20.4

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

Reproduce

herbie shell --seed 2020033 +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)))))