Average Error: 19.6 → 19.6
Time: 6.1s
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 r665458 = 2.0;
        double r665459 = x;
        double r665460 = y;
        double r665461 = r665459 * r665460;
        double r665462 = z;
        double r665463 = r665459 * r665462;
        double r665464 = r665461 + r665463;
        double r665465 = r665460 * r665462;
        double r665466 = r665464 + r665465;
        double r665467 = sqrt(r665466);
        double r665468 = r665458 * r665467;
        return r665468;
}
↓
double f(double x, double y, double z) {
        double r665469 = 2.0;
        double r665470 = x;
        double r665471 = y;
        double r665472 = r665470 * r665471;
        double r665473 = z;
        double r665474 = r665470 * r665473;
        double r665475 = r665472 + r665474;
        double r665476 = r665471 * r665473;
        double r665477 = r665475 + r665476;
        double r665478 = sqrt(r665477);
        double r665479 = r665469 * r665478;
        return r665479;
}

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

Original19.6
Target18.7
Herbie19.6
\[\begin{array}{l} \mathbf{if}\;z \lt 7.6369500905736745 \cdot 10^{176}:\\ \;\;\;\;2 \cdot \sqrt{\left(x + y\right) \cdot z + x \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\left(\left(0.25 \cdot \left(\left({y}^{-0.75} \cdot \left({z}^{-0.75} \cdot x\right)\right) \cdot \left(y + z\right)\right) + {z}^{0.25} \cdot {y}^{0.25}\right) \cdot \left(0.25 \cdot \left(\left({y}^{-0.75} \cdot \left({z}^{-0.75} \cdot x\right)\right) \cdot \left(y + z\right)\right) + {z}^{0.25} \cdot {y}^{0.25}\right)\right) \cdot 2\\ \end{array}\]

Derivation

  1. Initial program 19.6

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

  2. Final simplification19.6

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

Reproduce

herbie shell --seed 2020064 +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)))))