Average Error: 20.2 → 20.2
Time: 17.5s
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 r1716466 = 2.0;
        double r1716467 = x;
        double r1716468 = y;
        double r1716469 = r1716467 * r1716468;
        double r1716470 = z;
        double r1716471 = r1716467 * r1716470;
        double r1716472 = r1716469 + r1716471;
        double r1716473 = r1716468 * r1716470;
        double r1716474 = r1716472 + r1716473;
        double r1716475 = sqrt(r1716474);
        double r1716476 = r1716466 * r1716475;
        return r1716476;
}
↓
double f(double x, double y, double z) {
        double r1716477 = 2.0;
        double r1716478 = x;
        double r1716479 = y;
        double r1716480 = r1716478 * r1716479;
        double r1716481 = z;
        double r1716482 = r1716478 * r1716481;
        double r1716483 = r1716480 + r1716482;
        double r1716484 = r1716479 * r1716481;
        double r1716485 = r1716483 + r1716484;
        double r1716486 = sqrt(r1716485);
        double r1716487 = r1716477 * r1716486;
        return r1716487;
}

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

Original20.2
Target19.3
Herbie20.2
\[\begin{array}{l} \mathbf{if}\;z \lt 7.636950090573674520215292914121377944071 \cdot 10^{176}:\\ \;\;\;\;2 \cdot \sqrt{\left(x + y\right) \cdot z + x \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\left(\left(0.25 \cdot \left(\left({y}^{-0.75} \cdot \left({z}^{-0.75} \cdot x\right)\right) \cdot \left(y + z\right)\right) + {z}^{0.25} \cdot {y}^{0.25}\right) \cdot \left(0.25 \cdot \left(\left({y}^{-0.75} \cdot \left({z}^{-0.75} \cdot x\right)\right) \cdot \left(y + z\right)\right) + {z}^{0.25} \cdot {y}^{0.25}\right)\right) \cdot 2\\ \end{array}\]

Derivation

  1. Initial program 20.2

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

  2. Final simplification20.2

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

Reproduce

herbie shell --seed 2019235 
(FPCore (x y z)
  :name "Diagrams.TwoD.Apollonian:descartes from diagrams-contrib-1.3.0.5"
  :precision binary64

  :herbie-target
  (if (< z 7.6369500905736745e176) (* 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)))))