Average Error: 19.8 → 19.8
Time: 10.4s
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 r644570 = 2.0;
        double r644571 = x;
        double r644572 = y;
        double r644573 = r644571 * r644572;
        double r644574 = z;
        double r644575 = r644571 * r644574;
        double r644576 = r644573 + r644575;
        double r644577 = r644572 * r644574;
        double r644578 = r644576 + r644577;
        double r644579 = sqrt(r644578);
        double r644580 = r644570 * r644579;
        return r644580;
}
↓
double f(double x, double y, double z) {
        double r644581 = 2.0;
        double r644582 = x;
        double r644583 = y;
        double r644584 = r644582 * r644583;
        double r644585 = z;
        double r644586 = r644582 * r644585;
        double r644587 = r644584 + r644586;
        double r644588 = r644583 * r644585;
        double r644589 = r644587 + r644588;
        double r644590 = sqrt(r644589);
        double r644591 = r644581 * r644590;
        return r644591;
}

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

Original19.8
Target18.9
Herbie19.8
\[\begin{array}{l} \mathbf{if}\;z \lt 7.6369500905736745 \cdot 10^{176}:\\ \;\;\;\;2 \cdot \sqrt{\left(x + y\right) \cdot z + x \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\left(\left(0.25 \cdot \left(\left({y}^{-0.75} \cdot \left({z}^{-0.75} \cdot x\right)\right) \cdot \left(y + z\right)\right) + {z}^{0.25} \cdot {y}^{0.25}\right) \cdot \left(0.25 \cdot \left(\left({y}^{-0.75} \cdot \left({z}^{-0.75} \cdot x\right)\right) \cdot \left(y + z\right)\right) + {z}^{0.25} \cdot {y}^{0.25}\right)\right) \cdot 2\\ \end{array}\]

Derivation

  1. Initial program 19.8

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

  2. Final simplification19.8

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

Reproduce

herbie shell --seed 2020046 +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)))))