Average Error: 19.8 → 19.8
Time: 21.4s
Precision: 64
\[2 \cdot \sqrt{\left(x \cdot y + x \cdot z\right) + y \cdot z}\]
↓
\[2 \cdot \sqrt{x \cdot y + z \cdot \left(x + y\right)}\]
2 \cdot \sqrt{\left(x \cdot y + x \cdot z\right) + y \cdot z}
↓
2 \cdot \sqrt{x \cdot y + z \cdot \left(x + y\right)}
double f(double x, double y, double z) {
        double r514670 = 2.0;
        double r514671 = x;
        double r514672 = y;
        double r514673 = r514671 * r514672;
        double r514674 = z;
        double r514675 = r514671 * r514674;
        double r514676 = r514673 + r514675;
        double r514677 = r514672 * r514674;
        double r514678 = r514676 + r514677;
        double r514679 = sqrt(r514678);
        double r514680 = r514670 * r514679;
        return r514680;
}
↓
double f(double x, double y, double z) {
        double r514681 = 2.0;
        double r514682 = x;
        double r514683 = y;
        double r514684 = r514682 * r514683;
        double r514685 = z;
        double r514686 = r514682 + r514683;
        double r514687 = r514685 * r514686;
        double r514688 = r514684 + r514687;
        double r514689 = sqrt(r514688);
        double r514690 = r514681 * r514689;
        return r514690;
}

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
Target19.0
Herbie19.8
\[\begin{array}{l} \mathbf{if}\;z \lt 7.636950090573674520215292914121377944071 \cdot 10^{176}:\\ \;\;\;\;2 \cdot \sqrt{\left(x + y\right) \cdot z + x \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\left(\left(0.25 \cdot \left(\left({y}^{-0.75} \cdot \left({z}^{-0.75} \cdot x\right)\right) \cdot \left(y + z\right)\right) + {z}^{0.25} \cdot {y}^{0.25}\right) \cdot \left(0.25 \cdot \left(\left({y}^{-0.75} \cdot \left({z}^{-0.75} \cdot x\right)\right) \cdot \left(y + z\right)\right) + {z}^{0.25} \cdot {y}^{0.25}\right)\right) \cdot 2\\ \end{array}\]

Derivation

  1. Initial program 19.8

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

  3. Applied associate-+l+19.8

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

  4. Simplified19.8

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

  5. Final simplification19.8

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

Reproduce

herbie shell --seed 2019303 +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 7.6369500905736745e176) (* 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)))))