Average Error: 20.3 → 20.3
Time: 5.9s
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 r657502 = 2.0;
        double r657503 = x;
        double r657504 = y;
        double r657505 = r657503 * r657504;
        double r657506 = z;
        double r657507 = r657503 * r657506;
        double r657508 = r657505 + r657507;
        double r657509 = r657504 * r657506;
        double r657510 = r657508 + r657509;
        double r657511 = sqrt(r657510);
        double r657512 = r657502 * r657511;
        return r657512;
}
↓
double f(double x, double y, double z) {
        double r657513 = 2.0;
        double r657514 = x;
        double r657515 = y;
        double r657516 = r657514 * r657515;
        double r657517 = z;
        double r657518 = r657514 + r657515;
        double r657519 = r657517 * r657518;
        double r657520 = r657516 + r657519;
        double r657521 = sqrt(r657520);
        double r657522 = r657513 * r657521;
        return r657522;
}

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

Original20.3
Target19.4
Herbie20.3
\[\begin{array}{l} \mathbf{if}\;z \lt 7.636950090573674520215292914121377944071 \cdot 10^{176}:\\ \;\;\;\;2 \cdot \sqrt{\left(x + y\right) \cdot z + x \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\left(\left(0.25 \cdot \left(\left({y}^{-0.75} \cdot \left({z}^{-0.75} \cdot x\right)\right) \cdot \left(y + z\right)\right) + {z}^{0.25} \cdot {y}^{0.25}\right) \cdot \left(0.25 \cdot \left(\left({y}^{-0.75} \cdot \left({z}^{-0.75} \cdot x\right)\right) \cdot \left(y + z\right)\right) + {z}^{0.25} \cdot {y}^{0.25}\right)\right) \cdot 2\\ \end{array}\]

Derivation

  1. Initial program 20.3

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

  3. Applied associate-+l+20.3

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

  4. Simplified20.3

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

  5. Final simplification20.3

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

Reproduce

herbie shell --seed 1978988140 
(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)))))