Average Error: 19.6 → 19.6
Time: 4.1s
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 r650387 = 2.0;
        double r650388 = x;
        double r650389 = y;
        double r650390 = r650388 * r650389;
        double r650391 = z;
        double r650392 = r650388 * r650391;
        double r650393 = r650390 + r650392;
        double r650394 = r650389 * r650391;
        double r650395 = r650393 + r650394;
        double r650396 = sqrt(r650395);
        double r650397 = r650387 * r650396;
        return r650397;
}
↓
double f(double x, double y, double z) {
        double r650398 = 2.0;
        double r650399 = x;
        double r650400 = y;
        double r650401 = r650399 * r650400;
        double r650402 = z;
        double r650403 = r650399 + r650400;
        double r650404 = r650402 * r650403;
        double r650405 = r650401 + r650404;
        double r650406 = sqrt(r650405);
        double r650407 = r650398 * r650406;
        return r650407;
}

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
Target18.5
Herbie19.6
\[\begin{array}{l} \mathbf{if}\;z \lt 7.636950090573674520215292914121377944071 \cdot 10^{176}:\\ \;\;\;\;2 \cdot \sqrt{\left(x + y\right) \cdot z + x \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\left(\left(0.25 \cdot \left(\left({y}^{-0.75} \cdot \left({z}^{-0.75} \cdot x\right)\right) \cdot \left(y + z\right)\right) + {z}^{0.25} \cdot {y}^{0.25}\right) \cdot \left(0.25 \cdot \left(\left({y}^{-0.75} \cdot \left({z}^{-0.75} \cdot x\right)\right) \cdot \left(y + z\right)\right) + {z}^{0.25} \cdot {y}^{0.25}\right)\right) \cdot 2\\ \end{array}\]

Derivation

  1. Initial program 19.6

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

  3. Applied associate-+l+19.6

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

  4. Simplified19.6

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

  5. Final simplification19.6

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

Reproduce

herbie shell --seed 2019354 
(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)))))