Average Error: 20.2 → 20.2
Time: 13.3s
Precision: 64
\[2 \cdot \sqrt{\left(x \cdot y + x \cdot z\right) + y \cdot z}\]
↓
\[2 \cdot \sqrt{y \cdot z + \left(x \cdot y + x \cdot z\right)}\]
2 \cdot \sqrt{\left(x \cdot y + x \cdot z\right) + y \cdot z}
↓
2 \cdot \sqrt{y \cdot z + \left(x \cdot y + x \cdot z\right)}
double f(double x, double y, double z) {
        double r636996 = 2.0;
        double r636997 = x;
        double r636998 = y;
        double r636999 = r636997 * r636998;
        double r637000 = z;
        double r637001 = r636997 * r637000;
        double r637002 = r636999 + r637001;
        double r637003 = r636998 * r637000;
        double r637004 = r637002 + r637003;
        double r637005 = sqrt(r637004);
        double r637006 = r636996 * r637005;
        return r637006;
}
↓
double f(double x, double y, double z) {
        double r637007 = 2.0;
        double r637008 = y;
        double r637009 = z;
        double r637010 = r637008 * r637009;
        double r637011 = x;
        double r637012 = r637011 * r637008;
        double r637013 = r637011 * r637009;
        double r637014 = r637012 + r637013;
        double r637015 = r637010 + r637014;
        double r637016 = sqrt(r637015);
        double r637017 = r637007 * r637016;
        return r637017;
}

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
Target19.6
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. Using strategy rm

  3. Applied +-commutative20.2

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

  4. Final simplification20.2

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

Reproduce

herbie shell --seed 2019305 +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)))))