Average Error: 20.0 → 20.0
Time: 17.1s
Precision: 64
\[2 \cdot \sqrt{\left(x \cdot y + x \cdot z\right) + y \cdot z}\]
↓
\[2 \cdot \sqrt{y \cdot x + z \cdot \left(x + y\right)}\]
2 \cdot \sqrt{\left(x \cdot y + x \cdot z\right) + y \cdot z}
↓
2 \cdot \sqrt{y \cdot x + z \cdot \left(x + y\right)}
double f(double x, double y, double z) {
        double r35505107 = 2.0;
        double r35505108 = x;
        double r35505109 = y;
        double r35505110 = r35505108 * r35505109;
        double r35505111 = z;
        double r35505112 = r35505108 * r35505111;
        double r35505113 = r35505110 + r35505112;
        double r35505114 = r35505109 * r35505111;
        double r35505115 = r35505113 + r35505114;
        double r35505116 = sqrt(r35505115);
        double r35505117 = r35505107 * r35505116;
        return r35505117;
}
↓
double f(double x, double y, double z) {
        double r35505118 = 2.0;
        double r35505119 = y;
        double r35505120 = x;
        double r35505121 = r35505119 * r35505120;
        double r35505122 = z;
        double r35505123 = r35505120 + r35505119;
        double r35505124 = r35505122 * r35505123;
        double r35505125 = r35505121 + r35505124;
        double r35505126 = sqrt(r35505125);
        double r35505127 = r35505118 * r35505126;
        return r35505127;
}

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

Original20.0
Target19.1
Herbie20.0
\[\begin{array}{l} \mathbf{if}\;z \lt 7.636950090573674520215292914121377944071 \cdot 10^{176}:\\ \;\;\;\;2 \cdot \sqrt{\left(x + y\right) \cdot z + x \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\left(\left(0.25 \cdot \left(\left({y}^{-0.75} \cdot \left({z}^{-0.75} \cdot x\right)\right) \cdot \left(y + z\right)\right) + {z}^{0.25} \cdot {y}^{0.25}\right) \cdot \left(0.25 \cdot \left(\left({y}^{-0.75} \cdot \left({z}^{-0.75} \cdot x\right)\right) \cdot \left(y + z\right)\right) + {z}^{0.25} \cdot {y}^{0.25}\right)\right) \cdot 2\\ \end{array}\]

Derivation

  1. Initial program 20.0

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

  3. Applied associate-+l+20.0

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

  4. Simplified20.0

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

  5. Final simplification20.0

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

Reproduce

herbie shell --seed 2019171 
(FPCore (x y z)
  :name "Diagrams.TwoD.Apollonian:descartes from diagrams-contrib-1.3.0.5"

  :herbie-target
  (if (< z 7.636950090573675e+176) (* 2.0 (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)))) 2.0))

  (* 2.0 (sqrt (+ (+ (* x y) (* x z)) (* y z)))))