Average Error: 6.6 → 6.6
Time: 4.4s
Precision: 64
\[\frac{\frac{1}{x}}{y \cdot \left(1 + z \cdot z\right)}\]
↓
\[\frac{\frac{1}{1}}{\left(1 + z \cdot z\right) \cdot \left(x \cdot y\right)}\]
\frac{\frac{1}{x}}{y \cdot \left(1 + z \cdot z\right)}
↓
\frac{\frac{1}{1}}{\left(1 + z \cdot z\right) \cdot \left(x \cdot y\right)}
double f(double x, double y, double z) {
        double r425135 = 1.0;
        double r425136 = x;
        double r425137 = r425135 / r425136;
        double r425138 = y;
        double r425139 = z;
        double r425140 = r425139 * r425139;
        double r425141 = r425135 + r425140;
        double r425142 = r425138 * r425141;
        double r425143 = r425137 / r425142;
        return r425143;
}
↓
double f(double x, double y, double z) {
        double r425144 = 1.0;
        double r425145 = 1.0;
        double r425146 = r425144 / r425145;
        double r425147 = z;
        double r425148 = r425147 * r425147;
        double r425149 = r425144 + r425148;
        double r425150 = x;
        double r425151 = y;
        double r425152 = r425150 * r425151;
        double r425153 = r425149 * r425152;
        double r425154 = r425146 / r425153;
        return r425154;
}

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

Original6.6
Target5.9
Herbie6.6
\[\begin{array}{l} \mathbf{if}\;y \cdot \left(1 + z \cdot z\right) \lt -\infty:\\ \;\;\;\;\frac{\frac{1}{y}}{\left(1 + z \cdot z\right) \cdot x}\\ \mathbf{elif}\;y \cdot \left(1 + z \cdot z\right) \lt 8.680743250567251617010582226806563373013 \cdot 10^{305}:\\ \;\;\;\;\frac{\frac{1}{x}}{\left(1 + z \cdot z\right) \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{1}{y}}{\left(1 + z \cdot z\right) \cdot x}\\ \end{array}\]

Derivation

  1. Initial program 6.6

    \[\frac{\frac{1}{x}}{y \cdot \left(1 + z \cdot z\right)}\]
  2. Using strategy rm

  3. Applied associate-/r*6.4

    \[\leadsto \color{blue}{\frac{\frac{\frac{1}{x}}{y}}{1 + z \cdot z}}\]

  4. Simplified6.4

    \[\leadsto \frac{\color{blue}{\frac{\frac{1}{y}}{x}}}{1 + z \cdot z}\]
  5. Using strategy rm

  6. Applied *-un-lft-identity6.4

    \[\leadsto \frac{\frac{\frac{1}{y}}{\color{blue}{1 \cdot x}}}{1 + z \cdot z}\]

  7. Applied div-inv6.4

    \[\leadsto \frac{\frac{\color{blue}{1 \cdot \frac{1}{y}}}{1 \cdot x}}{1 + z \cdot z}\]

  8. Applied times-frac6.4

    \[\leadsto \frac{\color{blue}{\frac{1}{1} \cdot \frac{\frac{1}{y}}{x}}}{1 + z \cdot z}\]

  9. Applied associate-/l*6.7

    \[\leadsto \color{blue}{\frac{\frac{1}{1}}{\frac{1 + z \cdot z}{\frac{\frac{1}{y}}{x}}}}\]

  10. Simplified6.6

    \[\leadsto \frac{\frac{1}{1}}{\color{blue}{\left(1 + z \cdot z\right) \cdot \left(x \cdot y\right)}}\]

  11. Final simplification6.6

    \[\leadsto \frac{\frac{1}{1}}{\left(1 + z \cdot z\right) \cdot \left(x \cdot y\right)}\]

Reproduce

herbie shell --seed 2019362 
(FPCore (x y z)
  :name "Statistics.Distribution.CauchyLorentz:$cdensity from math-functions-0.1.5.2"
  :precision binary64

  :herbie-target
  (if (< (* y (+ 1 (* z z))) #f) (/ (/ 1 y) (* (+ 1 (* z z)) x)) (if (< (* y (+ 1 (* z z))) 8.680743250567252e+305) (/ (/ 1 x) (* (+ 1 (* z z)) y)) (/ (/ 1 y) (* (+ 1 (* z z)) x))))

  (/ (/ 1 x) (* y (+ 1 (* z z)))))