Average Error: 0.7 → 1.1
Time: 15.7s
Precision: 64
\[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)}\]
↓
\[1 - \frac{\frac{x}{y - t}}{y - z}\]
1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)}
↓
1 - \frac{\frac{x}{y - t}}{y - z}
double f(double x, double y, double z, double t) {
        double r159894 = 1.0;
        double r159895 = x;
        double r159896 = y;
        double r159897 = z;
        double r159898 = r159896 - r159897;
        double r159899 = t;
        double r159900 = r159896 - r159899;
        double r159901 = r159898 * r159900;
        double r159902 = r159895 / r159901;
        double r159903 = r159894 - r159902;
        return r159903;
}
↓
double f(double x, double y, double z, double t) {
        double r159904 = 1.0;
        double r159905 = x;
        double r159906 = y;
        double r159907 = t;
        double r159908 = r159906 - r159907;
        double r159909 = r159905 / r159908;
        double r159910 = z;
        double r159911 = r159906 - r159910;
        double r159912 = r159909 / r159911;
        double r159913 = r159904 - r159912;
        return r159913;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.7

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

  3. Applied *-un-lft-identity0.7

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

  4. Applied times-frac1.2

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

  6. Applied associate-*l/1.1

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

  7. Simplified1.1

    \[\leadsto 1 - \frac{\color{blue}{\frac{x}{y - t}}}{y - z}\]

  8. Final simplification1.1

    \[\leadsto 1 - \frac{\frac{x}{y - t}}{y - z}\]

Reproduce

herbie shell --seed 2019347 +o rules:numerics
(FPCore (x y z t)
  :name "Data.Random.Distribution.Triangular:triangularCDF from random-fu-0.2.6.2, A"
  :precision binary64
  (- 1 (/ x (* (- y z) (- y t)))))