Average Error: 0.5 → 1.2
Time: 6.7s
Precision: 64
\[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)}\]
↓
\[1 - 1 \cdot \frac{\frac{x}{y - t}}{y - z}\]
1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)}
↓
1 - 1 \cdot \frac{\frac{x}{y - t}}{y - z}
double f(double x, double y, double z, double t) {
        double r314823 = 1.0;
        double r314824 = x;
        double r314825 = y;
        double r314826 = z;
        double r314827 = r314825 - r314826;
        double r314828 = t;
        double r314829 = r314825 - r314828;
        double r314830 = r314827 * r314829;
        double r314831 = r314824 / r314830;
        double r314832 = r314823 - r314831;
        return r314832;
}
↓
double f(double x, double y, double z, double t) {
        double r314833 = 1.0;
        double r314834 = 1.0;
        double r314835 = x;
        double r314836 = y;
        double r314837 = t;
        double r314838 = r314836 - r314837;
        double r314839 = r314835 / r314838;
        double r314840 = z;
        double r314841 = r314836 - r314840;
        double r314842 = r314839 / r314841;
        double r314843 = r314834 * r314842;
        double r314844 = r314833 - r314843;
        return r314844;
}

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 0.5

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

  3. Applied *-un-lft-identity0.5

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

  4. Applied times-frac1.2

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

  6. Applied *-un-lft-identity1.2

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

  7. Applied associate-*l*1.2

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

  8. Simplified1.2

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

  9. Final simplification1.2

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

Reproduce

herbie shell --seed 2020021 
(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)))))