Average Error: 0.6 → 1.1
Time: 12.9s
Precision: 64
\[1.0 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)}\]
↓
\[1.0 - \frac{\frac{1}{y - t} \cdot x}{y - z}\]
1.0 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)}
↓
1.0 - \frac{\frac{1}{y - t} \cdot x}{y - z}
double f(double x, double y, double z, double t) {
        double r13820143 = 1.0;
        double r13820144 = x;
        double r13820145 = y;
        double r13820146 = z;
        double r13820147 = r13820145 - r13820146;
        double r13820148 = t;
        double r13820149 = r13820145 - r13820148;
        double r13820150 = r13820147 * r13820149;
        double r13820151 = r13820144 / r13820150;
        double r13820152 = r13820143 - r13820151;
        return r13820152;
}
↓
double f(double x, double y, double z, double t) {
        double r13820153 = 1.0;
        double r13820154 = 1.0;
        double r13820155 = y;
        double r13820156 = t;
        double r13820157 = r13820155 - r13820156;
        double r13820158 = r13820154 / r13820157;
        double r13820159 = x;
        double r13820160 = r13820158 * r13820159;
        double r13820161 = z;
        double r13820162 = r13820155 - r13820161;
        double r13820163 = r13820160 / r13820162;
        double r13820164 = r13820153 - r13820163;
        return r13820164;
}

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 0.6

    \[1.0 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)}\]
  2. Using strategy rm

  3. Applied *-un-lft-identity0.6

    \[\leadsto 1.0 - \frac{\color{blue}{1 \cdot x}}{\left(y - z\right) \cdot \left(y - t\right)}\]

  4. Applied times-frac1.1

    \[\leadsto 1.0 - \color{blue}{\frac{1}{y - z} \cdot \frac{x}{y - t}}\]
  5. Using strategy rm

  6. Applied associate-*l/1.1

    \[\leadsto 1.0 - \color{blue}{\frac{1 \cdot \frac{x}{y - t}}{y - z}}\]

  7. Simplified1.1

    \[\leadsto 1.0 - \frac{\color{blue}{\frac{x}{y - t}}}{y - z}\]
  8. Using strategy rm

  9. Applied div-inv1.1

    \[\leadsto 1.0 - \frac{\color{blue}{x \cdot \frac{1}{y - t}}}{y - z}\]

  10. Final simplification1.1

    \[\leadsto 1.0 - \frac{\frac{1}{y - t} \cdot x}{y - z}\]

Reproduce

herbie shell --seed 2019162 
(FPCore (x y z t)
  :name "Data.Random.Distribution.Triangular:triangularCDF from random-fu-0.2.6.2, A"
  (- 1.0 (/ x (* (- y z) (- y t)))))