Average Error: 0.5 → 0.5
Time: 12.5s
Precision: 64
\[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)}\]
↓
\[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)}\]
1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)}
↓
1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)}
double f(double x, double y, double z, double t) {
        double r190141 = 1.0;
        double r190142 = x;
        double r190143 = y;
        double r190144 = z;
        double r190145 = r190143 - r190144;
        double r190146 = t;
        double r190147 = r190143 - r190146;
        double r190148 = r190145 * r190147;
        double r190149 = r190142 / r190148;
        double r190150 = r190141 - r190149;
        return r190150;
}
↓
double f(double x, double y, double z, double t) {
        double r190151 = 1.0;
        double r190152 = x;
        double r190153 = y;
        double r190154 = z;
        double r190155 = r190153 - r190154;
        double r190156 = t;
        double r190157 = r190153 - r190156;
        double r190158 = r190155 * r190157;
        double r190159 = r190152 / r190158;
        double r190160 = r190151 - r190159;
        return r190160;
}

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 associate-/r*1.1

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

  5. Applied div-inv1.1

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

  6. Applied associate-/l*0.6

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

  7. Simplified0.5

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

  8. Final simplification0.5

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

Reproduce

herbie shell --seed 2019208 
(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)))))