Average Error: 0.7 → 0.8
Time: 11.2s
Precision: 64
\[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)}\]
↓
\[1 - x \cdot \frac{\frac{1}{y - z}}{y - t}\]
1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)}
↓
1 - x \cdot \frac{\frac{1}{y - z}}{y - t}
double f(double x, double y, double z, double t) {
        double r213796 = 1.0;
        double r213797 = x;
        double r213798 = y;
        double r213799 = z;
        double r213800 = r213798 - r213799;
        double r213801 = t;
        double r213802 = r213798 - r213801;
        double r213803 = r213800 * r213802;
        double r213804 = r213797 / r213803;
        double r213805 = r213796 - r213804;
        return r213805;
}
↓
double f(double x, double y, double z, double t) {
        double r213806 = 1.0;
        double r213807 = x;
        double r213808 = 1.0;
        double r213809 = y;
        double r213810 = z;
        double r213811 = r213809 - r213810;
        double r213812 = r213808 / r213811;
        double r213813 = t;
        double r213814 = r213809 - r213813;
        double r213815 = r213812 / r213814;
        double r213816 = r213807 * r213815;
        double r213817 = r213806 - r213816;
        return r213817;
}

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 div-inv0.8

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

  5. Applied associate-/r*0.8

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

  6. Final simplification0.8

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

Reproduce

herbie shell --seed 2020024 +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)))))