Average Error: 0.6 → 1.1
Time: 13.9s
Precision: 64
\[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)}\]
↓
\[1 - \frac{x}{y - z} \cdot \frac{1}{y - t}\]
1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)}
↓
1 - \frac{x}{y - z} \cdot \frac{1}{y - t}
double f(double x, double y, double z, double t) {
        double r191637 = 1.0;
        double r191638 = x;
        double r191639 = y;
        double r191640 = z;
        double r191641 = r191639 - r191640;
        double r191642 = t;
        double r191643 = r191639 - r191642;
        double r191644 = r191641 * r191643;
        double r191645 = r191638 / r191644;
        double r191646 = r191637 - r191645;
        return r191646;
}
↓
double f(double x, double y, double z, double t) {
        double r191647 = 1.0;
        double r191648 = x;
        double r191649 = y;
        double r191650 = z;
        double r191651 = r191649 - r191650;
        double r191652 = r191648 / r191651;
        double r191653 = 1.0;
        double r191654 = t;
        double r191655 = r191649 - r191654;
        double r191656 = r191653 / r191655;
        double r191657 = r191652 * r191656;
        double r191658 = r191647 - r191657;
        return r191658;
}

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

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

  3. Applied associate-/r*1.0

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

  5. Applied div-inv1.1

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

  6. Final simplification1.1

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

Reproduce

herbie shell --seed 2019303 
(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)))))