Average Error: 0.6 → 1.2
Time: 2.8s
Precision: 64
\[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)}\]
↓
\[1 - \frac{\frac{x}{y - z}}{y - t}\]
1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)}
↓
1 - \frac{\frac{x}{y - z}}{y - t}
double f(double x, double y, double z, double t) {
        double r169626 = 1.0;
        double r169627 = x;
        double r169628 = y;
        double r169629 = z;
        double r169630 = r169628 - r169629;
        double r169631 = t;
        double r169632 = r169628 - r169631;
        double r169633 = r169630 * r169632;
        double r169634 = r169627 / r169633;
        double r169635 = r169626 - r169634;
        return r169635;
}
↓
double f(double x, double y, double z, double t) {
        double r169636 = 1.0;
        double r169637 = x;
        double r169638 = y;
        double r169639 = z;
        double r169640 = r169638 - r169639;
        double r169641 = r169637 / r169640;
        double r169642 = t;
        double r169643 = r169638 - r169642;
        double r169644 = r169641 / r169643;
        double r169645 = r169636 - r169644;
        return r169645;
}

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*1.2

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

  4. Final simplification1.2

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

Reproduce

herbie shell --seed 2020025 +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)))))