Average Error: 0.5 → 0.5
Time: 13.8s
Precision: 64
\[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)}\]
↓
\[1 - \frac{x}{\left(y - t\right) \cdot \left(y - z\right)}\]
1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)}
↓
1 - \frac{x}{\left(y - t\right) \cdot \left(y - z\right)}
double f(double x, double y, double z, double t) {
        double r130990 = 1.0;
        double r130991 = x;
        double r130992 = y;
        double r130993 = z;
        double r130994 = r130992 - r130993;
        double r130995 = t;
        double r130996 = r130992 - r130995;
        double r130997 = r130994 * r130996;
        double r130998 = r130991 / r130997;
        double r130999 = r130990 - r130998;
        return r130999;
}
↓
double f(double x, double y, double z, double t) {
        double r131000 = 1.0;
        double r131001 = x;
        double r131002 = y;
        double r131003 = t;
        double r131004 = r131002 - r131003;
        double r131005 = z;
        double r131006 = r131002 - r131005;
        double r131007 = r131004 * r131006;
        double r131008 = r131001 / r131007;
        double r131009 = r131000 - r131008;
        return r131009;
}

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

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

  8. Final simplification0.5

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

Reproduce

herbie shell --seed 2019208 +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)))))