Average Error: 0.6 → 0.7
Time: 12.2s
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 r159036 = 1.0;
        double r159037 = x;
        double r159038 = y;
        double r159039 = z;
        double r159040 = r159038 - r159039;
        double r159041 = t;
        double r159042 = r159038 - r159041;
        double r159043 = r159040 * r159042;
        double r159044 = r159037 / r159043;
        double r159045 = r159036 - r159044;
        return r159045;
}
↓
double f(double x, double y, double z, double t) {
        double r159046 = 1.0;
        double r159047 = x;
        double r159048 = 1.0;
        double r159049 = y;
        double r159050 = z;
        double r159051 = r159049 - r159050;
        double r159052 = r159048 / r159051;
        double r159053 = t;
        double r159054 = r159049 - r159053;
        double r159055 = r159052 / r159054;
        double r159056 = r159047 * r159055;
        double r159057 = r159046 - r159056;
        return r159057;
}

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 div-inv0.7

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

  5. Applied associate-/r*0.7

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

  6. Final simplification0.7

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

Reproduce

herbie shell --seed 2019212 
(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)))))