Average Error: 0.6 → 1.1
Time: 15.0s
Precision: 64
\[1.0 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)}\]
↓
\[1.0 - \frac{\frac{1}{y - t} \cdot x}{y - z}\]
1.0 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)}
↓
1.0 - \frac{\frac{1}{y - t} \cdot x}{y - z}
double f(double x, double y, double z, double t) {
        double r10766347 = 1.0;
        double r10766348 = x;
        double r10766349 = y;
        double r10766350 = z;
        double r10766351 = r10766349 - r10766350;
        double r10766352 = t;
        double r10766353 = r10766349 - r10766352;
        double r10766354 = r10766351 * r10766353;
        double r10766355 = r10766348 / r10766354;
        double r10766356 = r10766347 - r10766355;
        return r10766356;
}
↓
double f(double x, double y, double z, double t) {
        double r10766357 = 1.0;
        double r10766358 = 1.0;
        double r10766359 = y;
        double r10766360 = t;
        double r10766361 = r10766359 - r10766360;
        double r10766362 = r10766358 / r10766361;
        double r10766363 = x;
        double r10766364 = r10766362 * r10766363;
        double r10766365 = z;
        double r10766366 = r10766359 - r10766365;
        double r10766367 = r10766364 / r10766366;
        double r10766368 = r10766357 - r10766367;
        return r10766368;
}

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

    \[1.0 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)}\]
  2. Using strategy rm

  3. Applied *-un-lft-identity0.6

    \[\leadsto 1.0 - \frac{\color{blue}{1 \cdot x}}{\left(y - z\right) \cdot \left(y - t\right)}\]

  4. Applied times-frac1.1

    \[\leadsto 1.0 - \color{blue}{\frac{1}{y - z} \cdot \frac{x}{y - t}}\]
  5. Using strategy rm

  6. Applied associate-*l/1.1

    \[\leadsto 1.0 - \color{blue}{\frac{1 \cdot \frac{x}{y - t}}{y - z}}\]

  7. Simplified1.1

    \[\leadsto 1.0 - \frac{\color{blue}{\frac{x}{y - t}}}{y - z}\]
  8. Using strategy rm

  9. Applied div-inv1.1

    \[\leadsto 1.0 - \frac{\color{blue}{x \cdot \frac{1}{y - t}}}{y - z}\]

  10. Final simplification1.1

    \[\leadsto 1.0 - \frac{\frac{1}{y - t} \cdot x}{y - z}\]

Reproduce

herbie shell --seed 2019162 +o rules:numerics
(FPCore (x y z t)
  :name "Data.Random.Distribution.Triangular:triangularCDF from random-fu-0.2.6.2, A"
  (- 1.0 (/ x (* (- y z) (- y t)))))