Average Error: 0.6 → 1.1
Time: 14.0s
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 r13993041 = 1.0;
        double r13993042 = x;
        double r13993043 = y;
        double r13993044 = z;
        double r13993045 = r13993043 - r13993044;
        double r13993046 = t;
        double r13993047 = r13993043 - r13993046;
        double r13993048 = r13993045 * r13993047;
        double r13993049 = r13993042 / r13993048;
        double r13993050 = r13993041 - r13993049;
        return r13993050;
}
↓
double f(double x, double y, double z, double t) {
        double r13993051 = 1.0;
        double r13993052 = 1.0;
        double r13993053 = y;
        double r13993054 = t;
        double r13993055 = r13993053 - r13993054;
        double r13993056 = r13993052 / r13993055;
        double r13993057 = x;
        double r13993058 = r13993056 * r13993057;
        double r13993059 = z;
        double r13993060 = r13993053 - r13993059;
        double r13993061 = r13993058 / r13993060;
        double r13993062 = r13993051 - r13993061;
        return r13993062;
}

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 
(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)))))