Average Error: 0.5 → 0.6
Time: 5.3s
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 r244013 = 1.0;
        double r244014 = x;
        double r244015 = y;
        double r244016 = z;
        double r244017 = r244015 - r244016;
        double r244018 = t;
        double r244019 = r244015 - r244018;
        double r244020 = r244017 * r244019;
        double r244021 = r244014 / r244020;
        double r244022 = r244013 - r244021;
        return r244022;
}
↓
double f(double x, double y, double z, double t) {
        double r244023 = 1.0;
        double r244024 = x;
        double r244025 = 1.0;
        double r244026 = y;
        double r244027 = z;
        double r244028 = r244026 - r244027;
        double r244029 = r244025 / r244028;
        double r244030 = t;
        double r244031 = r244026 - r244030;
        double r244032 = r244029 / r244031;
        double r244033 = r244024 * r244032;
        double r244034 = r244023 - r244033;
        return r244034;
}

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*1.0

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

  5. Applied *-un-lft-identity1.0

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

  6. Applied div-inv1.0

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

  7. Applied times-frac0.6

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

  8. Simplified0.6

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

  9. Final simplification0.6

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

Reproduce

herbie shell --seed 2020057 +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)))))