Average Error: 0.6 → 1.1
Time: 16.7s
Precision: 64
\[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)}\]
↓
\[1 - \frac{x}{y - z} \cdot \frac{1}{y - t}\]
1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)}
↓
1 - \frac{x}{y - z} \cdot \frac{1}{y - t}
double f(double x, double y, double z, double t) {
        double r167474 = 1.0;
        double r167475 = x;
        double r167476 = y;
        double r167477 = z;
        double r167478 = r167476 - r167477;
        double r167479 = t;
        double r167480 = r167476 - r167479;
        double r167481 = r167478 * r167480;
        double r167482 = r167475 / r167481;
        double r167483 = r167474 - r167482;
        return r167483;
}
↓
double f(double x, double y, double z, double t) {
        double r167484 = 1.0;
        double r167485 = x;
        double r167486 = y;
        double r167487 = z;
        double r167488 = r167486 - r167487;
        double r167489 = r167485 / r167488;
        double r167490 = 1.0;
        double r167491 = t;
        double r167492 = r167486 - r167491;
        double r167493 = r167490 / r167492;
        double r167494 = r167489 * r167493;
        double r167495 = r167484 - r167494;
        return r167495;
}

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 associate-/r*1.0

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

  5. Applied div-inv1.1

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

  6. Final simplification1.1

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

Reproduce

herbie shell --seed 2019303 +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)))))