Average Error: 0.6 → 1.1
Time: 16.8s
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 r212458 = 1.0;
        double r212459 = x;
        double r212460 = y;
        double r212461 = z;
        double r212462 = r212460 - r212461;
        double r212463 = t;
        double r212464 = r212460 - r212463;
        double r212465 = r212462 * r212464;
        double r212466 = r212459 / r212465;
        double r212467 = r212458 - r212466;
        return r212467;
}
↓
double f(double x, double y, double z, double t) {
        double r212468 = 1.0;
        double r212469 = x;
        double r212470 = y;
        double r212471 = z;
        double r212472 = r212470 - r212471;
        double r212473 = r212469 / r212472;
        double r212474 = 1.0;
        double r212475 = t;
        double r212476 = r212470 - r212475;
        double r212477 = r212474 / r212476;
        double r212478 = r212473 * r212477;
        double r212479 = r212468 - r212478;
        return r212479;
}

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)))))