Data.Random.Distribution.Triangular:triangularCDF from random-fu-0.2.6.2, B

Average Error: 7.2 → 2.1

Time: 20.0s

Precision: 64

Math

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

↓

\[\frac{\frac{x}{y - z}}{t - z}\]

C

double f(double x, double y, double z, double t) {
        double r33472344 = x;
        double r33472345 = y;
        double r33472346 = z;
        double r33472347 = r33472345 - r33472346;
        double r33472348 = t;
        double r33472349 = r33472348 - r33472346;
        double r33472350 = r33472347 * r33472349;
        double r33472351 = r33472344 / r33472350;
        return r33472351;
}

↓

double f(double x, double y, double z, double t) {
        double r33472352 = x;
        double r33472353 = y;
        double r33472354 = z;
        double r33472355 = r33472353 - r33472354;
        double r33472356 = r33472352 / r33472355;
        double r33472357 = t;
        double r33472358 = r33472357 - r33472354;
        double r33472359 = r33472356 / r33472358;
        return r33472359;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Target

Original	7.2
Target	8.0
Herbie	2.1

\[\begin{array}{l} \mathbf{if}\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \lt 0.0:\\ \;\;\;\;\frac{\frac{x}{y - z}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{1}{\left(y - z\right) \cdot \left(t - z\right)}\\ \end{array}\]

Derivation

1. Initial program 7.2

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

3. Applied associate-/r* 2.1

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

4. Final simplification 2.1

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

Reproduce

herbie shell --seed 2019172 
(FPCore (x y z t)
  :name "Data.Random.Distribution.Triangular:triangularCDF from random-fu-0.2.6.2, B"

  :herbie-target
  (if (< (/ x (* (- y z) (- t z))) 0.0) (/ (/ x (- y z)) (- t z)) (* x (/ 1.0 (* (- y z) (- t z)))))

  (/ x (* (- y z) (- t z))))