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

Average Error: 7.2 → 2.1

Time: 19.2s

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 r36364012 = x;
        double r36364013 = y;
        double r36364014 = z;
        double r36364015 = r36364013 - r36364014;
        double r36364016 = t;
        double r36364017 = r36364016 - r36364014;
        double r36364018 = r36364015 * r36364017;
        double r36364019 = r36364012 / r36364018;
        return r36364019;
}

↓

double f(double x, double y, double z, double t) {
        double r36364020 = x;
        double r36364021 = y;
        double r36364022 = z;
        double r36364023 = r36364021 - r36364022;
        double r36364024 = r36364020 / r36364023;
        double r36364025 = t;
        double r36364026 = r36364025 - r36364022;
        double r36364027 = r36364024 / r36364026;
        return r36364027;
}

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))))