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

Average Error: 7.2 → 2.1

Time: 24.1s

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 r33447056 = x;
        double r33447057 = y;
        double r33447058 = z;
        double r33447059 = r33447057 - r33447058;
        double r33447060 = t;
        double r33447061 = r33447060 - r33447058;
        double r33447062 = r33447059 * r33447061;
        double r33447063 = r33447056 / r33447062;
        return r33447063;
}

↓

double f(double x, double y, double z, double t) {
        double r33447064 = x;
        double r33447065 = y;
        double r33447066 = z;
        double r33447067 = r33447065 - r33447066;
        double r33447068 = r33447064 / r33447067;
        double r33447069 = t;
        double r33447070 = r33447069 - r33447066;
        double r33447071 = r33447068 / r33447070;
        return r33447071;
}

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 +o rules:numerics
(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))))