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

Average Error: 7.3 → 1.8

Time: 5.6s

Precision: binary64

Math

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

↓

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

C

double code(double x, double y, double z, double t) {
	return ((double) (x / ((double) (((double) (y - z)) * ((double) (t - z))))));
}

↓

double code(double x, double y, double z, double t) {
	double VAR;
	if ((((double) (x / ((double) (((double) (y - z)) * ((double) (t - z)))))) <= 0.0)) {
		VAR = ((double) (1.0 / ((double) (((double) (t - z)) / ((double) (x / ((double) (y - z))))))));
	} else {
		VAR = ((double) (x * ((double) (1.0 / ((double) (((double) (y - z)) * ((double) (t - z))))))));
	}
	return VAR;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Target

Original	7.3
Target	8.1
Herbie	1.8

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

Derivation

1. Split input into 2 regimes

2. if (/ x (* (- y z) (- t z))) < 0.0

   1. Initial program 9.1

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

   3. Applied associate-/r* 1.4

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

   5. Applied clear-num 1.9

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

   if 0.0 < (/ x (* (- y z) (- t z)))

   1. Initial program 1.4

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

   3. Applied div-inv 1.7

      \[\leadsto \color{blue}{x \cdot \frac{1}{\left(y - z\right) \cdot \left(t - z\right)}}\]
3. Recombined 2 regimes into one program.

4. Final simplification 1.8

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

Reproduce

herbie shell --seed 2020148 
(FPCore (x y z t)
  :name "Data.Random.Distribution.Triangular:triangularCDF from random-fu-0.2.6.2, B"
  :precision binary64

  :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))))