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

Average Error: 7.2 → 0.8

Time: 5.1s

Precision: 64

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;\left(y - z\right) \cdot \left(t - z\right) \le -1.22693690139242306 \cdot 10^{139} \lor \neg \left(\left(y - z\right) \cdot \left(t - z\right) \le 7.6884888330617321 \cdot 10^{302}\right):\\ \;\;\;\;\frac{\frac{x}{y - z}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\\ \end{array}\]

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) (((double) (y - z)) * ((double) (t - z)))) <= -1.226936901392423e+139) || !(((double) (((double) (y - z)) * ((double) (t - z)))) <= 7.688488833061732e+302))) {
		VAR = ((double) (((double) (x / ((double) (y - z)))) / ((double) (t - z))));
	} else {
		VAR = ((double) (x / ((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	7.2
Target	7.9
Herbie	0.8

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

Derivation

1. Split input into 2 regimes

2. if (* (- y z) (- t z)) < -1.226936901392423e+139 or 7.688488833061732e+302 < (* (- y z) (- t z))

   1. Initial program 13.2

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

   3. Applied associate-/r* 0.6

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

   if -1.226936901392423e+139 < (* (- y z) (- t z)) < 7.688488833061732e+302

   1. Initial program 1.1

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

4. Final simplification 0.8

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(y - z\right) \cdot \left(t - z\right) \le -1.22693690139242306 \cdot 10^{139} \lor \neg \left(\left(y - z\right) \cdot \left(t - z\right) \le 7.6884888330617321 \cdot 10^{302}\right):\\ \;\;\;\;\frac{\frac{x}{y - z}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\\ \end{array}\]

Reproduce

herbie shell --seed 2020124 
(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))))