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

Average Error: 7.6 → 1.2

Time: 4.3s

Precision: binary64

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;\left(y - z\right) \cdot \left(t - z\right) \le -1.9863512887713326 \cdot 10^{259}:\\ \;\;\;\;\frac{1}{y - z} \cdot \frac{1}{\left(t - z\right) \cdot \frac{1}{x}}\\ \mathbf{elif}\;\left(y - z\right) \cdot \left(t - z\right) \le -2.45856805714858837 \cdot 10^{-202}:\\ \;\;\;\;x \cdot \frac{1}{\left(y - z\right) \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{1}{y - z}}{\frac{t - z}{x}}\\ \end{array}\]

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)))) <= -1.9863512887713326e+259)) {
		VAR = ((double) (((double) (1.0 / ((double) (y - z)))) * ((double) (1.0 / ((double) (((double) (t - z)) * ((double) (1.0 / x))))))));
	} else {
		double VAR_1;
		if ((((double) (((double) (y - z)) * ((double) (t - z)))) <= -2.4585680571485884e-202)) {
			VAR_1 = ((double) (x * ((double) (1.0 / ((double) (((double) (y - z)) * ((double) (t - z))))))));
		} else {
			VAR_1 = ((double) (((double) (1.0 / ((double) (y - z)))) / ((double) (((double) (t - z)) / x))));
		}
		VAR = VAR_1;
	}
	return VAR;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Target

Original	7.6
Target	8.5
Herbie	1.2

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

Derivation

1. Split input into 3 regimes

2. if (* (- y z) (- t z)) < -1.9863512887713326e259

   1. Initial program 16.4

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

   3. Applied *-un-lft-identity 16.4

      \[\leadsto \frac{\color{blue}{1 \cdot x}}{\left(y - z\right) \cdot \left(t - z\right)}\]

   4. Applied times-frac 0.1

      \[\leadsto \color{blue}{\frac{1}{y - z} \cdot \frac{x}{t - z}}\]
   5. Using strategy rm

   6. Applied clear-num 0.2

      \[\leadsto \frac{1}{y - z} \cdot \color{blue}{\frac{1}{\frac{t - z}{x}}}\]
   7. Using strategy rm

   8. Applied div-inv 0.2

      \[\leadsto \frac{1}{y - z} \cdot \frac{1}{\color{blue}{\left(t - z\right) \cdot \frac{1}{x}}}\]

   if -1.9863512887713326e259 < (* (- y z) (- t z)) < -2.45856805714858837e-202

   1. Initial program 0.2

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

   3. Applied div-inv 0.3

      \[\leadsto \color{blue}{x \cdot \frac{1}{\left(y - z\right) \cdot \left(t - z\right)}}\]

   if -2.45856805714858837e-202 < (* (- y z) (- t z))

   1. Initial program 8.1

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

   3. Applied *-un-lft-identity 8.1

      \[\leadsto \frac{\color{blue}{1 \cdot x}}{\left(y - z\right) \cdot \left(t - z\right)}\]

   4. Applied times-frac 1.7

      \[\leadsto \color{blue}{\frac{1}{y - z} \cdot \frac{x}{t - z}}\]
   5. Using strategy rm

   6. Applied clear-num 1.8

      \[\leadsto \frac{1}{y - z} \cdot \color{blue}{\frac{1}{\frac{t - z}{x}}}\]
   7. Using strategy rm

   8. Applied un-div-inv 1.6

      \[\leadsto \color{blue}{\frac{\frac{1}{y - z}}{\frac{t - z}{x}}}\]
3. Recombined 3 regimes into one program.

4. Final simplification 1.2

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(y - z\right) \cdot \left(t - z\right) \le -1.9863512887713326 \cdot 10^{259}:\\ \;\;\;\;\frac{1}{y - z} \cdot \frac{1}{\left(t - z\right) \cdot \frac{1}{x}}\\ \mathbf{elif}\;\left(y - z\right) \cdot \left(t - z\right) \le -2.45856805714858837 \cdot 10^{-202}:\\ \;\;\;\;x \cdot \frac{1}{\left(y - z\right) \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{1}{y - z}}{\frac{t - z}{x}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020177 
(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))))