Numeric.Histogram:binBounds from Chart-1.5.3

Average Error: 6.5 → 1.3

Time: 2.9s

Precision: binary64

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;x + \frac{\left(y - x\right) \cdot z}{t} \le 2.2660388199885428 \cdot 10^{-191} \lor \neg \left(x + \frac{\left(y - x\right) \cdot z}{t} \le 5.1726733077705543 \cdot 10^{267}\right):\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1}{\frac{t}{\left(y - x\right) \cdot z}}\\ \end{array}\]

C

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

↓

double code(double x, double y, double z, double t) {
	double VAR;
	if (((((double) (x + ((double) (((double) (((double) (y - x)) * z)) / t)))) <= 2.2660388199885428e-191) || !(((double) (x + ((double) (((double) (((double) (y - x)) * z)) / t)))) <= 5.172673307770554e+267))) {
		VAR = ((double) (x + ((double) (((double) (y - x)) / ((double) (t / z))))));
	} else {
		VAR = ((double) (x + ((double) (1.0 / ((double) (t / ((double) (((double) (y - x)) * z))))))));
	}
	return VAR;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Target

Original	6.5
Target	1.9
Herbie	1.3

\[\begin{array}{l} \mathbf{if}\;x \lt -9.0255111955330046 \cdot 10^{-135}:\\ \;\;\;\;x - \frac{z}{t} \cdot \left(x - y\right)\\ \mathbf{elif}\;x \lt 4.2750321637007147 \cdot 10^{-250}:\\ \;\;\;\;x + \frac{y - x}{t} \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \end{array}\]

Derivation

1. Split input into 2 regimes

2. if (+ x (/ (* (- y x) z) t)) < 2.2660388199885428e-191 or 5.1726733077705543e267 < (+ x (/ (* (- y x) z) t))

   1. Initial program 10.3

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

   3. Applied associate-/l* 1.9

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

   if 2.2660388199885428e-191 < (+ x (/ (* (- y x) z) t)) < 5.1726733077705543e267

   1. Initial program 0.3

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

   3. Applied clear-num 0.3

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

4. Final simplification 1.3

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - x\right) \cdot z}{t} \le 2.2660388199885428 \cdot 10^{-191} \lor \neg \left(x + \frac{\left(y - x\right) \cdot z}{t} \le 5.1726733077705543 \cdot 10^{267}\right):\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1}{\frac{t}{\left(y - x\right) \cdot z}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020149 
(FPCore (x y z t)
  :name "Numeric.Histogram:binBounds from Chart-1.5.3"
  :precision binary64

  :herbie-target
  (if (< x -9.025511195533005e-135) (- x (* (/ z t) (- x y))) (if (< x 4.275032163700715e-250) (+ x (* (/ (- y x) t) z)) (+ x (/ (- y x) (/ t z)))))

  (+ x (/ (* (- y x) z) t)))