Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1, B

Average Error: 14.3 → 0.7

Time: 3.4s

Precision: binary64

Math

\[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]

↓

\[\begin{array}{l} \mathbf{if}\;\frac{y}{z} \le -5.4533453818113496 \cdot 10^{220} \lor \neg \left(\frac{y}{z} \le -1.67721356004383514 \cdot 10^{-118} \lor \neg \left(\frac{y}{z} \le 3.6179763990261918 \cdot 10^{-276} \lor \neg \left(\frac{y}{z} \le 5.2685120422095201 \cdot 10^{167}\right)\right)\right):\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \end{array}\]

C

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

↓

double code(double x, double y, double z, double t) {
	double VAR;
	if (((((double) (y / z)) <= -5.45334538181135e+220) || !((((double) (y / z)) <= -1.6772135600438351e-118) || !((((double) (y / z)) <= 3.617976399026192e-276) || !(((double) (y / z)) <= 5.26851204220952e+167))))) {
		VAR = ((double) (((double) (x * y)) / z));
	} else {
		VAR = ((double) (x * ((double) (y / z))));
	}
	return VAR;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Target

Original	14.3
Target	1.4
Herbie	0.7

\[\begin{array}{l} \mathbf{if}\;\frac{\frac{y}{z} \cdot t}{t} \lt -1.20672205123045005 \cdot 10^{245}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;\frac{\frac{y}{z} \cdot t}{t} \lt -5.90752223693390633 \cdot 10^{-275}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;\frac{\frac{y}{z} \cdot t}{t} \lt 5.65895442315341522 \cdot 10^{-65}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;\frac{\frac{y}{z} \cdot t}{t} \lt 2.0087180502407133 \cdot 10^{217}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \end{array}\]

Derivation

1. Split input into 2 regimes

2. if (/ y z) < -5.4533453818113496e220 or -1.67721356004383514e-118 < (/ y z) < 3.6179763990261918e-276 or 5.2685120422095201e167 < (/ y z)

   1. Initial program 23.4

      \[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]

   2. Simplified 14.7

      \[\leadsto \color{blue}{x \cdot \frac{y}{z}}\]
   3. Using strategy rm

   4. Applied associate-*r/ 1.5

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

   if -5.4533453818113496e220 < (/ y z) < -1.67721356004383514e-118 or 3.6179763990261918e-276 < (/ y z) < 5.2685120422095201e167

   1. Initial program 8.0

      \[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]

   2. Simplified 0.2

      \[\leadsto \color{blue}{x \cdot \frac{y}{z}}\]
3. Recombined 2 regimes into one program.

4. Final simplification 0.7

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} \le -5.4533453818113496 \cdot 10^{220} \lor \neg \left(\frac{y}{z} \le -1.67721356004383514 \cdot 10^{-118} \lor \neg \left(\frac{y}{z} \le 3.6179763990261918 \cdot 10^{-276} \lor \neg \left(\frac{y}{z} \le 5.2685120422095201 \cdot 10^{167}\right)\right)\right):\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \end{array}\]

Reproduce

herbie shell --seed 2020150 
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1, B"
  :precision binary64

  :herbie-target
  (if (< (/ (* (/ y z) t) t) -1.20672205123045e+245) (/ y (/ z x)) (if (< (/ (* (/ y z) t) t) -5.907522236933906e-275) (* x (/ y z)) (if (< (/ (* (/ y z) t) t) 5.658954423153415e-65) (/ y (/ z x)) (if (< (/ (* (/ y z) t) t) 2.0087180502407133e+217) (* x (/ y z)) (/ (* y x) z)))))

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