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

Average Error: 14.4 → 2.6

Time: 1.8s

Precision: 64

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;\frac{\frac{y}{z} \cdot t}{t} \le -2.07328337567161872 \cdot 10^{271}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;\frac{\frac{y}{z} \cdot t}{t} \le -1.6856462603070247 \cdot 10^{-202}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;\frac{\frac{y}{z} \cdot t}{t} \le 2.71166063239338584 \cdot 10^{-80}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \end{array}\]

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) (((double) (((double) (y / z)) * t)) / t)) <= -2.0732833756716187e+271)) {
		VAR = ((double) (((double) (x * y)) / z));
	} else {
		double VAR_1;
		if ((((double) (((double) (((double) (y / z)) * t)) / t)) <= -1.6856462603070247e-202)) {
			VAR_1 = ((double) (x * ((double) (y / z))));
		} else {
			double VAR_2;
			if ((((double) (((double) (((double) (y / z)) * t)) / t)) <= 2.711660632393386e-80)) {
				VAR_2 = ((double) (((double) (x * y)) / z));
			} else {
				VAR_2 = ((double) (x / ((double) (z / y))));
			}
			VAR_1 = VAR_2;
		}
		VAR = VAR_1;
	}
	return VAR;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Derivation

1. Split input into 3 regimes

2. if (/ (* (/ y z) t) t) < -2.0732833756716187e+271 or -1.6856462603070247e-202 < (/ (* (/ y z) t) t) < 2.711660632393386e-80

   1. Initial program 23.4

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

   2. Simplified 9.6

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

   4. Applied associate-*r/ 2.4

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

   if -2.0732833756716187e+271 < (/ (* (/ y z) t) t) < -1.6856462603070247e-202

   1. Initial program 0.6

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

   2. Simplified 0.2

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

   if 2.711660632393386e-80 < (/ (* (/ y z) t) t)

   1. Initial program 13.7

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

   2. Simplified 5.7

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

   4. Applied associate-*r/ 9.3

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

   6. Applied associate-/l* 5.3

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

4. Final simplification 2.6

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\frac{y}{z} \cdot t}{t} \le -2.07328337567161872 \cdot 10^{271}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;\frac{\frac{y}{z} \cdot t}{t} \le -1.6856462603070247 \cdot 10^{-202}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;\frac{\frac{y}{z} \cdot t}{t} \le 2.71166063239338584 \cdot 10^{-80}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020121 
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1"
  :precision binary64
  (* x (/ (* (/ y z) t) t)))