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

Average Error: 14.5 → 2.2

Time: 3.5s

Precision: 64

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;\frac{y}{z} = -inf.0 \lor \neg \left(\frac{y}{z} \le -8.1676513292150364 \cdot 10^{-166} \lor \neg \left(\frac{y}{z} \le 2.1792075432183381 \cdot 10^{-134}\right)\right):\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \end{array}\]

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)) <= -inf.0) || !((((double) (y / z)) <= -8.167651329215036e-166) || !(((double) (y / z)) <= 2.179207543218338e-134)))) {
		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	14.5
Target	1.4
Herbie	2.2

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

Derivation

1. Split input into 2 regimes

2. if (/ y z) < -inf.0 or -8.167651329215036e-166 < (/ y z) < 2.179207543218338e-134

   1. Initial program 19.5

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

   2. Simplified 12.3

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

   4. Applied associate-*r/ 1.4

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

   if -inf.0 < (/ y z) < -8.167651329215036e-166 or 2.179207543218338e-134 < (/ y z)

   1. Initial program 11.6

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

   2. Simplified 2.8

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

4. Final simplification 2.2

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} = -inf.0 \lor \neg \left(\frac{y}{z} \le -8.1676513292150364 \cdot 10^{-166} \lor \neg \left(\frac{y}{z} \le 2.1792075432183381 \cdot 10^{-134}\right)\right):\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \end{array}\]

Reproduce

herbie shell --seed 2020124 
(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)))