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

Average Error: 14.7 → 0.6

Time: 4.3s

Precision: binary64

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;\frac{y}{z} \leq -2.802544562542358 \cdot 10^{+152} \lor \neg \left(\frac{y}{z} \leq -2.4333236028189087 \cdot 10^{-202} \lor \neg \left(\frac{y}{z} \leq 5.271680016281766 \cdot 10^{-176}\right) \land \frac{y}{z} \leq 6.461351523313114 \cdot 10^{+157}\right):\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \end{array}\]

FPCore

(FPCore (x y z t) :precision binary64 (* x (/ (* (/ y z) t) t)))

↓

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ y z) -2.802544562542358e+152)
         (not
          (or (<= (/ y z) -2.4333236028189087e-202)
              (and (not (<= (/ y z) 5.271680016281766e-176))
                   (<= (/ y z) 6.461351523313114e+157)))))
   (/ (* y x) z)
   (* (/ y z) x)))

C

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

↓

double code(double x, double y, double z, double t) {
	double VAR;
	if ((((y / z) <= -2.802544562542358e+152) || !(((y / z) <= -2.4333236028189087e-202) || (!((y / z) <= 5.271680016281766e-176) && ((y / z) <= 6.461351523313114e+157))))) {
		VAR = (((double) (y * x)) / z);
	} else {
		VAR = ((double) ((y / z) * x));
	}
	return VAR;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Target

Original	14.7
Target	1.5
Herbie	0.6

\[\begin{array}{l} \mathbf{if}\;\frac{\frac{y}{z} \cdot t}{t} < -1.20672205123045 \cdot 10^{+245}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;\frac{\frac{y}{z} \cdot t}{t} < -5.907522236933906 \cdot 10^{-275}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;\frac{\frac{y}{z} \cdot t}{t} < 5.658954423153415 \cdot 10^{-65}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;\frac{\frac{y}{z} \cdot t}{t} < 2.0087180502407133 \cdot 10^{+217}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \end{array}\]

Derivation

1. Split input into 2 regimes

2. if (/ y z) < -2.80254456254235802e152 or -2.4333236028189087e-202 < (/ y z) < 5.27168001628176604e-176 or 6.4613515233131144e157 < (/ y z)

   1. Initial program 23.4

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

   2. Simplified 13.5

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

   4. Applied associate-*r/ 1.0

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

   if -2.80254456254235802e152 < (/ y z) < -2.4333236028189087e-202 or 5.27168001628176604e-176 < (/ y z) < 6.4613515233131144e157

   1. Initial program 7.4

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

   2. Simplified 0.2

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

4. Final simplification 0.6

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} \leq -2.802544562542358 \cdot 10^{+152} \lor \neg \left(\frac{y}{z} \leq -2.4333236028189087 \cdot 10^{-202} \lor \neg \left(\frac{y}{z} \leq 5.271680016281766 \cdot 10^{-176}\right) \land \frac{y}{z} \leq 6.461351523313114 \cdot 10^{+157}\right):\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \end{array}\]

Reproduce

herbie shell --seed 2020198 
(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)))