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

Average Error: 8.0 → 3.1

Time: 3.8s

Precision: binary64

Math

\[\]

↓

\[\]

C

double code(double x, double y, double z) {
	return ((double) (((double) (x + y)) / ((double) (1.0 - ((double) (y / z))))));
}

↓

double code(double x, double y, double z) {
	double VAR;
	if ((z <= -1.9474750866386186e+37)) {
		VAR = ((double) (((double) (x + y)) * ((double) (1.0 / ((double) (1.0 - ((double) (y / z))))))));
	} else {
		double VAR_1;
		if ((z <= 2.4081817776574713e-267)) {
			VAR_1 = ((double) (1.0 / ((double) (((double) (1.0 / ((double) (x + y)))) - ((double) (y / ((double) (z * ((double) (x + y))))))))));
		} else {
			double VAR_2;
			if ((z <= 4.6323173730091233e-219)) {
				VAR_2 = ((double) (1.0 / ((double) (((double) (1.0 - ((double) (y / z)))) * ((double) (1.0 / ((double) (x + y))))))));
			} else {
				double VAR_3;
				if ((z <= 1.0392004029497865e-35)) {
					VAR_3 = ((double) (1.0 / ((double) (((double) (1.0 / ((double) (x + y)))) - ((double) (y / ((double) (z * ((double) (x + y))))))))));
				} else {
					VAR_3 = ((double) (((double) (x + y)) * ((double) (1.0 / ((double) (1.0 - ((double) (y / z))))))));
				}
				VAR_2 = VAR_3;
			}
			VAR_1 = VAR_2;
		}
		VAR = VAR_1;
	}
	return VAR;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original	8.0
Target	4.1
Herbie	3.1

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Derivation

1. Split input into 3 regimes

2. if z < -1.94747508663861859e37 or 1.03920040294978652e-35 < z

   1. Initial program 0.1

      \[\]
   2. Using strategy rm

   3. Applied div-inv 0.2

      \[\leadsto \]

   if -1.94747508663861859e37 < z < 2.4081817776574713e-267 or 4.63231737300912332e-219 < z < 1.03920040294978652e-35

   1. Initial program 15.2

      \[\]
   2. Using strategy rm

   3. Applied clear-num 15.3

      \[\leadsto \]
   4. Using strategy rm

   5. Applied div-sub 15.3

      \[\leadsto \]

   6. Simplified 15.3

      \[\leadsto \]

   7. Simplified 4.8

      \[\leadsto \]

   if 2.4081817776574713e-267 < z < 4.63231737300912332e-219

   1. Initial program 22.1

      \[\]
   2. Using strategy rm

   3. Applied clear-num 22.2

      \[\leadsto \]
   4. Using strategy rm

   5. Applied div-inv 22.2

      \[\leadsto \]

   6. Simplified 22.2

      \[\leadsto \]
3. Recombined 3 regimes into one program.

4. Final simplification 3.1

   \[\leadsto \]

Reproduce

herbie shell --seed 2020180 
(FPCore (x y z)
  :name "Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1, A"
  :precision binary64

  :herbie-target
  (if (< y -3.7429310762689856e+171) (* (/ (+ y x) (neg y)) z) (if (< y 3.5534662456086734e+168) (/ (+ x y) (- 1.0 (/ y z))) (* (/ (+ y x) (neg y)) z)))

  (/ (+ x y) (- 1.0 (/ y z))))