Linear.Projection:perspective from linear-1.19.1.3, B

Average Error: 15.3 → 0.5

Time: 1.8s

Precision: binary64

Math

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↓

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C

double code(double x, double y) {
	return ((double) (((double) (((double) (x * 2.0)) * y)) / ((double) (x - y))));
}

↓

double code(double x, double y) {
	double VAR;
	if (((((double) (((double) (((double) (x * 2.0)) * y)) / ((double) (x - y)))) <= -1.1864643416555227e-17) || !((((double) (((double) (((double) (x * 2.0)) * y)) / ((double) (x - y)))) <= -3.468798690241185e-306) || (!(((double) (((double) (((double) (x * 2.0)) * y)) / ((double) (x - y)))) <= -0.0) && (((double) (((double) (((double) (x * 2.0)) * y)) / ((double) (x - y)))) <= 8.057782803603935e-39))))) {
		VAR = ((double) (x * ((double) (2.0 * ((double) (y / ((double) (x - y))))))));
	} else {
		VAR = ((double) (((double) (((double) (x * 2.0)) * y)) / ((double) (x - y))));
	}
	return VAR;
}

Error

Bits error versus x

Bits error versus y

Target

Original	15.3
Target	0.4
Herbie	0.5

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Derivation

1. Split input into 2 regimes

2. if (/ (* (* x 2.0) y) (- x y)) < -1.1864643416555227e-17 or -3.46879869024118526e-306 < (/ (* (* x 2.0) y) (- x y)) < -0.0 or 8.05778280360393456e-39 < (/ (* (* x 2.0) y) (- x y))

   1. Initial program 35.7

      \[\]

   2. Simplified 0.3

      \[\leadsto \]

   if -1.1864643416555227e-17 < (/ (* (* x 2.0) y) (- x y)) < -3.46879869024118526e-306 or -0.0 < (/ (* (* x 2.0) y) (- x y)) < 8.05778280360393456e-39

   1. Initial program 0.6

      \[\]
3. Recombined 2 regimes into one program.

4. Final simplification 0.5

   \[\leadsto \]

Reproduce

herbie shell --seed 2020190 
(FPCore (x y)
  :name "Linear.Projection:perspective from linear-1.19.1.3, B"
  :precision binary64

  :herbie-target
  (if (< x -1.7210442634149447e+81) (* (/ (* 2.0 x) (- x y)) y) (if (< x 8.364504563556443e+16) (/ (* x 2.0) (/ (- x y) y)) (* (/ (* 2.0 x) (- x y)) y)))

  (/ (* (* x 2.0) y) (- x y)))