fabs fraction 1

Average Error: 1.7 → 0.1

Time: 3.5s

Precision: binary64

Math

\[\]

↓

\[\]

C

double code(double x, double y, double z) {
	return ((double) fabs(((double) (((double) (((double) (x + 4.0)) / y)) - ((double) (((double) (x / y)) * z))))));
}

↓

double code(double x, double y, double z) {
	double VAR;
	if ((((double) fabs(((double) (((double) (((double) (x + 4.0)) / y)) - ((double) (((double) (x / y)) * z)))))) <= 2483.9734297796313)) {
		VAR = ((double) fabs(((double) (((double) (((double) (x + 4.0)) / y)) - ((double) (x * ((double) (z / y))))))));
	} else {
		VAR = ((double) fabs(((double) (((double) (((double) (x + 4.0)) / y)) - ((double) (((double) (x / y)) * z))))));
	}
	return VAR;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Derivation

1. Split input into 2 regimes

2. if (fabs (- (/ (+ x 4.0) y) (* (/ x y) z))) < 2483.9734297796313

   1. Initial program 4.1

      \[\]

   2. Simplified 0.1

      \[\leadsto \]
   3. Using strategy rm

   4. Applied associate-+r- 0.1

      \[\leadsto \]

   5. Applied div-sub 0.1

      \[\leadsto \]

   6. Simplified 0.1

      \[\leadsto \]

   if 2483.9734297796313 < (fabs (- (/ (+ x 4.0) y) (* (/ x y) z)))

   1. Initial program 0.1

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

4. Final simplification 0.1

   \[\leadsto \]

Reproduce

herbie shell --seed 2020191 
(FPCore (x y z)
  :name "fabs fraction 1"
  :precision binary64
  (fabs (- (/ (+ x 4.0) y) (* (/ x y) z))))