Henrywood and Agarwal, Equation (13)

Average Error: 59.7 → 31.5

Time: 17.8s

Precision: binary64

• could not determine a ground truth for program body

  1. c0 = -2.4549448851952512e+263
  2. w = -5.459407539174695e-306
  3. h = -1.4241350794010758e+21
  4. D = -5.385363393795738e-149
  5. d = 7.99503187581072e-13
  6. M = 1.0527116698312733e-13

Math

\[\]

↓

\[\]

C

double code(double c0, double w, double h, double D, double d, double M) {
	return ((double) (((double) (c0 / ((double) (2.0 * w)))) * ((double) (((double) (((double) (c0 * ((double) (d * d)))) / ((double) (((double) (w * h)) * ((double) (D * D)))))) + ((double) sqrt(((double) (((double) (((double) (((double) (c0 * ((double) (d * d)))) / ((double) (((double) (w * h)) * ((double) (D * D)))))) * ((double) (((double) (c0 * ((double) (d * d)))) / ((double) (((double) (w * h)) * ((double) (D * D)))))))) - ((double) (M * M))))))))));
}

↓

double code(double c0, double w, double h, double D, double d, double M) {
	double VAR;
	if ((d <= -5.0948708970042e-209)) {
		VAR = 0.0;
	} else {
		double VAR_1;
		if ((d <= 1.5861563218221685e-202)) {
			VAR_1 = ((double) (((double) (c0 / ((double) (2.0 * w)))) * ((double) (((double) (((double) (c0 / ((double) (w * h)))) * ((double) (((double) (d / D)) * ((double) (d / D)))))) * 2.0))));
		} else {
			VAR_1 = 0.0;
		}
		VAR = VAR_1;
	}
	return VAR;
}

Error

Bits error versus c0

Bits error versus w

Bits error versus h

Bits error versus D

Bits error versus d

Bits error versus M

Derivation

1. Split input into 2 regimes

2. if d < -5.09487089700420031e-209 or 1.5861563218221685e-202 < d

   1. Initial program 59.6

      \[\]

   2. Taylor expanded around inf 34.7

      \[\leadsto \]
   3. Using strategy rm

   4. Applied mul0-rgt 30.6

      \[\leadsto \]

   if -5.09487089700420031e-209 < d < 1.5861563218221685e-202

   1. Initial program 63.1

      \[\]
   2. Using strategy rm

   3. Applied flip-+ 64.0

      \[\leadsto \]

   4. Simplified 64.0

      \[\leadsto \]

   5. Simplified 63.9

      \[\leadsto \]

   6. Taylor expanded around 0 63.6

      \[\leadsto \]

   7. Simplified 47.1

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

4. Final simplification 31.5

   \[\leadsto \]

Reproduce

herbie shell --seed 2020191 
(FPCore (c0 w h D d M)
  :name "Henrywood and Agarwal, Equation (13)"
  :precision binary64
  (* (/ c0 (* 2.0 w)) (+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))))