Henrywood and Agarwal, Equation (13)

Average Error: 59.3 → 32.1

Time: 12.1s

Precision: binary64

• could not determine a ground truth for program body

  1. c0 = 1.2797229701533991e-84
  2. w = -4.889549147089551e-144
  3. h = 2.962836944315523e-261
  4. D = -1.405518446341921e-204
  5. d = -1.5262546079924936e+258
  6. M = -1.9865151292468643e+29

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 ((((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)))))))))) <= 1.864309660880015e+93)) {
		VAR = ((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 = 0.0;
	}
	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 (* (/ 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))))) < 1.86430966088001509e93

   1. Initial program 36.0

      \[\]
   2. Using strategy rm

   3. Applied flip-+ 52.6

      \[\leadsto \]

   4. Simplified 45.5

      \[\leadsto \]

   5. Simplified 51.5

      \[\leadsto \]

   6. Taylor expanded around 0 41.8

      \[\leadsto \]

   7. Simplified 38.7

      \[\leadsto \]

   if 1.86430966088001509e93 < (* (/ 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)))))

   1. Initial program 63.5

      \[\]

   2. Taylor expanded around inf 33.2

      \[\leadsto \]
   3. Using strategy rm

   4. Applied mul0-rgt 30.9

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

4. Final simplification 32.1

   \[\leadsto \]

Reproduce

herbie shell --seed 2020192 
(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))))))