Henrywood and Agarwal, Equation (13)

Average Error: 59.0 → 32.1

Time: 12.2s

Precision: binary64

• could not determine a ground truth for program body

  1. c0 = -1.3783876639543642e+308
  2. w = 5671304716357344.0
  3. h = 1.723452079469777e-61
  4. D = -1.918300208831901e-291
  5. d = 1.2426918741383374e+235
  6. M = 4.8225118586145144e+230

Math

\[\frac{c0}{2 \cdot w} \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right)\]

↓

\[\begin{array}{l} \mathbf{if}\;\frac{c0}{2 \cdot w} \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \le -0.0:\\ \;\;\;\;\frac{c0}{2 \cdot w} \cdot \left(M \cdot \frac{M}{\frac{c0}{w \cdot h} \cdot \left(\frac{d}{D} \cdot \frac{d}{D}\right) - \sqrt{\frac{c0}{w \cdot h} \cdot \left(\frac{c0}{w \cdot h} \cdot {\left(\frac{d}{D}\right)}^{4}\right) - M \cdot M}}\right)\\ \mathbf{elif}\;\frac{c0}{2 \cdot w} \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \le +inf.0:\\ \;\;\;\;\frac{c0}{2 \cdot w} \cdot \left(\left(\frac{c0}{w \cdot h} \cdot \left(\frac{d}{D} \cdot \frac{d}{D}\right)\right) \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array}\]

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)))))))))) <= -0.0)) {
		VAR = ((double) (((double) (c0 / ((double) (2.0 * w)))) * ((double) (M * ((double) (M / ((double) (((double) (((double) (c0 / ((double) (w * h)))) * ((double) (((double) (d / D)) * ((double) (d / D)))))) - ((double) sqrt(((double) (((double) (((double) (c0 / ((double) (w * h)))) * ((double) (((double) (c0 / ((double) (w * h)))) * ((double) pow(((double) (d / D)), 4.0)))))) - ((double) (M * M))))))))))))));
	} else {
		double VAR_1;
		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)))))))))) <= +inf.0)) {
			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 3 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))))) < -0.0

   1. Initial program 37.0

      \[\frac{c0}{2 \cdot w} \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right)\]
   2. Using strategy rm

   3. Applied flip-+ 49.9

      \[\leadsto \frac{c0}{2 \cdot w} \cdot \color{blue}{\frac{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M} \cdot \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}}{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}}}\]

   4. Simplified 42.0

      \[\leadsto \frac{c0}{2 \cdot w} \cdot \frac{\color{blue}{M \cdot M}}{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}}\]

   5. Simplified 49.3

      \[\leadsto \frac{c0}{2 \cdot w} \cdot \frac{M \cdot M}{\color{blue}{\frac{c0}{w \cdot h} \cdot \left(\frac{d}{D} \cdot \frac{d}{D}\right) - \sqrt{\frac{c0}{w \cdot h} \cdot \frac{{d}^{4} \cdot c0}{{D}^{4} \cdot \left(w \cdot h\right)} - M \cdot M}}}\]
   6. Using strategy rm

   7. Applied *-un-lft-identity 49.3

      \[\leadsto \frac{c0}{2 \cdot w} \cdot \frac{M \cdot M}{\color{blue}{1 \cdot \left(\frac{c0}{w \cdot h} \cdot \left(\frac{d}{D} \cdot \frac{d}{D}\right) - \sqrt{\frac{c0}{w \cdot h} \cdot \frac{{d}^{4} \cdot c0}{{D}^{4} \cdot \left(w \cdot h\right)} - M \cdot M}\right)}}\]

   8. Applied times-frac 49.0

      \[\leadsto \frac{c0}{2 \cdot w} \cdot \color{blue}{\left(\frac{M}{1} \cdot \frac{M}{\frac{c0}{w \cdot h} \cdot \left(\frac{d}{D} \cdot \frac{d}{D}\right) - \sqrt{\frac{c0}{w \cdot h} \cdot \frac{{d}^{4} \cdot c0}{{D}^{4} \cdot \left(w \cdot h\right)} - M \cdot M}}\right)}\]

   9. Simplified 49.0

      \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\color{blue}{M} \cdot \frac{M}{\frac{c0}{w \cdot h} \cdot \left(\frac{d}{D} \cdot \frac{d}{D}\right) - \sqrt{\frac{c0}{w \cdot h} \cdot \frac{{d}^{4} \cdot c0}{{D}^{4} \cdot \left(w \cdot h\right)} - M \cdot M}}\right)\]

   10. Simplified 41.9

       \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(M \cdot \color{blue}{\frac{M}{\frac{c0}{w \cdot h} \cdot \left(\frac{d}{D} \cdot \frac{d}{D}\right) - \sqrt{\left({\left(\frac{d}{D}\right)}^{4} \cdot \frac{c0}{w \cdot h}\right) \cdot \frac{c0}{w \cdot h} - M \cdot M}}}\right)\]

   if -0.0 < (* (/ 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))))) < +inf.0

   1. Initial program 47.4

      \[\frac{c0}{2 \cdot w} \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right)\]
   2. Using strategy rm

   3. Applied flip-+ 63.1

      \[\leadsto \frac{c0}{2 \cdot w} \cdot \color{blue}{\frac{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M} \cdot \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}}{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}}}\]

   4. Simplified 58.1

      \[\leadsto \frac{c0}{2 \cdot w} \cdot \frac{\color{blue}{M \cdot M}}{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}}\]

   5. Simplified 58.9

      \[\leadsto \frac{c0}{2 \cdot w} \cdot \frac{M \cdot M}{\color{blue}{\frac{c0}{w \cdot h} \cdot \left(\frac{d}{D} \cdot \frac{d}{D}\right) - \sqrt{\frac{c0}{w \cdot h} \cdot \frac{{d}^{4} \cdot c0}{{D}^{4} \cdot \left(w \cdot h\right)} - M \cdot M}}}\]

   6. Taylor expanded around 0 43.3

      \[\leadsto \frac{c0}{2 \cdot w} \cdot \color{blue}{\left(2 \cdot \frac{{d}^{2} \cdot c0}{w \cdot \left({D}^{2} \cdot h\right)}\right)}\]

   7. Simplified 37.1

      \[\leadsto \frac{c0}{2 \cdot w} \cdot \color{blue}{\left(\left(\frac{c0}{w \cdot h} \cdot \left(\frac{d}{D} \cdot \frac{d}{D}\right)\right) \cdot 2\right)}\]

   if +inf.0 < (* (/ 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 64.0

      \[\frac{c0}{2 \cdot w} \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right)\]

   2. Taylor expanded around inf 32.0

      \[\leadsto \frac{c0}{2 \cdot w} \cdot \color{blue}{0}\]
   3. Using strategy rm

   4. Applied mul0-rgt 29.8

      \[\leadsto \color{blue}{0}\]
3. Recombined 3 regimes into one program.

4. Final simplification 32.1

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{c0}{2 \cdot w} \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \le -0.0:\\ \;\;\;\;\frac{c0}{2 \cdot w} \cdot \left(M \cdot \frac{M}{\frac{c0}{w \cdot h} \cdot \left(\frac{d}{D} \cdot \frac{d}{D}\right) - \sqrt{\frac{c0}{w \cdot h} \cdot \left(\frac{c0}{w \cdot h} \cdot {\left(\frac{d}{D}\right)}^{4}\right) - M \cdot M}}\right)\\ \mathbf{elif}\;\frac{c0}{2 \cdot w} \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \le +inf.0:\\ \;\;\;\;\frac{c0}{2 \cdot w} \cdot \left(\left(\frac{c0}{w \cdot h} \cdot \left(\frac{d}{D} \cdot \frac{d}{D}\right)\right) \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array}\]

Reproduce

herbie shell --seed 2020185 
(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))))))