Henrywood and Agarwal, Equation (13)

Average Error: 59.4 → 34.1

Time: 12.0s

Precision: binary64

• could not determine a ground truth for program body

  1. c0 = 3.306879361733938e+248
  2. w = -3.316393714297958e-184
  3. h = 1.6303906359766505e-192
  4. D = 3.5658310453467295e-220
  5. d = 5.85489784208026e-38
  6. M = 2.850505817514757e+188

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;d \leq -1.175953897003222 \cdot 10^{-95}:\\ \;\;\;\;0\\ \mathbf{elif}\;d \leq -4.0770522499926086 \cdot 10^{-200}:\\ \;\;\;\;\frac{c0}{2 \cdot w} \cdot \left(\sqrt{\frac{c0}{w \cdot h} \cdot \left(\frac{d}{D} \cdot \frac{d}{D}\right) + \sqrt{\left(\frac{c0}{w \cdot h} \cdot \left(\frac{d}{D} \cdot \frac{d}{D}\right)\right) \cdot \left(\frac{c0}{w \cdot h} \cdot \left(\frac{d}{D} \cdot \frac{d}{D}\right)\right) - M \cdot M}} \cdot \sqrt{\frac{c0}{w \cdot h} \cdot \left(\frac{d}{D} \cdot \frac{d}{D}\right) + \sqrt{\left(\frac{c0}{w \cdot h} \cdot \left(\frac{d}{D} \cdot \frac{d}{D}\right)\right) \cdot \left(\frac{c0}{w \cdot h} \cdot \left(\frac{d}{D} \cdot \frac{d}{D}\right)\right) - M \cdot M}}\right)\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array}\]

C

double code(double c0, double w, double h, double D, double d, double M) {
	return ((double) ((c0 / ((double) (2.0 * w))) * ((double) ((((double) (c0 * ((double) (d * d)))) / ((double) (((double) (w * h)) * ((double) (D * D))))) + ((double) sqrt(((double) (((double) ((((double) (c0 * ((double) (d * d)))) / ((double) (((double) (w * h)) * ((double) (D * D))))) * (((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 <= -1.175953897003222e-95)) {
		VAR = 0.0;
	} else {
		double VAR_1;
		if ((d <= -4.0770522499926086e-200)) {
			VAR_1 = ((double) ((c0 / ((double) (2.0 * w))) * ((double) (((double) sqrt(((double) (((double) ((c0 / ((double) (w * h))) * ((double) ((d / D) * (d / D))))) + ((double) sqrt(((double) (((double) (((double) ((c0 / ((double) (w * h))) * ((double) ((d / D) * (d / D))))) * ((double) ((c0 / ((double) (w * h))) * ((double) ((d / D) * (d / D))))))) - ((double) (M * M)))))))))) * ((double) sqrt(((double) (((double) ((c0 / ((double) (w * h))) * ((double) ((d / D) * (d / D))))) + ((double) sqrt(((double) (((double) (((double) ((c0 / ((double) (w * h))) * ((double) ((d / D) * (d / D))))) * ((double) ((c0 / ((double) (w * h))) * ((double) ((d / D) * (d / D))))))) - ((double) (M * M))))))))))))));
		} 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 < -1.17595389700322196e-95 or -4.0770522499926086e-200 < d

   1. Initial program 59.4

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

   2. Taylor expanded around inf 35.2

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

   4. Applied mul0-rgt 33.4

      \[\leadsto \color{blue}{0}\]

   if -1.17595389700322196e-95 < d < -4.0770522499926086e-200

   1. Initial program 59.7

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

   3. Applied add-sqr-sqrt 59.8

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

   4. Simplified 60.6

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

   5. Simplified 48.1

      \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\sqrt{\frac{c0}{w \cdot h} \cdot \left(\frac{d}{D} \cdot \frac{d}{D}\right) + \sqrt{\left(\frac{c0}{w \cdot h} \cdot \left(\frac{d}{D} \cdot \frac{d}{D}\right)\right) \cdot \left(\frac{c0}{w \cdot h} \cdot \left(\frac{d}{D} \cdot \frac{d}{D}\right)\right) - M \cdot M}} \cdot \color{blue}{\sqrt{\frac{c0}{w \cdot h} \cdot \left(\frac{d}{D} \cdot \frac{d}{D}\right) + \sqrt{\left(\frac{c0}{w \cdot h} \cdot \left(\frac{d}{D} \cdot \frac{d}{D}\right)\right) \cdot \left(\frac{c0}{w \cdot h} \cdot \left(\frac{d}{D} \cdot \frac{d}{D}\right)\right) - M \cdot M}}}\right)\]
3. Recombined 2 regimes into one program.

4. Final simplification 34.1

   \[\leadsto \begin{array}{l} \mathbf{if}\;d \leq -1.175953897003222 \cdot 10^{-95}:\\ \;\;\;\;0\\ \mathbf{elif}\;d \leq -4.0770522499926086 \cdot 10^{-200}:\\ \;\;\;\;\frac{c0}{2 \cdot w} \cdot \left(\sqrt{\frac{c0}{w \cdot h} \cdot \left(\frac{d}{D} \cdot \frac{d}{D}\right) + \sqrt{\left(\frac{c0}{w \cdot h} \cdot \left(\frac{d}{D} \cdot \frac{d}{D}\right)\right) \cdot \left(\frac{c0}{w \cdot h} \cdot \left(\frac{d}{D} \cdot \frac{d}{D}\right)\right) - M \cdot M}} \cdot \sqrt{\frac{c0}{w \cdot h} \cdot \left(\frac{d}{D} \cdot \frac{d}{D}\right) + \sqrt{\left(\frac{c0}{w \cdot h} \cdot \left(\frac{d}{D} \cdot \frac{d}{D}\right)\right) \cdot \left(\frac{c0}{w \cdot h} \cdot \left(\frac{d}{D} \cdot \frac{d}{D}\right)\right) - M \cdot M}}\right)\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array}\]

Reproduce

herbie shell --seed 2020196 
(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))))))