Henrywood and Agarwal, Equation (13)

Average Error: 59.1 → 31.5

Time: 11.5s

Precision: binary64

• could not determine a ground truth for program body

  1. c0 = -2.891223160177993e+278
  2. w = 1.6057862524760164e+39
  3. h = 3.944645128782883e-117
  4. D = 1.6221071114823305e-301
  5. d = 5.692199602903769e+162
  6. M = 2.989365281891602e+56

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;\frac{c0}{2 \cdot w} \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) = -inf.0:\\ \;\;\;\;0\\ \mathbf{elif}\;\frac{c0}{2 \cdot w} \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \le 1.7098342510616604 \cdot 10^{218}:\\ \;\;\;\;\frac{c0}{2 \cdot w} \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right)\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array}\]

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)))))))))) <= -inf.0)) {
		VAR = 0.0;
	} 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)))))))))) <= 1.7098342510616604e+218)) {
			VAR_1 = ((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))))))))));
		} 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 (* (/ 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 or 1.7098342510616604e218 < (* (/ 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 63.8

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

   2. Taylor expanded around inf 35.0

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

   4. Applied mul0 32.8

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

   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))))) < 1.7098342510616604e218

   1. Initial program 21.1

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

4. Final simplification 31.5

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{c0}{2 \cdot w} \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) = -inf.0:\\ \;\;\;\;0\\ \mathbf{elif}\;\frac{c0}{2 \cdot w} \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \le 1.7098342510616604 \cdot 10^{218}:\\ \;\;\;\;\frac{c0}{2 \cdot w} \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right)\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array}\]

Reproduce

herbie shell --seed 2020147 
(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))))))