Henrywood and Agarwal, Equation (13)

Average Error: 59.6 → 32.3

Time: 5.3m

Precision: 64

• could not determine a ground truth for program body

  1. c0 = -1.0335410165725188e+93
  2. w = 1.4942319272395318e-18
  3. h = 2.054687936946674e-171
  4. D = 3.26847192345922e-304
  5. d = -2.8601668761643326e+241
  6. M = 1.4755203203888105e-296

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;\left(\frac{\left(d \cdot d\right) \cdot c0}{\left(D \cdot D\right) \cdot \left(w \cdot h\right)} + \sqrt{\frac{\left(d \cdot d\right) \cdot c0}{\left(D \cdot D\right) \cdot \left(w \cdot h\right)} \cdot \frac{\left(d \cdot d\right) \cdot c0}{\left(D \cdot D\right) \cdot \left(w \cdot h\right)} - M \cdot M}\right) \cdot \frac{c0}{w \cdot 2} \le 5.227488411028050344845658730793831779279 \cdot 10^{210}:\\ \;\;\;\;\frac{e^{\log \left(\sqrt{\frac{\frac{c0}{w} \cdot \left(\frac{d}{D} \cdot \frac{d}{D}\right)}{h} \cdot \frac{\frac{c0}{w} \cdot \left(\frac{d}{D} \cdot \frac{d}{D}\right)}{h} - M \cdot M} + \frac{\frac{c0}{w} \cdot \left(\frac{d}{D} \cdot \frac{d}{D}\right)}{h}\right)}}{2} \cdot \frac{c0}{w}\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array}\]

C

double f(double c0, double w, double h, double D, double d, double M) {
        double r5593626 = c0;
        double r5593627 = 2.0;
        double r5593628 = w;
        double r5593629 = r5593627 * r5593628;
        double r5593630 = r5593626 / r5593629;
        double r5593631 = d;
        double r5593632 = r5593631 * r5593631;
        double r5593633 = r5593626 * r5593632;
        double r5593634 = h;
        double r5593635 = r5593628 * r5593634;
        double r5593636 = D;
        double r5593637 = r5593636 * r5593636;
        double r5593638 = r5593635 * r5593637;
        double r5593639 = r5593633 / r5593638;
        double r5593640 = r5593639 * r5593639;
        double r5593641 = M;
        double r5593642 = r5593641 * r5593641;
        double r5593643 = r5593640 - r5593642;
        double r5593644 = sqrt(r5593643);
        double r5593645 = r5593639 + r5593644;
        double r5593646 = r5593630 * r5593645;
        return r5593646;
}

↓

double f(double c0, double w, double h, double D, double d, double M) {
        double r5593647 = d;
        double r5593648 = r5593647 * r5593647;
        double r5593649 = c0;
        double r5593650 = r5593648 * r5593649;
        double r5593651 = D;
        double r5593652 = r5593651 * r5593651;
        double r5593653 = w;
        double r5593654 = h;
        double r5593655 = r5593653 * r5593654;
        double r5593656 = r5593652 * r5593655;
        double r5593657 = r5593650 / r5593656;
        double r5593658 = r5593657 * r5593657;
        double r5593659 = M;
        double r5593660 = r5593659 * r5593659;
        double r5593661 = r5593658 - r5593660;
        double r5593662 = sqrt(r5593661);
        double r5593663 = r5593657 + r5593662;
        double r5593664 = 2.0;
        double r5593665 = r5593653 * r5593664;
        double r5593666 = r5593649 / r5593665;
        double r5593667 = r5593663 * r5593666;
        double r5593668 = 5.2274884110280503e+210;
        bool r5593669 = r5593667 <= r5593668;
        double r5593670 = r5593649 / r5593653;
        double r5593671 = r5593647 / r5593651;
        double r5593672 = r5593671 * r5593671;
        double r5593673 = r5593670 * r5593672;
        double r5593674 = r5593673 / r5593654;
        double r5593675 = r5593674 * r5593674;
        double r5593676 = r5593675 - r5593660;
        double r5593677 = sqrt(r5593676);
        double r5593678 = r5593677 + r5593674;
        double r5593679 = log(r5593678);
        double r5593680 = exp(r5593679);
        double r5593681 = r5593680 / r5593664;
        double r5593682 = r5593681 * r5593670;
        double r5593683 = 0.0;
        double r5593684 = r5593669 ? r5593682 : r5593683;
        return r5593684;
}

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))))) < 5.2274884110280503e+210

   1. Initial program 36.2

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

   2. Simplified 35.2

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

   4. Applied add-exp-log 37.2

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

   if 5.2274884110280503e+210 < (* (/ 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 63.9

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

   2. Simplified 56.5

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

   3. Taylor expanded around inf 33.4

      \[\leadsto \frac{c0}{w} \cdot \frac{\color{blue}{0}}{2}\]

   4. Taylor expanded around 0 31.4

      \[\leadsto \color{blue}{0}\]
3. Recombined 2 regimes into one program.

4. Final simplification 32.3

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\frac{\left(d \cdot d\right) \cdot c0}{\left(D \cdot D\right) \cdot \left(w \cdot h\right)} + \sqrt{\frac{\left(d \cdot d\right) \cdot c0}{\left(D \cdot D\right) \cdot \left(w \cdot h\right)} \cdot \frac{\left(d \cdot d\right) \cdot c0}{\left(D \cdot D\right) \cdot \left(w \cdot h\right)} - M \cdot M}\right) \cdot \frac{c0}{w \cdot 2} \le 5.227488411028050344845658730793831779279 \cdot 10^{210}:\\ \;\;\;\;\frac{e^{\log \left(\sqrt{\frac{\frac{c0}{w} \cdot \left(\frac{d}{D} \cdot \frac{d}{D}\right)}{h} \cdot \frac{\frac{c0}{w} \cdot \left(\frac{d}{D} \cdot \frac{d}{D}\right)}{h} - M \cdot M} + \frac{\frac{c0}{w} \cdot \left(\frac{d}{D} \cdot \frac{d}{D}\right)}{h}\right)}}{2} \cdot \frac{c0}{w}\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array}\]

Reproduce

herbie shell --seed 2019200 
(FPCore (c0 w h D d M)
  :name "Henrywood and Agarwal, Equation (13)"
  (* (/ 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))))))