Henrywood and Agarwal, Equation (13)

Average Error: 57.9 → 31.3

Time: 47.9s

Precision: 64

• could not determine a ground truth for program body

  1. c0 = 2.1349606945297384e+240
  2. w = 1.2254588308927825e-216
  3. h = -5.879678403871345e-165
  4. D = -4.041865292113949e+35
  5. d = -2.1293592977956366e+226
  6. M = 15.597049771107491

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;\frac{c0}{w \cdot 2} \cdot \left(\sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(D \cdot D\right) \cdot \left(w \cdot h\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(D \cdot D\right) \cdot \left(w \cdot h\right)} - M \cdot M} + \frac{c0 \cdot \left(d \cdot d\right)}{\left(D \cdot D\right) \cdot \left(w \cdot h\right)}\right) \le 3.2739293852189127 \cdot 10^{+299}:\\ \;\;\;\;\frac{c0}{w \cdot 2} \cdot \left(\sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(D \cdot D\right) \cdot \left(w \cdot h\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(D \cdot D\right) \cdot \left(w \cdot h\right)} - M \cdot M} + \frac{c0 \cdot \left(d \cdot d\right)}{\left(D \cdot D\right) \cdot \left(w \cdot h\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array}\]

C

double f(double c0, double w, double h, double D, double d, double M) {
        double r2837708 = c0;
        double r2837709 = 2.0;
        double r2837710 = w;
        double r2837711 = r2837709 * r2837710;
        double r2837712 = r2837708 / r2837711;
        double r2837713 = d;
        double r2837714 = r2837713 * r2837713;
        double r2837715 = r2837708 * r2837714;
        double r2837716 = h;
        double r2837717 = r2837710 * r2837716;
        double r2837718 = D;
        double r2837719 = r2837718 * r2837718;
        double r2837720 = r2837717 * r2837719;
        double r2837721 = r2837715 / r2837720;
        double r2837722 = r2837721 * r2837721;
        double r2837723 = M;
        double r2837724 = r2837723 * r2837723;
        double r2837725 = r2837722 - r2837724;
        double r2837726 = sqrt(r2837725);
        double r2837727 = r2837721 + r2837726;
        double r2837728 = r2837712 * r2837727;
        return r2837728;
}

↓

double f(double c0, double w, double h, double D, double d, double M) {
        double r2837729 = c0;
        double r2837730 = w;
        double r2837731 = 2.0;
        double r2837732 = r2837730 * r2837731;
        double r2837733 = r2837729 / r2837732;
        double r2837734 = d;
        double r2837735 = r2837734 * r2837734;
        double r2837736 = r2837729 * r2837735;
        double r2837737 = D;
        double r2837738 = r2837737 * r2837737;
        double r2837739 = h;
        double r2837740 = r2837730 * r2837739;
        double r2837741 = r2837738 * r2837740;
        double r2837742 = r2837736 / r2837741;
        double r2837743 = r2837742 * r2837742;
        double r2837744 = M;
        double r2837745 = r2837744 * r2837744;
        double r2837746 = r2837743 - r2837745;
        double r2837747 = sqrt(r2837746);
        double r2837748 = r2837747 + r2837742;
        double r2837749 = r2837733 * r2837748;
        double r2837750 = 3.2739293852189127e+299;
        bool r2837751 = r2837749 <= r2837750;
        double r2837752 = 0.0;
        double r2837753 = r2837751 ? r2837749 : r2837752;
        return r2837753;
}

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 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))))) < 3.2739293852189127e+299

   1. Initial program 33.2

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

   if 3.2739293852189127e+299 < (* (/ c0 (* 2 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 62.7

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

   2. Simplified 55.5

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

   3. Taylor expanded around -inf 33.2

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

   4. Taylor expanded around inf 31.0

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

4. Final simplification 31.3

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{c0}{w \cdot 2} \cdot \left(\sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(D \cdot D\right) \cdot \left(w \cdot h\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(D \cdot D\right) \cdot \left(w \cdot h\right)} - M \cdot M} + \frac{c0 \cdot \left(d \cdot d\right)}{\left(D \cdot D\right) \cdot \left(w \cdot h\right)}\right) \le 3.2739293852189127 \cdot 10^{+299}:\\ \;\;\;\;\frac{c0}{w \cdot 2} \cdot \left(\sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(D \cdot D\right) \cdot \left(w \cdot h\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(D \cdot D\right) \cdot \left(w \cdot h\right)} - M \cdot M} + \frac{c0 \cdot \left(d \cdot d\right)}{\left(D \cdot D\right) \cdot \left(w \cdot h\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array}\]

Reproduce

herbie shell --seed 2019149 +o rules:numerics
(FPCore (c0 w h D d M)
  :name "Henrywood and Agarwal, Equation (13)"
  (* (/ c0 (* 2 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))))))