Henrywood and Agarwal, Equation (13)

Average Error: 58.5 → 32.9

Time: 59.4s

Precision: 64

• could not determine a ground truth for program body

  1. c0 = 4.417426849345344e+133
  2. w = -3.487656603368592e+48
  3. h = 7.326426385492515e-250
  4. D = -7.2785279115581705e-242
  5. d = 6.179336453161865e+266
  6. M = -1004.3872661942555

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;\frac{c0}{w \cdot 2} \cdot \left(\sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(D \cdot D\right) \cdot \left(w \cdot h\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(D \cdot D\right) \cdot \left(w \cdot h\right)} - M \cdot M} + \frac{c0 \cdot \left(d \cdot d\right)}{\left(D \cdot D\right) \cdot \left(w \cdot h\right)}\right) \le 9.221058218589873 \cdot 10^{+88}:\\ \;\;\;\;\frac{c0}{w \cdot 2} \cdot \left(\sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(D \cdot D\right) \cdot \left(w \cdot h\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(D \cdot D\right) \cdot \left(w \cdot h\right)} - M \cdot M} + \frac{c0 \cdot \left(d \cdot d\right)}{\left(D \cdot D\right) \cdot \left(w \cdot h\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array}\]

C

double f(double c0, double w, double h, double D, double d, double M) {
        double r4587681 = c0;
        double r4587682 = 2.0;
        double r4587683 = w;
        double r4587684 = r4587682 * r4587683;
        double r4587685 = r4587681 / r4587684;
        double r4587686 = d;
        double r4587687 = r4587686 * r4587686;
        double r4587688 = r4587681 * r4587687;
        double r4587689 = h;
        double r4587690 = r4587683 * r4587689;
        double r4587691 = D;
        double r4587692 = r4587691 * r4587691;
        double r4587693 = r4587690 * r4587692;
        double r4587694 = r4587688 / r4587693;
        double r4587695 = r4587694 * r4587694;
        double r4587696 = M;
        double r4587697 = r4587696 * r4587696;
        double r4587698 = r4587695 - r4587697;
        double r4587699 = sqrt(r4587698);
        double r4587700 = r4587694 + r4587699;
        double r4587701 = r4587685 * r4587700;
        return r4587701;
}

↓

double f(double c0, double w, double h, double D, double d, double M) {
        double r4587702 = c0;
        double r4587703 = w;
        double r4587704 = 2.0;
        double r4587705 = r4587703 * r4587704;
        double r4587706 = r4587702 / r4587705;
        double r4587707 = d;
        double r4587708 = r4587707 * r4587707;
        double r4587709 = r4587702 * r4587708;
        double r4587710 = D;
        double r4587711 = r4587710 * r4587710;
        double r4587712 = h;
        double r4587713 = r4587703 * r4587712;
        double r4587714 = r4587711 * r4587713;
        double r4587715 = r4587709 / r4587714;
        double r4587716 = r4587715 * r4587715;
        double r4587717 = M;
        double r4587718 = r4587717 * r4587717;
        double r4587719 = r4587716 - r4587718;
        double r4587720 = sqrt(r4587719);
        double r4587721 = r4587720 + r4587715;
        double r4587722 = r4587706 * r4587721;
        double r4587723 = 9.221058218589873e+88;
        bool r4587724 = r4587722 <= r4587723;
        double r4587725 = 0.0;
        double r4587726 = r4587724 ? r4587722 : r4587725;
        return r4587726;
}

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))))) < 9.221058218589873e+88

   1. Initial program 37.0

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

   if 9.221058218589873e+88 < (* (/ 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 62.4

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

   2. Simplified 54.5

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

   3. Taylor expanded around -inf 32.1

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

4. Final simplification 32.9

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{c0}{w \cdot 2} \cdot \left(\sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(D \cdot D\right) \cdot \left(w \cdot h\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(D \cdot D\right) \cdot \left(w \cdot h\right)} - M \cdot M} + \frac{c0 \cdot \left(d \cdot d\right)}{\left(D \cdot D\right) \cdot \left(w \cdot h\right)}\right) \le 9.221058218589873 \cdot 10^{+88}:\\ \;\;\;\;\frac{c0}{w \cdot 2} \cdot \left(\sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(D \cdot D\right) \cdot \left(w \cdot h\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(D \cdot D\right) \cdot \left(w \cdot h\right)} - M \cdot M} + \frac{c0 \cdot \left(d \cdot d\right)}{\left(D \cdot D\right) \cdot \left(w \cdot h\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array}\]

Reproduce

herbie shell --seed 2019135 +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))))))