Henrywood and Agarwal, Equation (13)

Average Error: 59.2 → 32.1

Time: 8.2s

Precision: 64

• could not determine a ground truth for program body

  1. c0 = -1.4888806322782983e+185
  2. w = 6.122968714791307e-126
  3. h = 5.961486911483885e-67
  4. D = 1.557424007302578e-241
  5. d = -1.6385991472911562e+169
  6. M = 7.20527608435195e-205

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;\frac{c0}{2 \cdot w} \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \le 1.996806307158958 \cdot 10^{263}:\\ \;\;\;\;\frac{c0}{2 \cdot w} \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{0}{2 \cdot w}\\ \end{array}\]

C

double f(double c0, double w, double h, double D, double d, double M) {
        double r229676 = c0;
        double r229677 = 2.0;
        double r229678 = w;
        double r229679 = r229677 * r229678;
        double r229680 = r229676 / r229679;
        double r229681 = d;
        double r229682 = r229681 * r229681;
        double r229683 = r229676 * r229682;
        double r229684 = h;
        double r229685 = r229678 * r229684;
        double r229686 = D;
        double r229687 = r229686 * r229686;
        double r229688 = r229685 * r229687;
        double r229689 = r229683 / r229688;
        double r229690 = r229689 * r229689;
        double r229691 = M;
        double r229692 = r229691 * r229691;
        double r229693 = r229690 - r229692;
        double r229694 = sqrt(r229693);
        double r229695 = r229689 + r229694;
        double r229696 = r229680 * r229695;
        return r229696;
}

↓

double f(double c0, double w, double h, double D, double d, double M) {
        double r229697 = c0;
        double r229698 = 2.0;
        double r229699 = w;
        double r229700 = r229698 * r229699;
        double r229701 = r229697 / r229700;
        double r229702 = d;
        double r229703 = r229702 * r229702;
        double r229704 = r229697 * r229703;
        double r229705 = h;
        double r229706 = r229699 * r229705;
        double r229707 = D;
        double r229708 = r229707 * r229707;
        double r229709 = r229706 * r229708;
        double r229710 = r229704 / r229709;
        double r229711 = r229710 * r229710;
        double r229712 = M;
        double r229713 = r229712 * r229712;
        double r229714 = r229711 - r229713;
        double r229715 = sqrt(r229714);
        double r229716 = r229710 + r229715;
        double r229717 = r229701 * r229716;
        double r229718 = 1.996806307158958e+263;
        bool r229719 = r229717 <= r229718;
        double r229720 = 0.0;
        double r229721 = r229720 / r229700;
        double r229722 = r229719 ? r229717 : r229721;
        return r229722;
}

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))))) < 1.996806307158958e+263

   1. Initial program 34.7

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

   if 1.996806307158958e+263 < (* (/ 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. Taylor expanded around inf 33.9

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

   4. Applied associate-*l/ 31.6

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

   5. Simplified 31.6

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

4. Final simplification 32.1

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{c0}{2 \cdot w} \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \le 1.996806307158958 \cdot 10^{263}:\\ \;\;\;\;\frac{c0}{2 \cdot w} \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{0}{2 \cdot w}\\ \end{array}\]

Reproduce

herbie shell --seed 2020062 
(FPCore (c0 w h D d M)
  :name "Henrywood and Agarwal, Equation (13)"
  :precision binary64
  (* (/ 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))))))