Henrywood and Agarwal, Equation (13)

Average Error: 59.2 → 33.5

Time: 13.6s

Precision: 64

• Falling back on racket egraph because egg-herbie package not installed

• could not determine a ground truth for program body

  1. c0 = 1.082084726917846e+287
  2. w = 1.56037796305268e-83
  3. h = -9.379441670507973e-171
  4. D = -9.069080929345551e-285
  5. d = -2.7089457078913576e+37
  6. M = -1.4763414349710623e+154

Math

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

↓

\[\frac{0}{2 \cdot w}\]

C

double f(double c0, double w, double h, double D, double d, double M) {
        double r139753 = c0;
        double r139754 = 2.0;
        double r139755 = w;
        double r139756 = r139754 * r139755;
        double r139757 = r139753 / r139756;
        double r139758 = d;
        double r139759 = r139758 * r139758;
        double r139760 = r139753 * r139759;
        double r139761 = h;
        double r139762 = r139755 * r139761;
        double r139763 = D;
        double r139764 = r139763 * r139763;
        double r139765 = r139762 * r139764;
        double r139766 = r139760 / r139765;
        double r139767 = r139766 * r139766;
        double r139768 = M;
        double r139769 = r139768 * r139768;
        double r139770 = r139767 - r139769;
        double r139771 = sqrt(r139770);
        double r139772 = r139766 + r139771;
        double r139773 = r139757 * r139772;
        return r139773;
}

↓

double f(double __attribute__((unused)) c0, double w, double __attribute__((unused)) h, double __attribute__((unused)) D, double __attribute__((unused)) d, double __attribute__((unused)) M) {
        double r139774 = 0.0;
        double r139775 = 2.0;
        double r139776 = w;
        double r139777 = r139775 * r139776;
        double r139778 = r139774 / r139777;
        return r139778;
}

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. Initial program 59.2

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

2. Taylor expanded around inf 35.2

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

4. Applied associate-*l/ 33.5

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

5. Simplified 33.5

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

6. Final simplification 33.5

   \[\leadsto \frac{0}{2 \cdot w}\]

Reproduce

herbie shell --seed 2020046 
(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))))))