Henrywood and Agarwal, Equation (13)

Average Error: 59.4 → 33.2

Time: 10.7s

Precision: 64

• could not determine a ground truth for program body

  1. c0 = 5.836820474827695e+223
  2. w = 3.1518159930283016e-72
  3. h = -3.401998161412354e+66
  4. D = -4.0081454475175946e-95
  5. d = 6.318206988268696e+302
  6. M = -5.604437778614317e+202

Math

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

↓

\[0 \cdot \sqrt{0}\]

C

double f(double c0, double w, double h, double D, double d, double M) {
        double r167272 = c0;
        double r167273 = 2.0;
        double r167274 = w;
        double r167275 = r167273 * r167274;
        double r167276 = r167272 / r167275;
        double r167277 = d;
        double r167278 = r167277 * r167277;
        double r167279 = r167272 * r167278;
        double r167280 = h;
        double r167281 = r167274 * r167280;
        double r167282 = D;
        double r167283 = r167282 * r167282;
        double r167284 = r167281 * r167283;
        double r167285 = r167279 / r167284;
        double r167286 = r167285 * r167285;
        double r167287 = M;
        double r167288 = r167287 * r167287;
        double r167289 = r167286 - r167288;
        double r167290 = sqrt(r167289);
        double r167291 = r167285 + r167290;
        double r167292 = r167276 * r167291;
        return r167292;
}

↓

double f(double __attribute__((unused)) c0, double __attribute__((unused)) w, double __attribute__((unused)) h, double __attribute__((unused)) D, double __attribute__((unused)) d, double __attribute__((unused)) M) {
        double r167293 = 0.0;
        double r167294 = sqrt(r167293);
        double r167295 = r167293 * r167294;
        return r167295;
}

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 59.4

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

2. Taylor expanded around inf 35.2

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

4. Applied add-sqr-sqrt 35.2

   \[\leadsto \frac{c0}{2 \cdot w} \cdot \color{blue}{\left(\sqrt{0} \cdot \sqrt{0}\right)}\]

5. Applied associate-*r* 35.2

   \[\leadsto \color{blue}{\left(\frac{c0}{2 \cdot w} \cdot \sqrt{0}\right) \cdot \sqrt{0}}\]

6. Simplified 33.2

   \[\leadsto \color{blue}{0} \cdot \sqrt{0}\]

7. Final simplification 33.2

   \[\leadsto 0 \cdot \sqrt{0}\]

Reproduce

herbie shell --seed 2020033 
(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))))))