Average Error: 59.3 → 33.8
Time: 11.6s
Precision: 64
\[\frac{c0}{2 \cdot w} \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right)\]
↓
\[0 \cdot \sqrt{0}\]
\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}
double f(double c0, double w, double h, double D, double d, double M) {
        double r159288 = c0;
        double r159289 = 2.0;
        double r159290 = w;
        double r159291 = r159289 * r159290;
        double r159292 = r159288 / r159291;
        double r159293 = d;
        double r159294 = r159293 * r159293;
        double r159295 = r159288 * r159294;
        double r159296 = h;
        double r159297 = r159290 * r159296;
        double r159298 = D;
        double r159299 = r159298 * r159298;
        double r159300 = r159297 * r159299;
        double r159301 = r159295 / r159300;
        double r159302 = r159301 * r159301;
        double r159303 = M;
        double r159304 = r159303 * r159303;
        double r159305 = r159302 - r159304;
        double r159306 = sqrt(r159305);
        double r159307 = r159301 + r159306;
        double r159308 = r159292 * r159307;
        return r159308;
}
↓
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 r159309 = 0.0;
        double r159310 = sqrt(r159309);
        double r159311 = r159309 * r159310;
        return r159311;
}

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

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 59.3

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

  2. Taylor expanded around inf 35.7

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

  4. Applied add-sqr-sqrt35.7

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

  5. Applied associate-*r*35.7

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

  6. Simplified33.8

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

  7. Final simplification33.8

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

Reproduce

herbie shell --seed 2020089 +o rules:numerics
(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))))))