Average Error: 59.3 → 33.0
Time: 3.0m
Precision: 64
\[\frac{c0}{2 \cdot w} \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right)\]
↓
\[0\]
\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
double f(double c0, double w, double h, double D, double d, double M) {
        double r102197 = c0;
        double r102198 = 2.0;
        double r102199 = w;
        double r102200 = r102198 * r102199;
        double r102201 = r102197 / r102200;
        double r102202 = d;
        double r102203 = r102202 * r102202;
        double r102204 = r102197 * r102203;
        double r102205 = h;
        double r102206 = r102199 * r102205;
        double r102207 = D;
        double r102208 = r102207 * r102207;
        double r102209 = r102206 * r102208;
        double r102210 = r102204 / r102209;
        double r102211 = r102210 * r102210;
        double r102212 = M;
        double r102213 = r102212 * r102212;
        double r102214 = r102211 - r102213;
        double r102215 = sqrt(r102214);
        double r102216 = r102210 + r102215;
        double r102217 = r102201 * r102216;
        return r102217;
}
↓
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 r102218 = 0.0;
        return r102218;
}

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 34.9

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

  4. Applied pow134.9

    \[\leadsto \frac{c0}{2 \cdot w} \cdot \color{blue}{{0}^{1}}\]

  5. Applied pow134.9

    \[\leadsto \color{blue}{{\left(\frac{c0}{2 \cdot w}\right)}^{1}} \cdot {0}^{1}\]

  6. Applied pow-prod-down34.9

    \[\leadsto \color{blue}{{\left(\frac{c0}{2 \cdot w} \cdot 0\right)}^{1}}\]

  7. Simplified33.0

    \[\leadsto {\color{blue}{0}}^{1}\]

  8. Final simplification33.0

    \[\leadsto 0\]

Reproduce

herbie shell --seed 2019323 
(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))))))