Average Error: 59.1 → 33.5
Time: 8.7s
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 r182872 = c0;
        double r182873 = 2.0;
        double r182874 = w;
        double r182875 = r182873 * r182874;
        double r182876 = r182872 / r182875;
        double r182877 = d;
        double r182878 = r182877 * r182877;
        double r182879 = r182872 * r182878;
        double r182880 = h;
        double r182881 = r182874 * r182880;
        double r182882 = D;
        double r182883 = r182882 * r182882;
        double r182884 = r182881 * r182883;
        double r182885 = r182879 / r182884;
        double r182886 = r182885 * r182885;
        double r182887 = M;
        double r182888 = r182887 * r182887;
        double r182889 = r182886 - r182888;
        double r182890 = sqrt(r182889);
        double r182891 = r182885 + r182890;
        double r182892 = r182876 * r182891;
        return r182892;
}
↓
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 r182893 = 0.0;
        return r182893;
}

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 59.1

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

  2. Taylor expanded around inf 35.3

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

  4. Applied pow135.3

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

  5. Applied pow135.3

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

  6. Applied pow-prod-down35.3

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

  7. Simplified33.5

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

  8. Final simplification33.5

    \[\leadsto 0\]

Reproduce

herbie shell --seed 2020060 
(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))))))