Average Error: 59.3 → 33.9
Time: 30.4s
Precision: 64
\[\frac{c0}{2 \cdot w} \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right)\]
↓
\[\frac{0}{2 \cdot w}\]
\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}
double f(double c0, double w, double h, double D, double d, double M) {
        double r99796 = c0;
        double r99797 = 2.0;
        double r99798 = w;
        double r99799 = r99797 * r99798;
        double r99800 = r99796 / r99799;
        double r99801 = d;
        double r99802 = r99801 * r99801;
        double r99803 = r99796 * r99802;
        double r99804 = h;
        double r99805 = r99798 * r99804;
        double r99806 = D;
        double r99807 = r99806 * r99806;
        double r99808 = r99805 * r99807;
        double r99809 = r99803 / r99808;
        double r99810 = r99809 * r99809;
        double r99811 = M;
        double r99812 = r99811 * r99811;
        double r99813 = r99810 - r99812;
        double r99814 = sqrt(r99813);
        double r99815 = r99809 + r99814;
        double r99816 = r99800 * r99815;
        return r99816;
}
↓
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 r99817 = 0.0;
        double r99818 = 2.0;
        double r99819 = w;
        double r99820 = r99818 * r99819;
        double r99821 = r99817 / r99820;
        return r99821;
}

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 associate-*l/33.9

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

  5. Simplified33.9

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

  6. Final simplification33.9

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

Reproduce

herbie shell --seed 2019325 
(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))))))