Average Error: 59.2 → 33.7
Time: 46.7s
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 r5872965 = c0;
        double r5872966 = 2.0;
        double r5872967 = w;
        double r5872968 = r5872966 * r5872967;
        double r5872969 = r5872965 / r5872968;
        double r5872970 = d;
        double r5872971 = r5872970 * r5872970;
        double r5872972 = r5872965 * r5872971;
        double r5872973 = h;
        double r5872974 = r5872967 * r5872973;
        double r5872975 = D;
        double r5872976 = r5872975 * r5872975;
        double r5872977 = r5872974 * r5872976;
        double r5872978 = r5872972 / r5872977;
        double r5872979 = r5872978 * r5872978;
        double r5872980 = M;
        double r5872981 = r5872980 * r5872980;
        double r5872982 = r5872979 - r5872981;
        double r5872983 = sqrt(r5872982);
        double r5872984 = r5872978 + r5872983;
        double r5872985 = r5872969 * r5872984;
        return r5872985;
}
↓
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 r5872986 = 0.0;
        return r5872986;
}

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 59.2

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

  2. Simplified53.8

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

  3. Taylor expanded around inf 35.7

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

  4. Taylor expanded around 0 33.7

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

  5. Final simplification33.7

    \[\leadsto 0\]

Reproduce

herbie shell --seed 2019171 +o rules:numerics
(FPCore (c0 w h D d M)
  :name "Henrywood and Agarwal, Equation (13)"
  (* (/ c0 (* 2.0 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))))))