Average Error: 58.1 → 33.8
Time: 48.7s
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 r4212895 = c0;
        double r4212896 = 2.0;
        double r4212897 = w;
        double r4212898 = r4212896 * r4212897;
        double r4212899 = r4212895 / r4212898;
        double r4212900 = d;
        double r4212901 = r4212900 * r4212900;
        double r4212902 = r4212895 * r4212901;
        double r4212903 = h;
        double r4212904 = r4212897 * r4212903;
        double r4212905 = D;
        double r4212906 = r4212905 * r4212905;
        double r4212907 = r4212904 * r4212906;
        double r4212908 = r4212902 / r4212907;
        double r4212909 = r4212908 * r4212908;
        double r4212910 = M;
        double r4212911 = r4212910 * r4212910;
        double r4212912 = r4212909 - r4212911;
        double r4212913 = sqrt(r4212912);
        double r4212914 = r4212908 + r4212913;
        double r4212915 = r4212899 * r4212914;
        return r4212915;
}
↓
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 r4212916 = 0.0;
        return r4212916;
}

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 58.1

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

  2. Simplified52.9

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

  3. Taylor expanded around -inf 35.6

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

  4. Taylor expanded around -inf 33.8

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

  5. Final simplification33.8

    \[\leadsto 0\]

Reproduce

herbie shell --seed 2019142 +o rules:numerics
(FPCore (c0 w h D d M)
  :name "Henrywood and Agarwal, Equation (13)"
  (* (/ 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))))))