Average Error: 58.1 → 33.7
Time: 51.0s
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 r4361679 = c0;
        double r4361680 = 2.0;
        double r4361681 = w;
        double r4361682 = r4361680 * r4361681;
        double r4361683 = r4361679 / r4361682;
        double r4361684 = d;
        double r4361685 = r4361684 * r4361684;
        double r4361686 = r4361679 * r4361685;
        double r4361687 = h;
        double r4361688 = r4361681 * r4361687;
        double r4361689 = D;
        double r4361690 = r4361689 * r4361689;
        double r4361691 = r4361688 * r4361690;
        double r4361692 = r4361686 / r4361691;
        double r4361693 = r4361692 * r4361692;
        double r4361694 = M;
        double r4361695 = r4361694 * r4361694;
        double r4361696 = r4361693 - r4361695;
        double r4361697 = sqrt(r4361696);
        double r4361698 = r4361692 + r4361697;
        double r4361699 = r4361683 * r4361698;
        return r4361699;
}
↓
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 r4361700 = 0.0;
        return r4361700;
}

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. Simplified51.3

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

  3. Taylor expanded around -inf 33.7

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

  4. Final simplification33.7

    \[\leadsto 0\]

Reproduce

herbie shell --seed 2019130 +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))))))