Average Error: 59.5 → 33.7
Time: 19.1s
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 r99817 = c0;
        double r99818 = 2.0;
        double r99819 = w;
        double r99820 = r99818 * r99819;
        double r99821 = r99817 / r99820;
        double r99822 = d;
        double r99823 = r99822 * r99822;
        double r99824 = r99817 * r99823;
        double r99825 = h;
        double r99826 = r99819 * r99825;
        double r99827 = D;
        double r99828 = r99827 * r99827;
        double r99829 = r99826 * r99828;
        double r99830 = r99824 / r99829;
        double r99831 = r99830 * r99830;
        double r99832 = M;
        double r99833 = r99832 * r99832;
        double r99834 = r99831 - r99833;
        double r99835 = sqrt(r99834);
        double r99836 = r99830 + r99835;
        double r99837 = r99821 * r99836;
        return r99837;
}
↓
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 r99838 = 0.0;
        return r99838;
}

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 59.5

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

  2. Taylor expanded around inf 35.6

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

  4. Applied div-inv35.6

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

  5. Applied associate-*l*33.7

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

  6. Simplified33.7

    \[\leadsto c0 \cdot \color{blue}{0}\]

  7. Final simplification33.7

    \[\leadsto 0\]

Reproduce

herbie shell --seed 2019304 
(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))))))