Average Error: 59.1 → 33.5
Time: 9.6s
Precision: 64
\[\frac{c0}{2 \cdot w} \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right)\]
↓
\[c0 \cdot 0\]
\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)
↓
c0 \cdot 0
double f(double c0, double w, double h, double D, double d, double M) {
        double r165037 = c0;
        double r165038 = 2.0;
        double r165039 = w;
        double r165040 = r165038 * r165039;
        double r165041 = r165037 / r165040;
        double r165042 = d;
        double r165043 = r165042 * r165042;
        double r165044 = r165037 * r165043;
        double r165045 = h;
        double r165046 = r165039 * r165045;
        double r165047 = D;
        double r165048 = r165047 * r165047;
        double r165049 = r165046 * r165048;
        double r165050 = r165044 / r165049;
        double r165051 = r165050 * r165050;
        double r165052 = M;
        double r165053 = r165052 * r165052;
        double r165054 = r165051 - r165053;
        double r165055 = sqrt(r165054);
        double r165056 = r165050 + r165055;
        double r165057 = r165041 * r165056;
        return r165057;
}
↓
double f(double c0, double __attribute__((unused)) w, double __attribute__((unused)) h, double __attribute__((unused)) D, double __attribute__((unused)) d, double __attribute__((unused)) M) {
        double r165058 = c0;
        double r165059 = 0.0;
        double r165060 = r165058 * r165059;
        return r165060;
}

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 59.1

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

  2. Taylor expanded around inf 35.3

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

  4. Applied div-inv35.3

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

  5. Applied associate-*l*33.5

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

  6. Simplified33.5

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

  7. Final simplification33.5

    \[\leadsto c0 \cdot 0\]

Reproduce

herbie shell --seed 2020060 
(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))))))