Average Error: 59.3 → 33.4
Time: 29.8s
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 r140989 = c0;
        double r140990 = 2.0;
        double r140991 = w;
        double r140992 = r140990 * r140991;
        double r140993 = r140989 / r140992;
        double r140994 = d;
        double r140995 = r140994 * r140994;
        double r140996 = r140989 * r140995;
        double r140997 = h;
        double r140998 = r140991 * r140997;
        double r140999 = D;
        double r141000 = r140999 * r140999;
        double r141001 = r140998 * r141000;
        double r141002 = r140996 / r141001;
        double r141003 = r141002 * r141002;
        double r141004 = M;
        double r141005 = r141004 * r141004;
        double r141006 = r141003 - r141005;
        double r141007 = sqrt(r141006);
        double r141008 = r141002 + r141007;
        double r141009 = r140993 * r141008;
        return r141009;
}
↓
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 r141010 = 0.0;
        return r141010;
}

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 59.3

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

  2. Taylor expanded around inf 35.4

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

  4. Applied add-log-exp35.4

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

  5. Simplified33.4

    \[\leadsto \log \color{blue}{1}\]

  6. Final simplification33.4

    \[\leadsto 0\]

Reproduce

herbie shell --seed 2019303 +o rules:numerics
(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))))))