Average Error: 58.9 → 33.3
Time: 17.5s
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 r223656 = c0;
        double r223657 = 2.0;
        double r223658 = w;
        double r223659 = r223657 * r223658;
        double r223660 = r223656 / r223659;
        double r223661 = d;
        double r223662 = r223661 * r223661;
        double r223663 = r223656 * r223662;
        double r223664 = h;
        double r223665 = r223658 * r223664;
        double r223666 = D;
        double r223667 = r223666 * r223666;
        double r223668 = r223665 * r223667;
        double r223669 = r223663 / r223668;
        double r223670 = r223669 * r223669;
        double r223671 = M;
        double r223672 = r223671 * r223671;
        double r223673 = r223670 - r223672;
        double r223674 = sqrt(r223673);
        double r223675 = r223669 + r223674;
        double r223676 = r223660 * r223675;
        return r223676;
}
↓
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 r223677 = 0.0;
        return r223677;
}

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 58.9

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

  2. Taylor expanded around inf 35.2

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

  4. Applied *-un-lft-identity35.2

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

  5. Applied associate-*l*35.2

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

  6. Simplified33.3

    \[\leadsto 1 \cdot \color{blue}{0}\]

  7. Final simplification33.3

    \[\leadsto 0\]

Reproduce

herbie shell --seed 2019322 
(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))))))