Average Error: 59.2 → 33.9
Time: 8.4s
Precision: 64
\[\frac{c0}{2 \cdot w} \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right)\]
↓
\[\frac{1}{2} \cdot 0\]
\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)
↓
\frac{1}{2} \cdot 0
double f(double c0, double w, double h, double D, double d, double M) {
        double r119717 = c0;
        double r119718 = 2.0;
        double r119719 = w;
        double r119720 = r119718 * r119719;
        double r119721 = r119717 / r119720;
        double r119722 = d;
        double r119723 = r119722 * r119722;
        double r119724 = r119717 * r119723;
        double r119725 = h;
        double r119726 = r119719 * r119725;
        double r119727 = D;
        double r119728 = r119727 * r119727;
        double r119729 = r119726 * r119728;
        double r119730 = r119724 / r119729;
        double r119731 = r119730 * r119730;
        double r119732 = M;
        double r119733 = r119732 * r119732;
        double r119734 = r119731 - r119733;
        double r119735 = sqrt(r119734);
        double r119736 = r119730 + r119735;
        double r119737 = r119721 * r119736;
        return r119737;
}
↓
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 r119738 = 1.0;
        double r119739 = 2.0;
        double r119740 = r119738 / r119739;
        double r119741 = 0.0;
        double r119742 = r119740 * r119741;
        return r119742;
}

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 59.2

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

  2. Taylor expanded around inf 35.8

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

  4. Applied *-un-lft-identity35.8

    \[\leadsto \frac{\color{blue}{1 \cdot c0}}{2 \cdot w} \cdot 0\]

  5. Applied times-frac35.8

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

  6. Applied associate-*l*35.8

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

  7. Simplified33.9

    \[\leadsto \frac{1}{2} \cdot \color{blue}{0}\]

  8. Final simplification33.9

    \[\leadsto \frac{1}{2} \cdot 0\]

Reproduce

herbie shell --seed 2020065 
(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))))))