Average Error: 59.3 → 33.8
Time: 28.5s
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 r91197 = c0;
        double r91198 = 2.0;
        double r91199 = w;
        double r91200 = r91198 * r91199;
        double r91201 = r91197 / r91200;
        double r91202 = d;
        double r91203 = r91202 * r91202;
        double r91204 = r91197 * r91203;
        double r91205 = h;
        double r91206 = r91199 * r91205;
        double r91207 = D;
        double r91208 = r91207 * r91207;
        double r91209 = r91206 * r91208;
        double r91210 = r91204 / r91209;
        double r91211 = r91210 * r91210;
        double r91212 = M;
        double r91213 = r91212 * r91212;
        double r91214 = r91211 - r91213;
        double r91215 = sqrt(r91214);
        double r91216 = r91210 + r91215;
        double r91217 = r91201 * r91216;
        return r91217;
}
↓
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 r91218 = 0.0;
        return r91218;
}

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 35.7

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

  4. Applied add-log-exp35.7

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

  5. Simplified33.8

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

  6. Final simplification33.8

    \[\leadsto 0\]

Reproduce

herbie shell --seed 2019326 
(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))))))