Average Error: 59.3 → 33.8
Time: 28.1s
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 r109350 = c0;
        double r109351 = 2.0;
        double r109352 = w;
        double r109353 = r109351 * r109352;
        double r109354 = r109350 / r109353;
        double r109355 = d;
        double r109356 = r109355 * r109355;
        double r109357 = r109350 * r109356;
        double r109358 = h;
        double r109359 = r109352 * r109358;
        double r109360 = D;
        double r109361 = r109360 * r109360;
        double r109362 = r109359 * r109361;
        double r109363 = r109357 / r109362;
        double r109364 = r109363 * r109363;
        double r109365 = M;
        double r109366 = r109365 * r109365;
        double r109367 = r109364 - r109366;
        double r109368 = sqrt(r109367);
        double r109369 = r109363 + r109368;
        double r109370 = r109354 * r109369;
        return r109370;
}
↓
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 r109371 = 0.0;
        return r109371;
}

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 +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))))))