Average Error: 59.0 → 34.5
Time: 21.9s
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 r169414 = c0;
        double r169415 = 2.0;
        double r169416 = w;
        double r169417 = r169415 * r169416;
        double r169418 = r169414 / r169417;
        double r169419 = d;
        double r169420 = r169419 * r169419;
        double r169421 = r169414 * r169420;
        double r169422 = h;
        double r169423 = r169416 * r169422;
        double r169424 = D;
        double r169425 = r169424 * r169424;
        double r169426 = r169423 * r169425;
        double r169427 = r169421 / r169426;
        double r169428 = r169427 * r169427;
        double r169429 = M;
        double r169430 = r169429 * r169429;
        double r169431 = r169428 - r169430;
        double r169432 = sqrt(r169431);
        double r169433 = r169427 + r169432;
        double r169434 = r169418 * r169433;
        return r169434;
}
↓
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 r169435 = 0.0;
        return r169435;
}

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 59.0

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

  2. Taylor expanded around inf 36.1

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

  4. Applied add-log-exp36.1

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

  5. Simplified34.5

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

  6. Final simplification34.5

    \[\leadsto 0\]

Reproduce

herbie shell --seed 2019209 +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))))))