Average Error: 58.8 → 33.3
Time: 15.9s
Precision: 64
\[\frac{c0}{2 \cdot w} \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right)\]
↓
\[\frac{0}{2 \cdot w}\]
\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{0}{2 \cdot w}
double f(double c0, double w, double h, double D, double d, double M) {
        double r137421 = c0;
        double r137422 = 2.0;
        double r137423 = w;
        double r137424 = r137422 * r137423;
        double r137425 = r137421 / r137424;
        double r137426 = d;
        double r137427 = r137426 * r137426;
        double r137428 = r137421 * r137427;
        double r137429 = h;
        double r137430 = r137423 * r137429;
        double r137431 = D;
        double r137432 = r137431 * r137431;
        double r137433 = r137430 * r137432;
        double r137434 = r137428 / r137433;
        double r137435 = r137434 * r137434;
        double r137436 = M;
        double r137437 = r137436 * r137436;
        double r137438 = r137435 - r137437;
        double r137439 = sqrt(r137438);
        double r137440 = r137434 + r137439;
        double r137441 = r137425 * r137440;
        return r137441;
}
↓
double f(double __attribute__((unused)) c0, double w, double __attribute__((unused)) h, double __attribute__((unused)) D, double __attribute__((unused)) d, double __attribute__((unused)) M) {
        double r137442 = 0.0;
        double r137443 = 2.0;
        double r137444 = w;
        double r137445 = r137443 * r137444;
        double r137446 = r137442 / r137445;
        return r137446;
}

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 58.8

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

  2. Taylor expanded around inf 35.2

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

  4. Applied associate-*l/33.3

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

  5. Simplified33.3

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

  6. Final simplification33.3

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

Reproduce

herbie shell --seed 2019350 +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))))))