Average Error: 59.2 → 33.6
Time: 9.6s
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 r263199 = c0;
        double r263200 = 2.0;
        double r263201 = w;
        double r263202 = r263200 * r263201;
        double r263203 = r263199 / r263202;
        double r263204 = d;
        double r263205 = r263204 * r263204;
        double r263206 = r263199 * r263205;
        double r263207 = h;
        double r263208 = r263201 * r263207;
        double r263209 = D;
        double r263210 = r263209 * r263209;
        double r263211 = r263208 * r263210;
        double r263212 = r263206 / r263211;
        double r263213 = r263212 * r263212;
        double r263214 = M;
        double r263215 = r263214 * r263214;
        double r263216 = r263213 - r263215;
        double r263217 = sqrt(r263216);
        double r263218 = r263212 + r263217;
        double r263219 = r263203 * r263218;
        return r263219;
}
↓
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 r263220 = 0.0;
        double r263221 = 2.0;
        double r263222 = w;
        double r263223 = r263221 * r263222;
        double r263224 = r263220 / r263223;
        return r263224;
}

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 35.2

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

  4. Applied associate-*l/33.6

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

  5. Simplified33.6

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

  6. Final simplification33.6

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

Reproduce

herbie shell --seed 2020047 +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))))))