Average Error: 59.0 → 33.6
Time: 27.6s
Precision: 64
\[\frac{c0}{2 \cdot w} \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right)\]
↓
\[\frac{0}{w \cdot 2}\]
\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)
↓
\frac{0}{w \cdot 2}
double f(double c0, double w, double h, double D, double d, double M) {
        double r119402 = c0;
        double r119403 = 2.0;
        double r119404 = w;
        double r119405 = r119403 * r119404;
        double r119406 = r119402 / r119405;
        double r119407 = d;
        double r119408 = r119407 * r119407;
        double r119409 = r119402 * r119408;
        double r119410 = h;
        double r119411 = r119404 * r119410;
        double r119412 = D;
        double r119413 = r119412 * r119412;
        double r119414 = r119411 * r119413;
        double r119415 = r119409 / r119414;
        double r119416 = r119415 * r119415;
        double r119417 = M;
        double r119418 = r119417 * r119417;
        double r119419 = r119416 - r119418;
        double r119420 = sqrt(r119419);
        double r119421 = r119415 + r119420;
        double r119422 = r119406 * r119421;
        return r119422;
}
↓
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 r119423 = 0.0;
        double r119424 = w;
        double r119425 = 2.0;
        double r119426 = r119424 * r119425;
        double r119427 = r119423 / r119426;
        return r119427;
}

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 35.6

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

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

Reproduce

herbie shell --seed 2019179 +o rules:numerics
(FPCore (c0 w h D d M)
  :name "Henrywood and Agarwal, Equation (13)"
  (* (/ c0 (* 2.0 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))))))