Average Error: 59.2 → 33.8
Time: 21.4s
Precision: 64
\[\frac{c0}{2 \cdot w} \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right)\]
↓
\[\frac{1}{2} \cdot 0\]
\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)
↓
\frac{1}{2} \cdot 0
double f(double c0, double w, double h, double D, double d, double M) {
        double r359 = c0;
        double r360 = 2.0;
        double r361 = w;
        double r362 = r360 * r361;
        double r363 = r359 / r362;
        double r364 = d;
        double r365 = r364 * r364;
        double r366 = r359 * r365;
        double r367 = h;
        double r368 = r361 * r367;
        double r369 = D;
        double r370 = r369 * r369;
        double r371 = r368 * r370;
        double r372 = r366 / r371;
        double r373 = r372 * r372;
        double r374 = M;
        double r375 = r374 * r374;
        double r376 = r373 - r375;
        double r377 = sqrt(r376);
        double r378 = r372 + r377;
        double r379 = r363 * r378;
        return r379;
}
↓
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 r380 = 1.0;
        double r381 = 2.0;
        double r382 = r380 / r381;
        double r383 = 0.0;
        double r384 = r382 * r383;
        return r384;
}

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 35.7

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

  4. Applied *-un-lft-identity35.7

    \[\leadsto \frac{\color{blue}{1 \cdot c0}}{2 \cdot w} \cdot 0\]

  5. Applied times-frac35.7

    \[\leadsto \color{blue}{\left(\frac{1}{2} \cdot \frac{c0}{w}\right)} \cdot 0\]

  6. Applied associate-*l*35.7

    \[\leadsto \color{blue}{\frac{1}{2} \cdot \left(\frac{c0}{w} \cdot 0\right)}\]

  7. Simplified33.8

    \[\leadsto \frac{1}{2} \cdot \color{blue}{0}\]

  8. Final simplification33.8

    \[\leadsto \frac{1}{2} \cdot 0\]

Reproduce

herbie shell --seed 2020025 +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))))))