Average Error: 59.4 → 33.1
Time: 29.0s
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 r124405 = c0;
        double r124406 = 2.0;
        double r124407 = w;
        double r124408 = r124406 * r124407;
        double r124409 = r124405 / r124408;
        double r124410 = d;
        double r124411 = r124410 * r124410;
        double r124412 = r124405 * r124411;
        double r124413 = h;
        double r124414 = r124407 * r124413;
        double r124415 = D;
        double r124416 = r124415 * r124415;
        double r124417 = r124414 * r124416;
        double r124418 = r124412 / r124417;
        double r124419 = r124418 * r124418;
        double r124420 = M;
        double r124421 = r124420 * r124420;
        double r124422 = r124419 - r124421;
        double r124423 = sqrt(r124422);
        double r124424 = r124418 + r124423;
        double r124425 = r124409 * r124424;
        return r124425;
}
↓
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 r124426 = 0.0;
        return r124426;
}

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 59.4

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

  2. Taylor expanded around inf 35.2

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

  4. Applied add-cube-cbrt35.2

    \[\leadsto \color{blue}{\left(\sqrt[3]{\frac{c0}{2 \cdot w} \cdot 0} \cdot \sqrt[3]{\frac{c0}{2 \cdot w} \cdot 0}\right) \cdot \sqrt[3]{\frac{c0}{2 \cdot w} \cdot 0}}\]

  5. Simplified35.2

    \[\leadsto \color{blue}{0} \cdot \sqrt[3]{\frac{c0}{2 \cdot w} \cdot 0}\]

  6. Simplified33.1

    \[\leadsto 0 \cdot \color{blue}{0}\]

  7. Final simplification33.1

    \[\leadsto 0\]

Reproduce

herbie shell --seed 2019194 
(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))))))