Average Error: 59.4 → 33.1
Time: 29.0s
Precision: 64
\[\frac{c0}{2 \cdot w} \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right)\]
↓
\[\frac{1}{2} \cdot 0\]
\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 r116201 = c0;
        double r116202 = 2.0;
        double r116203 = w;
        double r116204 = r116202 * r116203;
        double r116205 = r116201 / r116204;
        double r116206 = d;
        double r116207 = r116206 * r116206;
        double r116208 = r116201 * r116207;
        double r116209 = h;
        double r116210 = r116203 * r116209;
        double r116211 = D;
        double r116212 = r116211 * r116211;
        double r116213 = r116210 * r116212;
        double r116214 = r116208 / r116213;
        double r116215 = r116214 * r116214;
        double r116216 = M;
        double r116217 = r116216 * r116216;
        double r116218 = r116215 - r116217;
        double r116219 = sqrt(r116218);
        double r116220 = r116214 + r116219;
        double r116221 = r116205 * r116220;
        return r116221;
}
↓
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 r116222 = 1.0;
        double r116223 = 2.0;
        double r116224 = r116222 / r116223;
        double r116225 = 0.0;
        double r116226 = r116224 * r116225;
        return r116226;
}

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 *-un-lft-identity35.2

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

  5. Applied times-frac35.2

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

  6. Applied associate-*l*35.2

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

  7. Simplified33.1

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

  8. Final simplification33.1

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

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))))))