Average Error: 59.1 → 33.2
Time: 11.2s
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 r188929 = c0;
        double r188930 = 2.0;
        double r188931 = w;
        double r188932 = r188930 * r188931;
        double r188933 = r188929 / r188932;
        double r188934 = d;
        double r188935 = r188934 * r188934;
        double r188936 = r188929 * r188935;
        double r188937 = h;
        double r188938 = r188931 * r188937;
        double r188939 = D;
        double r188940 = r188939 * r188939;
        double r188941 = r188938 * r188940;
        double r188942 = r188936 / r188941;
        double r188943 = r188942 * r188942;
        double r188944 = M;
        double r188945 = r188944 * r188944;
        double r188946 = r188943 - r188945;
        double r188947 = sqrt(r188946);
        double r188948 = r188942 + r188947;
        double r188949 = r188933 * r188948;
        return r188949;
}
↓
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 r188950 = 0.0;
        return r188950;
}

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 59.1

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

  2. Taylor expanded around inf 35.1

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

  4. Applied *-un-lft-identity35.1

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

  5. Applied associate-*l*35.1

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

  6. Simplified33.2

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

  7. Final simplification33.2

    \[\leadsto 0\]

Reproduce

herbie shell --seed 2020001 +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))))))