Average Error: 59.4 → 33.2
Time: 13.7s
Precision: 64
\[\frac{c0}{2 \cdot w} \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right)\]
↓
\[\frac{0}{2 \cdot w}\]
\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}{2 \cdot w}
double f(double c0, double w, double h, double D, double d, double M) {
        double r203934 = c0;
        double r203935 = 2.0;
        double r203936 = w;
        double r203937 = r203935 * r203936;
        double r203938 = r203934 / r203937;
        double r203939 = d;
        double r203940 = r203939 * r203939;
        double r203941 = r203934 * r203940;
        double r203942 = h;
        double r203943 = r203936 * r203942;
        double r203944 = D;
        double r203945 = r203944 * r203944;
        double r203946 = r203943 * r203945;
        double r203947 = r203941 / r203946;
        double r203948 = r203947 * r203947;
        double r203949 = M;
        double r203950 = r203949 * r203949;
        double r203951 = r203948 - r203950;
        double r203952 = sqrt(r203951);
        double r203953 = r203947 + r203952;
        double r203954 = r203938 * r203953;
        return r203954;
}
↓
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 r203955 = 0.0;
        double r203956 = 2.0;
        double r203957 = w;
        double r203958 = r203956 * r203957;
        double r203959 = r203955 / r203958;
        return r203959;
}

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 35.0

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

  4. Applied associate-*l/33.2

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

  5. Simplified33.2

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

  6. Final simplification33.2

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

Reproduce

herbie shell --seed 2020036 +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))))))