Average Error: 59.2 → 33.5
Time: 9.0s
Precision: 64
\[\frac{c0}{2 \cdot w} \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right)\]
↓
\[c0 \cdot 0\]
\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)
↓
c0 \cdot 0
double f(double c0, double w, double h, double D, double d, double M) {
        double r70018 = c0;
        double r70019 = 2.0;
        double r70020 = w;
        double r70021 = r70019 * r70020;
        double r70022 = r70018 / r70021;
        double r70023 = d;
        double r70024 = r70023 * r70023;
        double r70025 = r70018 * r70024;
        double r70026 = h;
        double r70027 = r70020 * r70026;
        double r70028 = D;
        double r70029 = r70028 * r70028;
        double r70030 = r70027 * r70029;
        double r70031 = r70025 / r70030;
        double r70032 = r70031 * r70031;
        double r70033 = M;
        double r70034 = r70033 * r70033;
        double r70035 = r70032 - r70034;
        double r70036 = sqrt(r70035);
        double r70037 = r70031 + r70036;
        double r70038 = r70022 * r70037;
        return r70038;
}
↓
double f(double c0, double __attribute__((unused)) w, double __attribute__((unused)) h, double __attribute__((unused)) D, double __attribute__((unused)) d, double __attribute__((unused)) M) {
        double r70039 = c0;
        double r70040 = 0.0;
        double r70041 = r70039 * r70040;
        return r70041;
}

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 35.2

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

  4. Applied div-inv35.2

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

  5. Applied associate-*l*33.5

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

  6. Simplified33.5

    \[\leadsto c0 \cdot \color{blue}{0}\]

  7. Final simplification33.5

    \[\leadsto c0 \cdot 0\]

Reproduce

herbie shell --seed 2020046 +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))))))