Average Error: 59.4 → 33.8
Time: 9.6s
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 r126015 = c0;
        double r126016 = 2.0;
        double r126017 = w;
        double r126018 = r126016 * r126017;
        double r126019 = r126015 / r126018;
        double r126020 = d;
        double r126021 = r126020 * r126020;
        double r126022 = r126015 * r126021;
        double r126023 = h;
        double r126024 = r126017 * r126023;
        double r126025 = D;
        double r126026 = r126025 * r126025;
        double r126027 = r126024 * r126026;
        double r126028 = r126022 / r126027;
        double r126029 = r126028 * r126028;
        double r126030 = M;
        double r126031 = r126030 * r126030;
        double r126032 = r126029 - r126031;
        double r126033 = sqrt(r126032);
        double r126034 = r126028 + r126033;
        double r126035 = r126019 * r126034;
        return r126035;
}
↓
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 r126036 = 0.0;
        return r126036;
}

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 35.7

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

  4. Applied *-un-lft-identity35.7

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

  5. Applied associate-*l*35.7

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

  6. Simplified33.8

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

  7. Final simplification33.8

    \[\leadsto 0\]

Reproduce

herbie shell --seed 2020020 
(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))))))