Average Error: 59.2 → 33.6
Time: 31.9s
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 r124479 = c0;
        double r124480 = 2.0;
        double r124481 = w;
        double r124482 = r124480 * r124481;
        double r124483 = r124479 / r124482;
        double r124484 = d;
        double r124485 = r124484 * r124484;
        double r124486 = r124479 * r124485;
        double r124487 = h;
        double r124488 = r124481 * r124487;
        double r124489 = D;
        double r124490 = r124489 * r124489;
        double r124491 = r124488 * r124490;
        double r124492 = r124486 / r124491;
        double r124493 = r124492 * r124492;
        double r124494 = M;
        double r124495 = r124494 * r124494;
        double r124496 = r124493 - r124495;
        double r124497 = sqrt(r124496);
        double r124498 = r124492 + r124497;
        double r124499 = r124483 * r124498;
        return r124499;
}
↓
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 r124500 = 0.0;
        return r124500;
}

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 35.3

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

  4. Applied *-un-lft-identity35.3

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

  5. Applied associate-*l*35.3

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

  6. Simplified33.6

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

  7. Final simplification33.6

    \[\leadsto 0\]

Reproduce

herbie shell --seed 2019298 
(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))))))