Average Error: 0.1 → 0.1
Time: 15.0s
Precision: 64
\[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c\]
↓
\[\left(\left(x \cdot y + \frac{z}{\sqrt{16}} \cdot \frac{t}{\sqrt{16}}\right) - \frac{1}{\frac{4}{a \cdot b}}\right) + c\]
\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c
↓
\left(\left(x \cdot y + \frac{z}{\sqrt{16}} \cdot \frac{t}{\sqrt{16}}\right) - \frac{1}{\frac{4}{a \cdot b}}\right) + c
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r224227 = x;
        double r224228 = y;
        double r224229 = r224227 * r224228;
        double r224230 = z;
        double r224231 = t;
        double r224232 = r224230 * r224231;
        double r224233 = 16.0;
        double r224234 = r224232 / r224233;
        double r224235 = r224229 + r224234;
        double r224236 = a;
        double r224237 = b;
        double r224238 = r224236 * r224237;
        double r224239 = 4.0;
        double r224240 = r224238 / r224239;
        double r224241 = r224235 - r224240;
        double r224242 = c;
        double r224243 = r224241 + r224242;
        return r224243;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r224244 = x;
        double r224245 = y;
        double r224246 = r224244 * r224245;
        double r224247 = z;
        double r224248 = 16.0;
        double r224249 = sqrt(r224248);
        double r224250 = r224247 / r224249;
        double r224251 = t;
        double r224252 = r224251 / r224249;
        double r224253 = r224250 * r224252;
        double r224254 = r224246 + r224253;
        double r224255 = 1.0;
        double r224256 = 4.0;
        double r224257 = a;
        double r224258 = b;
        double r224259 = r224257 * r224258;
        double r224260 = r224256 / r224259;
        double r224261 = r224255 / r224260;
        double r224262 = r224254 - r224261;
        double r224263 = c;
        double r224264 = r224262 + r224263;
        return r224264;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Bits error versus b

Bits error versus c

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.1

    \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c\]
  2. Using strategy rm

  3. Applied add-sqr-sqrt0.1

    \[\leadsto \left(\left(x \cdot y + \frac{z \cdot t}{\color{blue}{\sqrt{16} \cdot \sqrt{16}}}\right) - \frac{a \cdot b}{4}\right) + c\]

  4. Applied times-frac0.1

    \[\leadsto \left(\left(x \cdot y + \color{blue}{\frac{z}{\sqrt{16}} \cdot \frac{t}{\sqrt{16}}}\right) - \frac{a \cdot b}{4}\right) + c\]
  5. Using strategy rm

  6. Applied clear-num0.1

    \[\leadsto \left(\left(x \cdot y + \frac{z}{\sqrt{16}} \cdot \frac{t}{\sqrt{16}}\right) - \color{blue}{\frac{1}{\frac{4}{a \cdot b}}}\right) + c\]

  7. Final simplification0.1

    \[\leadsto \left(\left(x \cdot y + \frac{z}{\sqrt{16}} \cdot \frac{t}{\sqrt{16}}\right) - \frac{1}{\frac{4}{a \cdot b}}\right) + c\]

Reproduce

herbie shell --seed 2019303 
(FPCore (x y z t a b c)
  :name "Diagrams.Solve.Polynomial:quartForm  from diagrams-solve-0.1, C"
  :precision binary64
  (+ (- (+ (* x y) (/ (* z t) 16)) (/ (* a b) 4)) c))