Average Error: 0.1 → 0.1
Time: 10.2s
Precision: 64
\[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c\]
↓
\[\left(\left(x \cdot y + z \cdot \frac{t}{16}\right) - \frac{a \cdot b}{4}\right) + c\]
\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c
↓
\left(\left(x \cdot y + z \cdot \frac{t}{16}\right) - \frac{a \cdot b}{4}\right) + c
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r279263 = x;
        double r279264 = y;
        double r279265 = r279263 * r279264;
        double r279266 = z;
        double r279267 = t;
        double r279268 = r279266 * r279267;
        double r279269 = 16.0;
        double r279270 = r279268 / r279269;
        double r279271 = r279265 + r279270;
        double r279272 = a;
        double r279273 = b;
        double r279274 = r279272 * r279273;
        double r279275 = 4.0;
        double r279276 = r279274 / r279275;
        double r279277 = r279271 - r279276;
        double r279278 = c;
        double r279279 = r279277 + r279278;
        return r279279;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r279280 = x;
        double r279281 = y;
        double r279282 = r279280 * r279281;
        double r279283 = z;
        double r279284 = t;
        double r279285 = 16.0;
        double r279286 = r279284 / r279285;
        double r279287 = r279283 * r279286;
        double r279288 = r279282 + r279287;
        double r279289 = a;
        double r279290 = b;
        double r279291 = r279289 * r279290;
        double r279292 = 4.0;
        double r279293 = r279291 / r279292;
        double r279294 = r279288 - r279293;
        double r279295 = c;
        double r279296 = r279294 + r279295;
        return r279296;
}

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 *-un-lft-identity0.1

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

  4. Applied times-frac0.1

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

  5. Simplified0.1

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

  6. Final simplification0.1

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

Reproduce

herbie shell --seed 2020045 
(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))