Average Error: 0.1 → 0.1
Time: 17.4s
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 r202279 = x;
        double r202280 = y;
        double r202281 = r202279 * r202280;
        double r202282 = z;
        double r202283 = t;
        double r202284 = r202282 * r202283;
        double r202285 = 16.0;
        double r202286 = r202284 / r202285;
        double r202287 = r202281 + r202286;
        double r202288 = a;
        double r202289 = b;
        double r202290 = r202288 * r202289;
        double r202291 = 4.0;
        double r202292 = r202290 / r202291;
        double r202293 = r202287 - r202292;
        double r202294 = c;
        double r202295 = r202293 + r202294;
        return r202295;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r202296 = x;
        double r202297 = y;
        double r202298 = r202296 * r202297;
        double r202299 = z;
        double r202300 = t;
        double r202301 = 16.0;
        double r202302 = r202300 / r202301;
        double r202303 = r202299 * r202302;
        double r202304 = r202298 + r202303;
        double r202305 = a;
        double r202306 = b;
        double r202307 = r202305 * r202306;
        double r202308 = 4.0;
        double r202309 = r202307 / r202308;
        double r202310 = r202304 - r202309;
        double r202311 = c;
        double r202312 = r202310 + r202311;
        return r202312;
}

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 2019212 
(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))