Average Error: 0.1 → 0.0
Time: 5.8s
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 r226365 = x;
        double r226366 = y;
        double r226367 = r226365 * r226366;
        double r226368 = z;
        double r226369 = t;
        double r226370 = r226368 * r226369;
        double r226371 = 16.0;
        double r226372 = r226370 / r226371;
        double r226373 = r226367 + r226372;
        double r226374 = a;
        double r226375 = b;
        double r226376 = r226374 * r226375;
        double r226377 = 4.0;
        double r226378 = r226376 / r226377;
        double r226379 = r226373 - r226378;
        double r226380 = c;
        double r226381 = r226379 + r226380;
        return r226381;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r226382 = x;
        double r226383 = y;
        double r226384 = r226382 * r226383;
        double r226385 = z;
        double r226386 = t;
        double r226387 = 16.0;
        double r226388 = r226386 / r226387;
        double r226389 = r226385 * r226388;
        double r226390 = r226384 + r226389;
        double r226391 = a;
        double r226392 = b;
        double r226393 = r226391 * r226392;
        double r226394 = 4.0;
        double r226395 = r226393 / r226394;
        double r226396 = r226390 - r226395;
        double r226397 = c;
        double r226398 = r226396 + r226397;
        return r226398;
}

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-frac0.0

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

  5. Simplified0.0

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

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2020046 
(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))