Average Error: 0.2 → 0.1
Time: 4.4s
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 r207382 = x;
        double r207383 = y;
        double r207384 = r207382 * r207383;
        double r207385 = z;
        double r207386 = t;
        double r207387 = r207385 * r207386;
        double r207388 = 16.0;
        double r207389 = r207387 / r207388;
        double r207390 = r207384 + r207389;
        double r207391 = a;
        double r207392 = b;
        double r207393 = r207391 * r207392;
        double r207394 = 4.0;
        double r207395 = r207393 / r207394;
        double r207396 = r207390 - r207395;
        double r207397 = c;
        double r207398 = r207396 + r207397;
        return r207398;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r207399 = x;
        double r207400 = y;
        double r207401 = r207399 * r207400;
        double r207402 = z;
        double r207403 = t;
        double r207404 = 16.0;
        double r207405 = r207403 / r207404;
        double r207406 = r207402 * r207405;
        double r207407 = r207401 + r207406;
        double r207408 = a;
        double r207409 = b;
        double r207410 = r207408 * r207409;
        double r207411 = 4.0;
        double r207412 = r207410 / r207411;
        double r207413 = r207407 - r207412;
        double r207414 = c;
        double r207415 = r207413 + r207414;
        return r207415;
}

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 0.2

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

  3. Applied *-un-lft-identity0.2

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

  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 2020100 
(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))