Average Error: 0.1 → 0.0
Time: 8.9s
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 r272462 = x;
        double r272463 = y;
        double r272464 = r272462 * r272463;
        double r272465 = z;
        double r272466 = t;
        double r272467 = r272465 * r272466;
        double r272468 = 16.0;
        double r272469 = r272467 / r272468;
        double r272470 = r272464 + r272469;
        double r272471 = a;
        double r272472 = b;
        double r272473 = r272471 * r272472;
        double r272474 = 4.0;
        double r272475 = r272473 / r272474;
        double r272476 = r272470 - r272475;
        double r272477 = c;
        double r272478 = r272476 + r272477;
        return r272478;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r272479 = x;
        double r272480 = y;
        double r272481 = r272479 * r272480;
        double r272482 = z;
        double r272483 = t;
        double r272484 = 16.0;
        double r272485 = r272483 / r272484;
        double r272486 = r272482 * r272485;
        double r272487 = r272481 + r272486;
        double r272488 = a;
        double r272489 = b;
        double r272490 = r272488 * r272489;
        double r272491 = 4.0;
        double r272492 = r272490 / r272491;
        double r272493 = r272487 - r272492;
        double r272494 = c;
        double r272495 = r272493 + r272494;
        return r272495;
}

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))