Average Error: 0.1 → 0.0
Time: 23.8s
Precision: 64
\[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c\]
↓
\[\left(\left(z \cdot \frac{t}{16} + x \cdot y\right) - \frac{a \cdot b}{4}\right) + c\]
\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c
↓
\left(\left(z \cdot \frac{t}{16} + x \cdot y\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 r11158361 = x;
        double r11158362 = y;
        double r11158363 = r11158361 * r11158362;
        double r11158364 = z;
        double r11158365 = t;
        double r11158366 = r11158364 * r11158365;
        double r11158367 = 16.0;
        double r11158368 = r11158366 / r11158367;
        double r11158369 = r11158363 + r11158368;
        double r11158370 = a;
        double r11158371 = b;
        double r11158372 = r11158370 * r11158371;
        double r11158373 = 4.0;
        double r11158374 = r11158372 / r11158373;
        double r11158375 = r11158369 - r11158374;
        double r11158376 = c;
        double r11158377 = r11158375 + r11158376;
        return r11158377;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r11158378 = z;
        double r11158379 = t;
        double r11158380 = 16.0;
        double r11158381 = r11158379 / r11158380;
        double r11158382 = r11158378 * r11158381;
        double r11158383 = x;
        double r11158384 = y;
        double r11158385 = r11158383 * r11158384;
        double r11158386 = r11158382 + r11158385;
        double r11158387 = a;
        double r11158388 = b;
        double r11158389 = r11158387 * r11158388;
        double r11158390 = 4.0;
        double r11158391 = r11158389 / r11158390;
        double r11158392 = r11158386 - r11158391;
        double r11158393 = c;
        double r11158394 = r11158392 + r11158393;
        return r11158394;
}

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

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

Reproduce

herbie shell --seed 2019170 
(FPCore (x y z t a b c)
  :name "Diagrams.Solve.Polynomial:quartForm  from diagrams-solve-0.1, C"
  (+ (- (+ (* x y) (/ (* z t) 16.0)) (/ (* a b) 4.0)) c))