Average Error: 0.2 → 0.1
Time: 5.3m
Precision: 64
\[\left(\left(x \cdot y + \frac{z \cdot t}{16.0}\right) - \frac{a \cdot b}{4.0}\right) + c\]
↓
\[\left(\left(z \cdot \frac{t}{16.0} + x \cdot y\right) - \frac{a \cdot b}{4.0}\right) + c\]
\left(\left(x \cdot y + \frac{z \cdot t}{16.0}\right) - \frac{a \cdot b}{4.0}\right) + c
↓
\left(\left(z \cdot \frac{t}{16.0} + x \cdot y\right) - \frac{a \cdot b}{4.0}\right) + c
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r9199419 = x;
        double r9199420 = y;
        double r9199421 = r9199419 * r9199420;
        double r9199422 = z;
        double r9199423 = t;
        double r9199424 = r9199422 * r9199423;
        double r9199425 = 16.0;
        double r9199426 = r9199424 / r9199425;
        double r9199427 = r9199421 + r9199426;
        double r9199428 = a;
        double r9199429 = b;
        double r9199430 = r9199428 * r9199429;
        double r9199431 = 4.0;
        double r9199432 = r9199430 / r9199431;
        double r9199433 = r9199427 - r9199432;
        double r9199434 = c;
        double r9199435 = r9199433 + r9199434;
        return r9199435;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r9199436 = z;
        double r9199437 = t;
        double r9199438 = 16.0;
        double r9199439 = r9199437 / r9199438;
        double r9199440 = r9199436 * r9199439;
        double r9199441 = x;
        double r9199442 = y;
        double r9199443 = r9199441 * r9199442;
        double r9199444 = r9199440 + r9199443;
        double r9199445 = a;
        double r9199446 = b;
        double r9199447 = r9199445 * r9199446;
        double r9199448 = 4.0;
        double r9199449 = r9199447 / r9199448;
        double r9199450 = r9199444 - r9199449;
        double r9199451 = c;
        double r9199452 = r9199450 + r9199451;
        return r9199452;
}

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

    \[\left(\left(x \cdot y + \frac{z \cdot t}{16.0}\right) - \frac{a \cdot b}{4.0}\right) + c\]
  2. Using strategy rm

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

    \[\leadsto \left(\left(x \cdot y + \frac{z \cdot t}{\color{blue}{1 \cdot 16.0}}\right) - \frac{a \cdot b}{4.0}\right) + c\]

  4. Applied times-frac0.1

    \[\leadsto \left(\left(x \cdot y + \color{blue}{\frac{z}{1} \cdot \frac{t}{16.0}}\right) - \frac{a \cdot b}{4.0}\right) + c\]

  5. Simplified0.1

    \[\leadsto \left(\left(x \cdot y + \color{blue}{z} \cdot \frac{t}{16.0}\right) - \frac{a \cdot b}{4.0}\right) + c\]

  6. Final simplification0.1

    \[\leadsto \left(\left(z \cdot \frac{t}{16.0} + x \cdot y\right) - \frac{a \cdot b}{4.0}\right) + c\]

Reproduce

herbie shell --seed 2019158 
(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))