Average Error: 0.2 → 0.1
Time: 8.8m
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 r4829312 = x;
        double r4829313 = y;
        double r4829314 = r4829312 * r4829313;
        double r4829315 = z;
        double r4829316 = t;
        double r4829317 = r4829315 * r4829316;
        double r4829318 = 16.0;
        double r4829319 = r4829317 / r4829318;
        double r4829320 = r4829314 + r4829319;
        double r4829321 = a;
        double r4829322 = b;
        double r4829323 = r4829321 * r4829322;
        double r4829324 = 4.0;
        double r4829325 = r4829323 / r4829324;
        double r4829326 = r4829320 - r4829325;
        double r4829327 = c;
        double r4829328 = r4829326 + r4829327;
        return r4829328;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r4829329 = z;
        double r4829330 = t;
        double r4829331 = 16.0;
        double r4829332 = r4829330 / r4829331;
        double r4829333 = r4829329 * r4829332;
        double r4829334 = x;
        double r4829335 = y;
        double r4829336 = r4829334 * r4829335;
        double r4829337 = r4829333 + r4829336;
        double r4829338 = a;
        double r4829339 = b;
        double r4829340 = r4829338 * r4829339;
        double r4829341 = 4.0;
        double r4829342 = r4829340 / r4829341;
        double r4829343 = r4829337 - r4829342;
        double r4829344 = c;
        double r4829345 = r4829343 + r4829344;
        return r4829345;
}

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))