Average Error: 0.1 → 0.1
Time: 21.1s
Precision: 64
\[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c\]
↓
\[\left(\left(\frac{z}{\frac{16}{t}} + x \cdot y\right) - \frac{a \cdot b}{4}\right) + c\]
\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c
↓
\left(\left(\frac{z}{\frac{16}{t}} + 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 r183444 = x;
        double r183445 = y;
        double r183446 = r183444 * r183445;
        double r183447 = z;
        double r183448 = t;
        double r183449 = r183447 * r183448;
        double r183450 = 16.0;
        double r183451 = r183449 / r183450;
        double r183452 = r183446 + r183451;
        double r183453 = a;
        double r183454 = b;
        double r183455 = r183453 * r183454;
        double r183456 = 4.0;
        double r183457 = r183455 / r183456;
        double r183458 = r183452 - r183457;
        double r183459 = c;
        double r183460 = r183458 + r183459;
        return r183460;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r183461 = z;
        double r183462 = 16.0;
        double r183463 = t;
        double r183464 = r183462 / r183463;
        double r183465 = r183461 / r183464;
        double r183466 = x;
        double r183467 = y;
        double r183468 = r183466 * r183467;
        double r183469 = r183465 + r183468;
        double r183470 = a;
        double r183471 = b;
        double r183472 = r183470 * r183471;
        double r183473 = 4.0;
        double r183474 = r183472 / r183473;
        double r183475 = r183469 - r183474;
        double r183476 = c;
        double r183477 = r183475 + r183476;
        return r183477;
}

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 associate-/l*0.1

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

  4. Final simplification0.1

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

Reproduce

herbie shell --seed 2019194 
(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))