Average Error: 0.1 → 0.0
Time: 4.3s
Precision: 64
\[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c\]
↓
\[\mathsf{fma}\left(\frac{z}{16}, t, \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{a}{4}, -b, c\right)\right)\right)\]
\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c
↓
\mathsf{fma}\left(\frac{z}{16}, t, \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{a}{4}, -b, c\right)\right)\right)
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r46317 = x;
        double r46318 = y;
        double r46319 = r46317 * r46318;
        double r46320 = z;
        double r46321 = t;
        double r46322 = r46320 * r46321;
        double r46323 = 16.0;
        double r46324 = r46322 / r46323;
        double r46325 = r46319 + r46324;
        double r46326 = a;
        double r46327 = b;
        double r46328 = r46326 * r46327;
        double r46329 = 4.0;
        double r46330 = r46328 / r46329;
        double r46331 = r46325 - r46330;
        double r46332 = c;
        double r46333 = r46331 + r46332;
        return r46333;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r46334 = z;
        double r46335 = 16.0;
        double r46336 = r46334 / r46335;
        double r46337 = t;
        double r46338 = x;
        double r46339 = y;
        double r46340 = a;
        double r46341 = 4.0;
        double r46342 = r46340 / r46341;
        double r46343 = b;
        double r46344 = -r46343;
        double r46345 = c;
        double r46346 = fma(r46342, r46344, r46345);
        double r46347 = fma(r46338, r46339, r46346);
        double r46348 = fma(r46336, r46337, r46347);
        return r46348;
}

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

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. Simplified0.0

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2020045 +o rules:numerics
(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))