Average Error: 0.1 → 0.0
Time: 7.2s
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 r12310 = x;
        double r12311 = y;
        double r12312 = r12310 * r12311;
        double r12313 = z;
        double r12314 = t;
        double r12315 = r12313 * r12314;
        double r12316 = 16.0;
        double r12317 = r12315 / r12316;
        double r12318 = r12312 + r12317;
        double r12319 = a;
        double r12320 = b;
        double r12321 = r12319 * r12320;
        double r12322 = 4.0;
        double r12323 = r12321 / r12322;
        double r12324 = r12318 - r12323;
        double r12325 = c;
        double r12326 = r12324 + r12325;
        return r12326;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r12327 = z;
        double r12328 = 16.0;
        double r12329 = r12327 / r12328;
        double r12330 = t;
        double r12331 = x;
        double r12332 = y;
        double r12333 = a;
        double r12334 = 4.0;
        double r12335 = r12333 / r12334;
        double r12336 = b;
        double r12337 = -r12336;
        double r12338 = c;
        double r12339 = fma(r12335, r12337, r12338);
        double r12340 = fma(r12331, r12332, r12339);
        double r12341 = fma(r12329, r12330, r12340);
        return r12341;
}

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 2019315 +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))