Average Error: 0.2 → 0.0
Time: 5.9m
Precision: 64
\[\left(\left(x \cdot y + \frac{z \cdot t}{16.0}\right) - \frac{a \cdot b}{4.0}\right) + c\]
↓
\[\mathsf{fma}\left(\frac{t}{16.0}, z, \mathsf{fma}\left(y, x, c\right) - \frac{b \cdot a}{4.0}\right)\]
\left(\left(x \cdot y + \frac{z \cdot t}{16.0}\right) - \frac{a \cdot b}{4.0}\right) + c
↓
\mathsf{fma}\left(\frac{t}{16.0}, z, \mathsf{fma}\left(y, x, c\right) - \frac{b \cdot a}{4.0}\right)
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r9372315 = x;
        double r9372316 = y;
        double r9372317 = r9372315 * r9372316;
        double r9372318 = z;
        double r9372319 = t;
        double r9372320 = r9372318 * r9372319;
        double r9372321 = 16.0;
        double r9372322 = r9372320 / r9372321;
        double r9372323 = r9372317 + r9372322;
        double r9372324 = a;
        double r9372325 = b;
        double r9372326 = r9372324 * r9372325;
        double r9372327 = 4.0;
        double r9372328 = r9372326 / r9372327;
        double r9372329 = r9372323 - r9372328;
        double r9372330 = c;
        double r9372331 = r9372329 + r9372330;
        return r9372331;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r9372332 = t;
        double r9372333 = 16.0;
        double r9372334 = r9372332 / r9372333;
        double r9372335 = z;
        double r9372336 = y;
        double r9372337 = x;
        double r9372338 = c;
        double r9372339 = fma(r9372336, r9372337, r9372338);
        double r9372340 = b;
        double r9372341 = a;
        double r9372342 = r9372340 * r9372341;
        double r9372343 = 4.0;
        double r9372344 = r9372342 / r9372343;
        double r9372345 = r9372339 - r9372344;
        double r9372346 = fma(r9372334, r9372335, r9372345);
        return r9372346;
}

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 0.2

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

  2. Simplified0.0

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019158 +o rules:numerics
(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))