Average Error: 0.1 → 0.0
Time: 6.7s
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 r174224 = x;
        double r174225 = y;
        double r174226 = r174224 * r174225;
        double r174227 = z;
        double r174228 = t;
        double r174229 = r174227 * r174228;
        double r174230 = 16.0;
        double r174231 = r174229 / r174230;
        double r174232 = r174226 + r174231;
        double r174233 = a;
        double r174234 = b;
        double r174235 = r174233 * r174234;
        double r174236 = 4.0;
        double r174237 = r174235 / r174236;
        double r174238 = r174232 - r174237;
        double r174239 = c;
        double r174240 = r174238 + r174239;
        return r174240;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r174241 = z;
        double r174242 = 16.0;
        double r174243 = r174241 / r174242;
        double r174244 = t;
        double r174245 = x;
        double r174246 = y;
        double r174247 = a;
        double r174248 = 4.0;
        double r174249 = r174247 / r174248;
        double r174250 = b;
        double r174251 = -r174250;
        double r174252 = c;
        double r174253 = fma(r174249, r174251, r174252);
        double r174254 = fma(r174245, r174246, r174253);
        double r174255 = fma(r174243, r174244, r174254);
        return r174255;
}

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 2019323 +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))