Average Error: 0.1 → 0.0
Time: 3.0s
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 r206222 = x;
        double r206223 = y;
        double r206224 = r206222 * r206223;
        double r206225 = z;
        double r206226 = t;
        double r206227 = r206225 * r206226;
        double r206228 = 16.0;
        double r206229 = r206227 / r206228;
        double r206230 = r206224 + r206229;
        double r206231 = a;
        double r206232 = b;
        double r206233 = r206231 * r206232;
        double r206234 = 4.0;
        double r206235 = r206233 / r206234;
        double r206236 = r206230 - r206235;
        double r206237 = c;
        double r206238 = r206236 + r206237;
        return r206238;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r206239 = z;
        double r206240 = 16.0;
        double r206241 = r206239 / r206240;
        double r206242 = t;
        double r206243 = x;
        double r206244 = y;
        double r206245 = a;
        double r206246 = 4.0;
        double r206247 = r206245 / r206246;
        double r206248 = b;
        double r206249 = -r206248;
        double r206250 = c;
        double r206251 = fma(r206247, r206249, r206250);
        double r206252 = fma(r206243, r206244, r206251);
        double r206253 = fma(r206241, r206242, r206252);
        return r206253;
}

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))