Average Error: 0.1 → 0.0
Time: 5.6s
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 r24211 = x;
        double r24212 = y;
        double r24213 = r24211 * r24212;
        double r24214 = z;
        double r24215 = t;
        double r24216 = r24214 * r24215;
        double r24217 = 16.0;
        double r24218 = r24216 / r24217;
        double r24219 = r24213 + r24218;
        double r24220 = a;
        double r24221 = b;
        double r24222 = r24220 * r24221;
        double r24223 = 4.0;
        double r24224 = r24222 / r24223;
        double r24225 = r24219 - r24224;
        double r24226 = c;
        double r24227 = r24225 + r24226;
        return r24227;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r24228 = z;
        double r24229 = 16.0;
        double r24230 = r24228 / r24229;
        double r24231 = t;
        double r24232 = x;
        double r24233 = y;
        double r24234 = a;
        double r24235 = 4.0;
        double r24236 = r24234 / r24235;
        double r24237 = b;
        double r24238 = -r24237;
        double r24239 = c;
        double r24240 = fma(r24236, r24238, r24239);
        double r24241 = fma(r24232, r24233, r24240);
        double r24242 = fma(r24230, r24231, r24241);
        return r24242;
}

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 2019310 +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))