Average Error: 0.1 → 0.0
Time: 4.7s
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 r225238 = x;
        double r225239 = y;
        double r225240 = r225238 * r225239;
        double r225241 = z;
        double r225242 = t;
        double r225243 = r225241 * r225242;
        double r225244 = 16.0;
        double r225245 = r225243 / r225244;
        double r225246 = r225240 + r225245;
        double r225247 = a;
        double r225248 = b;
        double r225249 = r225247 * r225248;
        double r225250 = 4.0;
        double r225251 = r225249 / r225250;
        double r225252 = r225246 - r225251;
        double r225253 = c;
        double r225254 = r225252 + r225253;
        return r225254;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r225255 = z;
        double r225256 = 16.0;
        double r225257 = r225255 / r225256;
        double r225258 = t;
        double r225259 = x;
        double r225260 = y;
        double r225261 = a;
        double r225262 = 4.0;
        double r225263 = r225261 / r225262;
        double r225264 = b;
        double r225265 = -r225264;
        double r225266 = c;
        double r225267 = fma(r225263, r225265, r225266);
        double r225268 = fma(r225259, r225260, r225267);
        double r225269 = fma(r225257, r225258, r225268);
        return r225269;
}

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))