Average Error: 0.1 → 0.0
Time: 11.1s
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 r147168 = x;
        double r147169 = y;
        double r147170 = r147168 * r147169;
        double r147171 = z;
        double r147172 = t;
        double r147173 = r147171 * r147172;
        double r147174 = 16.0;
        double r147175 = r147173 / r147174;
        double r147176 = r147170 + r147175;
        double r147177 = a;
        double r147178 = b;
        double r147179 = r147177 * r147178;
        double r147180 = 4.0;
        double r147181 = r147179 / r147180;
        double r147182 = r147176 - r147181;
        double r147183 = c;
        double r147184 = r147182 + r147183;
        return r147184;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r147185 = z;
        double r147186 = 16.0;
        double r147187 = r147185 / r147186;
        double r147188 = t;
        double r147189 = x;
        double r147190 = y;
        double r147191 = a;
        double r147192 = 4.0;
        double r147193 = r147191 / r147192;
        double r147194 = b;
        double r147195 = -r147194;
        double r147196 = c;
        double r147197 = fma(r147193, r147195, r147196);
        double r147198 = fma(r147189, r147190, r147197);
        double r147199 = fma(r147187, r147188, r147198);
        return r147199;
}

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 2019303 +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))