Average Error: 0.2 → 0.0
Time: 5.0s
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 r115158 = x;
        double r115159 = y;
        double r115160 = r115158 * r115159;
        double r115161 = z;
        double r115162 = t;
        double r115163 = r115161 * r115162;
        double r115164 = 16.0;
        double r115165 = r115163 / r115164;
        double r115166 = r115160 + r115165;
        double r115167 = a;
        double r115168 = b;
        double r115169 = r115167 * r115168;
        double r115170 = 4.0;
        double r115171 = r115169 / r115170;
        double r115172 = r115166 - r115171;
        double r115173 = c;
        double r115174 = r115172 + r115173;
        return r115174;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r115175 = z;
        double r115176 = 16.0;
        double r115177 = r115175 / r115176;
        double r115178 = t;
        double r115179 = x;
        double r115180 = y;
        double r115181 = a;
        double r115182 = 4.0;
        double r115183 = r115181 / r115182;
        double r115184 = b;
        double r115185 = -r115184;
        double r115186 = c;
        double r115187 = fma(r115183, r115185, r115186);
        double r115188 = fma(r115179, r115180, r115187);
        double r115189 = fma(r115177, r115178, r115188);
        return r115189;
}

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 0.2

    \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c\]

  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 2019322 +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))