Average Error: 0.2 → 0.0
Time: 5.9s
Precision: 64
\[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c\]
↓
\[\mathsf{fma}\left(z, \frac{t}{16}, \mathsf{fma}\left(y, x, \mathsf{fma}\left(-\frac{a}{4}, b, c\right)\right)\right)\]
\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c
↓
\mathsf{fma}\left(z, \frac{t}{16}, \mathsf{fma}\left(y, x, \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 r207244 = x;
        double r207245 = y;
        double r207246 = r207244 * r207245;
        double r207247 = z;
        double r207248 = t;
        double r207249 = r207247 * r207248;
        double r207250 = 16.0;
        double r207251 = r207249 / r207250;
        double r207252 = r207246 + r207251;
        double r207253 = a;
        double r207254 = b;
        double r207255 = r207253 * r207254;
        double r207256 = 4.0;
        double r207257 = r207255 / r207256;
        double r207258 = r207252 - r207257;
        double r207259 = c;
        double r207260 = r207258 + r207259;
        return r207260;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r207261 = z;
        double r207262 = t;
        double r207263 = 16.0;
        double r207264 = r207262 / r207263;
        double r207265 = y;
        double r207266 = x;
        double r207267 = a;
        double r207268 = 4.0;
        double r207269 = r207267 / r207268;
        double r207270 = -r207269;
        double r207271 = b;
        double r207272 = c;
        double r207273 = fma(r207270, r207271, r207272);
        double r207274 = fma(r207265, r207266, r207273);
        double r207275 = fma(r207261, r207264, r207274);
        return r207275;
}

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

    \[\leadsto \color{blue}{\mathsf{fma}\left(z, \frac{t}{16}, \mathsf{fma}\left(y, x, \mathsf{fma}\left(-\frac{a}{4}, b, c\right)\right)\right)}\]

  3. Final simplification0.0

    \[\leadsto \mathsf{fma}\left(z, \frac{t}{16}, \mathsf{fma}\left(y, x, \mathsf{fma}\left(-\frac{a}{4}, b, c\right)\right)\right)\]

Reproduce

herbie shell --seed 2020001 +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))