Average Error: 0.1 → 0.0
Time: 5.6s
Precision: 64
\[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c\]
↓
\[\mathsf{fma}\left(z, \frac{t}{16}, \mathsf{fma}\left(y, x, \mathsf{fma}\left(-\frac{a}{4}, b, c\right)\right)\right)\]
\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 r186157 = x;
        double r186158 = y;
        double r186159 = r186157 * r186158;
        double r186160 = z;
        double r186161 = t;
        double r186162 = r186160 * r186161;
        double r186163 = 16.0;
        double r186164 = r186162 / r186163;
        double r186165 = r186159 + r186164;
        double r186166 = a;
        double r186167 = b;
        double r186168 = r186166 * r186167;
        double r186169 = 4.0;
        double r186170 = r186168 / r186169;
        double r186171 = r186165 - r186170;
        double r186172 = c;
        double r186173 = r186171 + r186172;
        return r186173;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r186174 = z;
        double r186175 = t;
        double r186176 = 16.0;
        double r186177 = r186175 / r186176;
        double r186178 = y;
        double r186179 = x;
        double r186180 = a;
        double r186181 = 4.0;
        double r186182 = r186180 / r186181;
        double r186183 = -r186182;
        double r186184 = b;
        double r186185 = c;
        double r186186 = fma(r186183, r186184, r186185);
        double r186187 = fma(r186178, r186179, r186186);
        double r186188 = fma(r186174, r186177, r186187);
        return r186188;
}

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

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

  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 2020057 +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))