Average Error: 0.1 → 0.0
Time: 1.7s
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 r193958 = x;
        double r193959 = y;
        double r193960 = r193958 * r193959;
        double r193961 = z;
        double r193962 = t;
        double r193963 = r193961 * r193962;
        double r193964 = 16.0;
        double r193965 = r193963 / r193964;
        double r193966 = r193960 + r193965;
        double r193967 = a;
        double r193968 = b;
        double r193969 = r193967 * r193968;
        double r193970 = 4.0;
        double r193971 = r193969 / r193970;
        double r193972 = r193966 - r193971;
        double r193973 = c;
        double r193974 = r193972 + r193973;
        return r193974;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r193975 = z;
        double r193976 = t;
        double r193977 = 16.0;
        double r193978 = r193976 / r193977;
        double r193979 = y;
        double r193980 = x;
        double r193981 = a;
        double r193982 = 4.0;
        double r193983 = r193981 / r193982;
        double r193984 = -r193983;
        double r193985 = b;
        double r193986 = c;
        double r193987 = fma(r193984, r193985, r193986);
        double r193988 = fma(r193979, r193980, r193987);
        double r193989 = fma(r193975, r193978, r193988);
        return r193989;
}

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 2020002 +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))