Average Error: 0.2 → 0.0
Time: 6.2s
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 r254743 = x;
        double r254744 = y;
        double r254745 = r254743 * r254744;
        double r254746 = z;
        double r254747 = t;
        double r254748 = r254746 * r254747;
        double r254749 = 16.0;
        double r254750 = r254748 / r254749;
        double r254751 = r254745 + r254750;
        double r254752 = a;
        double r254753 = b;
        double r254754 = r254752 * r254753;
        double r254755 = 4.0;
        double r254756 = r254754 / r254755;
        double r254757 = r254751 - r254756;
        double r254758 = c;
        double r254759 = r254757 + r254758;
        return r254759;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r254760 = z;
        double r254761 = t;
        double r254762 = 16.0;
        double r254763 = r254761 / r254762;
        double r254764 = y;
        double r254765 = x;
        double r254766 = a;
        double r254767 = 4.0;
        double r254768 = r254766 / r254767;
        double r254769 = -r254768;
        double r254770 = b;
        double r254771 = c;
        double r254772 = fma(r254769, r254770, r254771);
        double r254773 = fma(r254764, r254765, r254772);
        double r254774 = fma(r254760, r254763, r254773);
        return r254774;
}

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 2020100 +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))