Average Error: 0.2 → 0.0
Time: 7.8s
Precision: 64
\[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c\]
↓
\[\mathsf{fma}\left(t, \frac{z}{16}, \mathsf{fma}\left(x, y, c - \frac{a \cdot b}{4}\right)\right)\]
\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c
↓
\mathsf{fma}\left(t, \frac{z}{16}, \mathsf{fma}\left(x, y, c - \frac{a \cdot b}{4}\right)\right)
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r15018804 = x;
        double r15018805 = y;
        double r15018806 = r15018804 * r15018805;
        double r15018807 = z;
        double r15018808 = t;
        double r15018809 = r15018807 * r15018808;
        double r15018810 = 16.0;
        double r15018811 = r15018809 / r15018810;
        double r15018812 = r15018806 + r15018811;
        double r15018813 = a;
        double r15018814 = b;
        double r15018815 = r15018813 * r15018814;
        double r15018816 = 4.0;
        double r15018817 = r15018815 / r15018816;
        double r15018818 = r15018812 - r15018817;
        double r15018819 = c;
        double r15018820 = r15018818 + r15018819;
        return r15018820;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r15018821 = t;
        double r15018822 = z;
        double r15018823 = 16.0;
        double r15018824 = r15018822 / r15018823;
        double r15018825 = x;
        double r15018826 = y;
        double r15018827 = c;
        double r15018828 = a;
        double r15018829 = b;
        double r15018830 = r15018828 * r15018829;
        double r15018831 = 4.0;
        double r15018832 = r15018830 / r15018831;
        double r15018833 = r15018827 - r15018832;
        double r15018834 = fma(r15018825, r15018826, r15018833);
        double r15018835 = fma(r15018821, r15018824, r15018834);
        return r15018835;
}

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

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019174 +o rules:numerics
(FPCore (x y z t a b c)
  :name "Diagrams.Solve.Polynomial:quartForm  from diagrams-solve-0.1, C"
  (+ (- (+ (* x y) (/ (* z t) 16.0)) (/ (* a b) 4.0)) c))