Average Error: 0.1 → 0.0
Time: 4.6m
Precision: 64
\[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c\]
↓
\[\mathsf{fma}\left(\frac{z}{16}, t, \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{a}{4}, -b, c\right)\right)\right)\]
\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c
↓
\mathsf{fma}\left(\frac{z}{16}, t, \mathsf{fma}\left(x, y, \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 r239818 = x;
        double r239819 = y;
        double r239820 = r239818 * r239819;
        double r239821 = z;
        double r239822 = t;
        double r239823 = r239821 * r239822;
        double r239824 = 16.0;
        double r239825 = r239823 / r239824;
        double r239826 = r239820 + r239825;
        double r239827 = a;
        double r239828 = b;
        double r239829 = r239827 * r239828;
        double r239830 = 4.0;
        double r239831 = r239829 / r239830;
        double r239832 = r239826 - r239831;
        double r239833 = c;
        double r239834 = r239832 + r239833;
        return r239834;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r239835 = z;
        double r239836 = 16.0;
        double r239837 = r239835 / r239836;
        double r239838 = t;
        double r239839 = x;
        double r239840 = y;
        double r239841 = a;
        double r239842 = 4.0;
        double r239843 = r239841 / r239842;
        double r239844 = b;
        double r239845 = -r239844;
        double r239846 = c;
        double r239847 = fma(r239843, r239845, r239846);
        double r239848 = fma(r239839, r239840, r239847);
        double r239849 = fma(r239837, r239838, r239848);
        return r239849;
}

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

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019351 +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))