Average Error: 0.1 → 0.0
Time: 7.0s
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 r114733 = x;
        double r114734 = y;
        double r114735 = r114733 * r114734;
        double r114736 = z;
        double r114737 = t;
        double r114738 = r114736 * r114737;
        double r114739 = 16.0;
        double r114740 = r114738 / r114739;
        double r114741 = r114735 + r114740;
        double r114742 = a;
        double r114743 = b;
        double r114744 = r114742 * r114743;
        double r114745 = 4.0;
        double r114746 = r114744 / r114745;
        double r114747 = r114741 - r114746;
        double r114748 = c;
        double r114749 = r114747 + r114748;
        return r114749;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r114750 = z;
        double r114751 = 16.0;
        double r114752 = r114750 / r114751;
        double r114753 = t;
        double r114754 = x;
        double r114755 = y;
        double r114756 = a;
        double r114757 = 4.0;
        double r114758 = r114756 / r114757;
        double r114759 = b;
        double r114760 = -r114759;
        double r114761 = c;
        double r114762 = fma(r114758, r114760, r114761);
        double r114763 = fma(r114754, r114755, r114762);
        double r114764 = fma(r114752, r114753, r114763);
        return r114764;
}

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 2019325 +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))