Average Error: 0.2 → 0.0
Time: 8.0s
Precision: 64
\[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c\]
↓
\[\mathsf{fma}\left(t, \frac{z}{16}, \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{-b}{4}, a, c\right)\right)\right)\]
\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c
↓
\mathsf{fma}\left(t, \frac{z}{16}, \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{-b}{4}, a, c\right)\right)\right)
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r130997 = x;
        double r130998 = y;
        double r130999 = r130997 * r130998;
        double r131000 = z;
        double r131001 = t;
        double r131002 = r131000 * r131001;
        double r131003 = 16.0;
        double r131004 = r131002 / r131003;
        double r131005 = r130999 + r131004;
        double r131006 = a;
        double r131007 = b;
        double r131008 = r131006 * r131007;
        double r131009 = 4.0;
        double r131010 = r131008 / r131009;
        double r131011 = r131005 - r131010;
        double r131012 = c;
        double r131013 = r131011 + r131012;
        return r131013;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r131014 = t;
        double r131015 = z;
        double r131016 = 16.0;
        double r131017 = r131015 / r131016;
        double r131018 = x;
        double r131019 = y;
        double r131020 = b;
        double r131021 = -r131020;
        double r131022 = 4.0;
        double r131023 = r131021 / r131022;
        double r131024 = a;
        double r131025 = c;
        double r131026 = fma(r131023, r131024, r131025);
        double r131027 = fma(r131018, r131019, r131026);
        double r131028 = fma(r131014, r131017, r131027);
        return r131028;
}

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

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

  3. Final simplification0.0

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

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))