Average Error: 0.1 → 0.0
Time: 14.4s
Precision: 64
\[\left(\left(x \cdot y + \frac{z \cdot t}{16.0}\right) - \frac{a \cdot b}{4.0}\right) + c\]
↓
\[\mathsf{fma}\left(\frac{t}{16.0}, z, \mathsf{fma}\left(y, x, c\right) - \frac{b \cdot a}{4.0}\right)\]
\left(\left(x \cdot y + \frac{z \cdot t}{16.0}\right) - \frac{a \cdot b}{4.0}\right) + c
↓
\mathsf{fma}\left(\frac{t}{16.0}, z, \mathsf{fma}\left(y, x, c\right) - \frac{b \cdot a}{4.0}\right)
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r5899848 = x;
        double r5899849 = y;
        double r5899850 = r5899848 * r5899849;
        double r5899851 = z;
        double r5899852 = t;
        double r5899853 = r5899851 * r5899852;
        double r5899854 = 16.0;
        double r5899855 = r5899853 / r5899854;
        double r5899856 = r5899850 + r5899855;
        double r5899857 = a;
        double r5899858 = b;
        double r5899859 = r5899857 * r5899858;
        double r5899860 = 4.0;
        double r5899861 = r5899859 / r5899860;
        double r5899862 = r5899856 - r5899861;
        double r5899863 = c;
        double r5899864 = r5899862 + r5899863;
        return r5899864;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r5899865 = t;
        double r5899866 = 16.0;
        double r5899867 = r5899865 / r5899866;
        double r5899868 = z;
        double r5899869 = y;
        double r5899870 = x;
        double r5899871 = c;
        double r5899872 = fma(r5899869, r5899870, r5899871);
        double r5899873 = b;
        double r5899874 = a;
        double r5899875 = r5899873 * r5899874;
        double r5899876 = 4.0;
        double r5899877 = r5899875 / r5899876;
        double r5899878 = r5899872 - r5899877;
        double r5899879 = fma(r5899867, r5899868, r5899878);
        return r5899879;
}

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

    \[\left(\left(x \cdot y + \frac{z \cdot t}{16.0}\right) - \frac{a \cdot b}{4.0}\right) + c\]

  2. Simplified0.0

    \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{t}{16.0}, z, \mathsf{fma}\left(y, x, c\right) - \frac{a \cdot b}{4.0}\right)}\]

  3. Final simplification0.0

    \[\leadsto \mathsf{fma}\left(\frac{t}{16.0}, z, \mathsf{fma}\left(y, x, c\right) - \frac{b \cdot a}{4.0}\right)\]

Reproduce

herbie shell --seed 2019162 +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))