Average Error: 0.1 → 0.0
Time: 3.1s
Precision: 64
\[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c\]
↓
\[\mathsf{fma}\left(z, \frac{t}{16}, \mathsf{fma}\left(y, x, \mathsf{fma}\left(-\frac{a}{4}, b, c\right)\right)\right)\]
\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c
↓
\mathsf{fma}\left(z, \frac{t}{16}, \mathsf{fma}\left(y, x, \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 r216907 = x;
        double r216908 = y;
        double r216909 = r216907 * r216908;
        double r216910 = z;
        double r216911 = t;
        double r216912 = r216910 * r216911;
        double r216913 = 16.0;
        double r216914 = r216912 / r216913;
        double r216915 = r216909 + r216914;
        double r216916 = a;
        double r216917 = b;
        double r216918 = r216916 * r216917;
        double r216919 = 4.0;
        double r216920 = r216918 / r216919;
        double r216921 = r216915 - r216920;
        double r216922 = c;
        double r216923 = r216921 + r216922;
        return r216923;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r216924 = z;
        double r216925 = t;
        double r216926 = 16.0;
        double r216927 = r216925 / r216926;
        double r216928 = y;
        double r216929 = x;
        double r216930 = a;
        double r216931 = 4.0;
        double r216932 = r216930 / r216931;
        double r216933 = -r216932;
        double r216934 = b;
        double r216935 = c;
        double r216936 = fma(r216933, r216934, r216935);
        double r216937 = fma(r216928, r216929, r216936);
        double r216938 = fma(r216924, r216927, r216937);
        return r216938;
}

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

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019354 +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))