Average Error: 0.1 → 0.0
Time: 4.7s
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 r119082 = x;
        double r119083 = y;
        double r119084 = r119082 * r119083;
        double r119085 = z;
        double r119086 = t;
        double r119087 = r119085 * r119086;
        double r119088 = 16.0;
        double r119089 = r119087 / r119088;
        double r119090 = r119084 + r119089;
        double r119091 = a;
        double r119092 = b;
        double r119093 = r119091 * r119092;
        double r119094 = 4.0;
        double r119095 = r119093 / r119094;
        double r119096 = r119090 - r119095;
        double r119097 = c;
        double r119098 = r119096 + r119097;
        return r119098;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r119099 = z;
        double r119100 = 16.0;
        double r119101 = r119099 / r119100;
        double r119102 = t;
        double r119103 = x;
        double r119104 = y;
        double r119105 = a;
        double r119106 = 4.0;
        double r119107 = r119105 / r119106;
        double r119108 = b;
        double r119109 = -r119108;
        double r119110 = c;
        double r119111 = fma(r119107, r119109, r119110);
        double r119112 = fma(r119103, r119104, r119111);
        double r119113 = fma(r119101, r119102, r119112);
        return r119113;
}

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 2019347 +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))