Average Error: 0.2 → 0.0
Time: 8.6s
Precision: 64
\[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c\]
↓
\[\mathsf{fma}\left(\frac{t}{16}, z, \mathsf{fma}\left(y, x, c\right) - \frac{b \cdot a}{4}\right)\]
\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c
↓
\mathsf{fma}\left(\frac{t}{16}, z, \mathsf{fma}\left(y, x, c\right) - \frac{b \cdot a}{4}\right)
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r7571159 = x;
        double r7571160 = y;
        double r7571161 = r7571159 * r7571160;
        double r7571162 = z;
        double r7571163 = t;
        double r7571164 = r7571162 * r7571163;
        double r7571165 = 16.0;
        double r7571166 = r7571164 / r7571165;
        double r7571167 = r7571161 + r7571166;
        double r7571168 = a;
        double r7571169 = b;
        double r7571170 = r7571168 * r7571169;
        double r7571171 = 4.0;
        double r7571172 = r7571170 / r7571171;
        double r7571173 = r7571167 - r7571172;
        double r7571174 = c;
        double r7571175 = r7571173 + r7571174;
        return r7571175;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r7571176 = t;
        double r7571177 = 16.0;
        double r7571178 = r7571176 / r7571177;
        double r7571179 = z;
        double r7571180 = y;
        double r7571181 = x;
        double r7571182 = c;
        double r7571183 = fma(r7571180, r7571181, r7571182);
        double r7571184 = b;
        double r7571185 = a;
        double r7571186 = r7571184 * r7571185;
        double r7571187 = 4.0;
        double r7571188 = r7571186 / r7571187;
        double r7571189 = r7571183 - r7571188;
        double r7571190 = fma(r7571178, r7571179, r7571189);
        return r7571190;
}

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

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019169 +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))