Average Error: 0.1 → 0.0
Time: 6.7m
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 r195117 = x;
        double r195118 = y;
        double r195119 = r195117 * r195118;
        double r195120 = z;
        double r195121 = t;
        double r195122 = r195120 * r195121;
        double r195123 = 16.0;
        double r195124 = r195122 / r195123;
        double r195125 = r195119 + r195124;
        double r195126 = a;
        double r195127 = b;
        double r195128 = r195126 * r195127;
        double r195129 = 4.0;
        double r195130 = r195128 / r195129;
        double r195131 = r195125 - r195130;
        double r195132 = c;
        double r195133 = r195131 + r195132;
        return r195133;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r195134 = z;
        double r195135 = 16.0;
        double r195136 = r195134 / r195135;
        double r195137 = t;
        double r195138 = x;
        double r195139 = y;
        double r195140 = a;
        double r195141 = 4.0;
        double r195142 = r195140 / r195141;
        double r195143 = b;
        double r195144 = -r195143;
        double r195145 = c;
        double r195146 = fma(r195142, r195144, r195145);
        double r195147 = fma(r195138, r195139, r195146);
        double r195148 = fma(r195136, r195137, r195147);
        return r195148;
}

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 2019199 +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))