Average Error: 0.1 → 0.0
Time: 17.5s
Precision: 64
\[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c\]
↓
\[\mathsf{fma}\left(t, \frac{z}{16}, \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{-b}{4}, a, c\right)\right)\right)\]
\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c
↓
\mathsf{fma}\left(t, \frac{z}{16}, \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{-b}{4}, a, c\right)\right)\right)
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r222112 = x;
        double r222113 = y;
        double r222114 = r222112 * r222113;
        double r222115 = z;
        double r222116 = t;
        double r222117 = r222115 * r222116;
        double r222118 = 16.0;
        double r222119 = r222117 / r222118;
        double r222120 = r222114 + r222119;
        double r222121 = a;
        double r222122 = b;
        double r222123 = r222121 * r222122;
        double r222124 = 4.0;
        double r222125 = r222123 / r222124;
        double r222126 = r222120 - r222125;
        double r222127 = c;
        double r222128 = r222126 + r222127;
        return r222128;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r222129 = t;
        double r222130 = z;
        double r222131 = 16.0;
        double r222132 = r222130 / r222131;
        double r222133 = x;
        double r222134 = y;
        double r222135 = b;
        double r222136 = -r222135;
        double r222137 = 4.0;
        double r222138 = r222136 / r222137;
        double r222139 = a;
        double r222140 = c;
        double r222141 = fma(r222138, r222139, r222140);
        double r222142 = fma(r222133, r222134, r222141);
        double r222143 = fma(r222129, r222132, r222142);
        return r222143;
}

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

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019194 +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))