Average Error: 0.2 → 0.0
Time: 5.8s
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 r193481 = x;
        double r193482 = y;
        double r193483 = r193481 * r193482;
        double r193484 = z;
        double r193485 = t;
        double r193486 = r193484 * r193485;
        double r193487 = 16.0;
        double r193488 = r193486 / r193487;
        double r193489 = r193483 + r193488;
        double r193490 = a;
        double r193491 = b;
        double r193492 = r193490 * r193491;
        double r193493 = 4.0;
        double r193494 = r193492 / r193493;
        double r193495 = r193489 - r193494;
        double r193496 = c;
        double r193497 = r193495 + r193496;
        return r193497;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r193498 = z;
        double r193499 = t;
        double r193500 = 16.0;
        double r193501 = r193499 / r193500;
        double r193502 = y;
        double r193503 = x;
        double r193504 = a;
        double r193505 = 4.0;
        double r193506 = r193504 / r193505;
        double r193507 = -r193506;
        double r193508 = b;
        double r193509 = c;
        double r193510 = fma(r193507, r193508, r193509);
        double r193511 = fma(r193502, r193503, r193510);
        double r193512 = fma(r193498, r193501, r193511);
        return r193512;
}

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

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

  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 2020001 +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))