Average Error: 0.1 → 0.0
Time: 8.2s
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 r264533 = x;
        double r264534 = y;
        double r264535 = r264533 * r264534;
        double r264536 = z;
        double r264537 = t;
        double r264538 = r264536 * r264537;
        double r264539 = 16.0;
        double r264540 = r264538 / r264539;
        double r264541 = r264535 + r264540;
        double r264542 = a;
        double r264543 = b;
        double r264544 = r264542 * r264543;
        double r264545 = 4.0;
        double r264546 = r264544 / r264545;
        double r264547 = r264541 - r264546;
        double r264548 = c;
        double r264549 = r264547 + r264548;
        return r264549;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r264550 = z;
        double r264551 = 16.0;
        double r264552 = r264550 / r264551;
        double r264553 = t;
        double r264554 = x;
        double r264555 = y;
        double r264556 = a;
        double r264557 = 4.0;
        double r264558 = r264556 / r264557;
        double r264559 = b;
        double r264560 = -r264559;
        double r264561 = c;
        double r264562 = fma(r264558, r264560, r264561);
        double r264563 = fma(r264554, r264555, r264562);
        double r264564 = fma(r264552, r264553, r264563);
        return r264564;
}

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 2020047 +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))