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 r183399 = x;
        double r183400 = y;
        double r183401 = r183399 * r183400;
        double r183402 = z;
        double r183403 = t;
        double r183404 = r183402 * r183403;
        double r183405 = 16.0;
        double r183406 = r183404 / r183405;
        double r183407 = r183401 + r183406;
        double r183408 = a;
        double r183409 = b;
        double r183410 = r183408 * r183409;
        double r183411 = 4.0;
        double r183412 = r183410 / r183411;
        double r183413 = r183407 - r183412;
        double r183414 = c;
        double r183415 = r183413 + r183414;
        return r183415;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r183416 = z;
        double r183417 = t;
        double r183418 = 16.0;
        double r183419 = r183417 / r183418;
        double r183420 = y;
        double r183421 = x;
        double r183422 = a;
        double r183423 = 4.0;
        double r183424 = r183422 / r183423;
        double r183425 = -r183424;
        double r183426 = b;
        double r183427 = c;
        double r183428 = fma(r183425, r183426, r183427);
        double r183429 = fma(r183420, r183421, r183428);
        double r183430 = fma(r183416, r183419, r183429);
        return r183430;
}

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))