Average Error: 0.1 → 0.0
Time: 6.5s
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 r117630 = x;
        double r117631 = y;
        double r117632 = r117630 * r117631;
        double r117633 = z;
        double r117634 = t;
        double r117635 = r117633 * r117634;
        double r117636 = 16.0;
        double r117637 = r117635 / r117636;
        double r117638 = r117632 + r117637;
        double r117639 = a;
        double r117640 = b;
        double r117641 = r117639 * r117640;
        double r117642 = 4.0;
        double r117643 = r117641 / r117642;
        double r117644 = r117638 - r117643;
        double r117645 = c;
        double r117646 = r117644 + r117645;
        return r117646;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r117647 = z;
        double r117648 = 16.0;
        double r117649 = r117647 / r117648;
        double r117650 = t;
        double r117651 = x;
        double r117652 = y;
        double r117653 = a;
        double r117654 = 4.0;
        double r117655 = r117653 / r117654;
        double r117656 = b;
        double r117657 = -r117656;
        double r117658 = c;
        double r117659 = fma(r117655, r117657, r117658);
        double r117660 = fma(r117651, r117652, r117659);
        double r117661 = fma(r117649, r117650, r117660);
        return r117661;
}

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 2019325 +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))