Average Error: 0.1 → 0.0
Time: 46.2s
Precision: 64
\[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c\]
↓
\[\mathsf{fma}\left(\frac{t}{16}, z, \mathsf{fma}\left(y, x, c\right) - \frac{b}{4} \cdot a\right)\]
\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c
↓
\mathsf{fma}\left(\frac{t}{16}, z, \mathsf{fma}\left(y, x, c\right) - \frac{b}{4} \cdot a\right)
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r9382619 = x;
        double r9382620 = y;
        double r9382621 = r9382619 * r9382620;
        double r9382622 = z;
        double r9382623 = t;
        double r9382624 = r9382622 * r9382623;
        double r9382625 = 16.0;
        double r9382626 = r9382624 / r9382625;
        double r9382627 = r9382621 + r9382626;
        double r9382628 = a;
        double r9382629 = b;
        double r9382630 = r9382628 * r9382629;
        double r9382631 = 4.0;
        double r9382632 = r9382630 / r9382631;
        double r9382633 = r9382627 - r9382632;
        double r9382634 = c;
        double r9382635 = r9382633 + r9382634;
        return r9382635;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r9382636 = t;
        double r9382637 = 16.0;
        double r9382638 = r9382636 / r9382637;
        double r9382639 = z;
        double r9382640 = y;
        double r9382641 = x;
        double r9382642 = c;
        double r9382643 = fma(r9382640, r9382641, r9382642);
        double r9382644 = b;
        double r9382645 = 4.0;
        double r9382646 = r9382644 / r9382645;
        double r9382647 = a;
        double r9382648 = r9382646 * r9382647;
        double r9382649 = r9382643 - r9382648;
        double r9382650 = fma(r9382638, r9382639, r9382649);
        return r9382650;
}

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

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

  4. Applied *-un-lft-identity0.0

    \[\leadsto \mathsf{fma}\left(\frac{t}{16}, z, \mathsf{fma}\left(y, x, c\right) - \frac{a \cdot b}{\color{blue}{1 \cdot 4}}\right)\]

  5. Applied times-frac0.0

    \[\leadsto \mathsf{fma}\left(\frac{t}{16}, z, \mathsf{fma}\left(y, x, c\right) - \color{blue}{\frac{a}{1} \cdot \frac{b}{4}}\right)\]

  6. Simplified0.0

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

  7. Final simplification0.0

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

Reproduce

herbie shell --seed 2019168 +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))