Diagrams.Solve.Polynomial:quartForm from diagrams-solve-0.1, B

Average Error: 0.0 → 0.0

Time: 7.1s

Precision: 64

Math

\[\left(\frac{1}{8} \cdot x - \frac{y \cdot z}{2}\right) + t\]

↓

\[\mathsf{fma}\left(-\frac{y}{2}, z, \mathsf{fma}\left(x, \frac{1}{8}, t\right)\right)\]

C

double f(double x, double y, double z, double t) {
        double r508614 = 1.0;
        double r508615 = 8.0;
        double r508616 = r508614 / r508615;
        double r508617 = x;
        double r508618 = r508616 * r508617;
        double r508619 = y;
        double r508620 = z;
        double r508621 = r508619 * r508620;
        double r508622 = 2.0;
        double r508623 = r508621 / r508622;
        double r508624 = r508618 - r508623;
        double r508625 = t;
        double r508626 = r508624 + r508625;
        return r508626;
}

↓

double f(double x, double y, double z, double t) {
        double r508627 = y;
        double r508628 = 2.0;
        double r508629 = r508627 / r508628;
        double r508630 = -r508629;
        double r508631 = z;
        double r508632 = x;
        double r508633 = 1.0;
        double r508634 = 8.0;
        double r508635 = r508633 / r508634;
        double r508636 = t;
        double r508637 = fma(r508632, r508635, r508636);
        double r508638 = fma(r508630, r508631, r508637);
        return r508638;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Target

Original	0.0
Target	0.0
Herbie	0.0

\[\left(\frac{x}{8} + t\right) - \frac{z}{2} \cdot y\]

Derivation

1. Initial program 0.0

   \[\left(\frac{1}{8} \cdot x - \frac{y \cdot z}{2}\right) + t\]

2. Simplified 0.0

   \[\leadsto \color{blue}{\mathsf{fma}\left(-\frac{y}{2}, z, \mathsf{fma}\left(x, \frac{1}{8}, t\right)\right)}\]

3. Final simplification 0.0

   \[\leadsto \mathsf{fma}\left(-\frac{y}{2}, z, \mathsf{fma}\left(x, \frac{1}{8}, t\right)\right)\]

Reproduce

herbie shell --seed 2019198 +o rules:numerics
(FPCore (x y z t)
  :name "Diagrams.Solve.Polynomial:quartForm  from diagrams-solve-0.1, B"

  :herbie-target
  (- (+ (/ x 8.0) t) (* (/ z 2.0) y))

  (+ (- (* (/ 1.0 8.0) x) (/ (* y z) 2.0)) t))