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

Average Error: 0.0 → 0.0

Time: 2.3s

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 r407690 = 1.0;
        double r407691 = 8.0;
        double r407692 = r407690 / r407691;
        double r407693 = x;
        double r407694 = r407692 * r407693;
        double r407695 = y;
        double r407696 = z;
        double r407697 = r407695 * r407696;
        double r407698 = 2.0;
        double r407699 = r407697 / r407698;
        double r407700 = r407694 - r407699;
        double r407701 = t;
        double r407702 = r407700 + r407701;
        return r407702;
}

↓

double f(double x, double y, double z, double t) {
        double r407703 = y;
        double r407704 = 2.0;
        double r407705 = r407703 / r407704;
        double r407706 = -r407705;
        double r407707 = z;
        double r407708 = x;
        double r407709 = 1.0;
        double r407710 = 8.0;
        double r407711 = r407709 / r407710;
        double r407712 = t;
        double r407713 = fma(r407708, r407711, r407712);
        double r407714 = fma(r407706, r407707, r407713);
        return r407714;
}

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 2019325 +o rules:numerics
(FPCore (x y z t)
  :name "Diagrams.Solve.Polynomial:quartForm  from diagrams-solve-0.1, B"
  :precision binary64

  :herbie-target
  (- (+ (/ x 8) t) (* (/ z 2) y))

  (+ (- (* (/ 1 8) x) (/ (* y z) 2)) t))