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

Average Error: 0.0 → 0.0

Time: 35.4s

Precision: 64

Math

\[\left(\frac{1.0}{8.0} \cdot x - \frac{y \cdot z}{2.0}\right) + t\]

↓

\[\mathsf{fma}\left(\frac{x}{8.0}, 1.0, t - \frac{z \cdot y}{2.0}\right)\]

C

double f(double x, double y, double z, double t) {
        double r30869704 = 1.0;
        double r30869705 = 8.0;
        double r30869706 = r30869704 / r30869705;
        double r30869707 = x;
        double r30869708 = r30869706 * r30869707;
        double r30869709 = y;
        double r30869710 = z;
        double r30869711 = r30869709 * r30869710;
        double r30869712 = 2.0;
        double r30869713 = r30869711 / r30869712;
        double r30869714 = r30869708 - r30869713;
        double r30869715 = t;
        double r30869716 = r30869714 + r30869715;
        return r30869716;
}

↓

double f(double x, double y, double z, double t) {
        double r30869717 = x;
        double r30869718 = 8.0;
        double r30869719 = r30869717 / r30869718;
        double r30869720 = 1.0;
        double r30869721 = t;
        double r30869722 = z;
        double r30869723 = y;
        double r30869724 = r30869722 * r30869723;
        double r30869725 = 2.0;
        double r30869726 = r30869724 / r30869725;
        double r30869727 = r30869721 - r30869726;
        double r30869728 = fma(r30869719, r30869720, r30869727);
        return r30869728;
}

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

\[\left(\frac{x}{8.0} + t\right) - \frac{z}{2.0} \cdot y\]

Derivation

1. Initial program 0.0

   \[\left(\frac{1.0}{8.0} \cdot x - \frac{y \cdot z}{2.0}\right) + t\]

2. Simplified 0.0

   \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{x}{8.0}, 1.0, t - \frac{z \cdot y}{2.0}\right)}\]

3. Final simplification 0.0

   \[\leadsto \mathsf{fma}\left(\frac{x}{8.0}, 1.0, t - \frac{z \cdot y}{2.0}\right)\]

Reproduce

herbie shell --seed 2019162 +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))