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

Average Error: 0.0 → 0.0

Time: 2.5s

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 r501540 = 1.0;
        double r501541 = 8.0;
        double r501542 = r501540 / r501541;
        double r501543 = x;
        double r501544 = r501542 * r501543;
        double r501545 = y;
        double r501546 = z;
        double r501547 = r501545 * r501546;
        double r501548 = 2.0;
        double r501549 = r501547 / r501548;
        double r501550 = r501544 - r501549;
        double r501551 = t;
        double r501552 = r501550 + r501551;
        return r501552;
}

↓

double f(double x, double y, double z, double t) {
        double r501553 = y;
        double r501554 = 2.0;
        double r501555 = r501553 / r501554;
        double r501556 = -r501555;
        double r501557 = z;
        double r501558 = x;
        double r501559 = 1.0;
        double r501560 = 8.0;
        double r501561 = r501559 / r501560;
        double r501562 = t;
        double r501563 = fma(r501558, r501561, r501562);
        double r501564 = fma(r501556, r501557, r501563);
        return r501564;
}

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 2019303 +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))