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

Average Error: 0.0 → 0.0

Time: 1.7s

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 r404489 = 1.0;
        double r404490 = 8.0;
        double r404491 = r404489 / r404490;
        double r404492 = x;
        double r404493 = r404491 * r404492;
        double r404494 = y;
        double r404495 = z;
        double r404496 = r404494 * r404495;
        double r404497 = 2.0;
        double r404498 = r404496 / r404497;
        double r404499 = r404493 - r404498;
        double r404500 = t;
        double r404501 = r404499 + r404500;
        return r404501;
}

↓

double f(double x, double y, double z, double t) {
        double r404502 = y;
        double r404503 = 2.0;
        double r404504 = r404502 / r404503;
        double r404505 = -r404504;
        double r404506 = z;
        double r404507 = x;
        double r404508 = 1.0;
        double r404509 = 8.0;
        double r404510 = r404508 / r404509;
        double r404511 = t;
        double r404512 = fma(r404507, r404510, r404511);
        double r404513 = fma(r404505, r404506, r404512);
        return r404513;
}

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 2019347 +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))