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

Average Error: 0.0 → 0.0

Time: 2.2s

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 r459299 = 1.0;
        double r459300 = 8.0;
        double r459301 = r459299 / r459300;
        double r459302 = x;
        double r459303 = r459301 * r459302;
        double r459304 = y;
        double r459305 = z;
        double r459306 = r459304 * r459305;
        double r459307 = 2.0;
        double r459308 = r459306 / r459307;
        double r459309 = r459303 - r459308;
        double r459310 = t;
        double r459311 = r459309 + r459310;
        return r459311;
}

↓

double f(double x, double y, double z, double t) {
        double r459312 = y;
        double r459313 = 2.0;
        double r459314 = r459312 / r459313;
        double r459315 = -r459314;
        double r459316 = z;
        double r459317 = x;
        double r459318 = 1.0;
        double r459319 = 8.0;
        double r459320 = r459318 / r459319;
        double r459321 = t;
        double r459322 = fma(r459317, r459320, r459321);
        double r459323 = fma(r459315, r459316, r459322);
        return r459323;
}

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 2019323 +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))