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

Average Error: 0.0 → 0.0

Time: 1.1s

Precision: 64

• Falling back on racket egraph because egg-herbie package not installed

Math

\[\left(\frac{1}{8} \cdot x - \frac{y \cdot z}{2}\right) + t\]

↓

\[\mathsf{fma}\left(-\frac{y}{2}, z, \mathsf{fma}\left(\frac{1}{8}, x, t\right)\right)\]

C

double f(double x, double y, double z, double t) {
        double r631271 = 1.0;
        double r631272 = 8.0;
        double r631273 = r631271 / r631272;
        double r631274 = x;
        double r631275 = r631273 * r631274;
        double r631276 = y;
        double r631277 = z;
        double r631278 = r631276 * r631277;
        double r631279 = 2.0;
        double r631280 = r631278 / r631279;
        double r631281 = r631275 - r631280;
        double r631282 = t;
        double r631283 = r631281 + r631282;
        return r631283;
}

↓

double f(double x, double y, double z, double t) {
        double r631284 = y;
        double r631285 = 2.0;
        double r631286 = r631284 / r631285;
        double r631287 = -r631286;
        double r631288 = z;
        double r631289 = 1.0;
        double r631290 = 8.0;
        double r631291 = r631289 / r631290;
        double r631292 = x;
        double r631293 = t;
        double r631294 = fma(r631291, r631292, r631293);
        double r631295 = fma(r631287, r631288, r631294);
        return r631295;
}

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

   \[\leadsto \color{blue}{\mathsf{fma}\left(-\frac{y}{2}, z, \mathsf{fma}\left(\frac{1}{8}, x, t\right)\right)}\]

3. Final simplification 0.0

   \[\leadsto \mathsf{fma}\left(-\frac{y}{2}, z, \mathsf{fma}\left(\frac{1}{8}, x, t\right)\right)\]

Reproduce

herbie shell --seed 2020047 +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))