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

Average Error: 0.0 → 0.0

Time: 1.5s

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 r674404 = 1.0;
        double r674405 = 8.0;
        double r674406 = r674404 / r674405;
        double r674407 = x;
        double r674408 = r674406 * r674407;
        double r674409 = y;
        double r674410 = z;
        double r674411 = r674409 * r674410;
        double r674412 = 2.0;
        double r674413 = r674411 / r674412;
        double r674414 = r674408 - r674413;
        double r674415 = t;
        double r674416 = r674414 + r674415;
        return r674416;
}

↓

double f(double x, double y, double z, double t) {
        double r674417 = y;
        double r674418 = -r674417;
        double r674419 = 2.0;
        double r674420 = r674418 / r674419;
        double r674421 = z;
        double r674422 = 1.0;
        double r674423 = 8.0;
        double r674424 = r674422 / r674423;
        double r674425 = x;
        double r674426 = t;
        double r674427 = fma(r674424, r674425, r674426);
        double r674428 = fma(r674420, r674421, r674427);
        return r674428;
}

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 2020045 +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))