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

Average Error: 0.0 → 0.0

Time: 793.0ms

Precision: 64

Math

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

↓

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

C

double f(double x, double y, double z, double t) {
        double r727397 = 1.0;
        double r727398 = 8.0;
        double r727399 = r727397 / r727398;
        double r727400 = x;
        double r727401 = r727399 * r727400;
        double r727402 = y;
        double r727403 = z;
        double r727404 = r727402 * r727403;
        double r727405 = 2.0;
        double r727406 = r727404 / r727405;
        double r727407 = r727401 - r727406;
        double r727408 = t;
        double r727409 = r727407 + r727408;
        return r727409;
}

↓

double f(double x, double y, double z, double t) {
        double r727410 = x;
        double r727411 = 8.0;
        double r727412 = r727410 / r727411;
        double r727413 = 1.0;
        double r727414 = y;
        double r727415 = 2.0;
        double r727416 = r727414 / r727415;
        double r727417 = -r727416;
        double r727418 = z;
        double r727419 = t;
        double r727420 = fma(r727417, r727418, r727419);
        double r727421 = fma(r727412, r727413, r727420);
        return r727421;
}

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

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

3. Final simplification 0.0

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

Reproduce

herbie shell --seed 2020064 +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))