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

Average Error: 0.0 → 0.0

Time: 943.0ms

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 r672403 = 1.0;
        double r672404 = 8.0;
        double r672405 = r672403 / r672404;
        double r672406 = x;
        double r672407 = r672405 * r672406;
        double r672408 = y;
        double r672409 = z;
        double r672410 = r672408 * r672409;
        double r672411 = 2.0;
        double r672412 = r672410 / r672411;
        double r672413 = r672407 - r672412;
        double r672414 = t;
        double r672415 = r672413 + r672414;
        return r672415;
}

↓

double f(double x, double y, double z, double t) {
        double r672416 = x;
        double r672417 = 8.0;
        double r672418 = r672416 / r672417;
        double r672419 = 1.0;
        double r672420 = y;
        double r672421 = 2.0;
        double r672422 = r672420 / r672421;
        double r672423 = -r672422;
        double r672424 = z;
        double r672425 = t;
        double r672426 = fma(r672423, r672424, r672425);
        double r672427 = fma(r672418, r672419, r672426);
        return r672427;
}

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 2020036 +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))