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

Average Error: 0.0 → 0.0

Time: 2.7s

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 r71472 = 1.0;
        double r71473 = 8.0;
        double r71474 = r71472 / r71473;
        double r71475 = x;
        double r71476 = r71474 * r71475;
        double r71477 = y;
        double r71478 = z;
        double r71479 = r71477 * r71478;
        double r71480 = 2.0;
        double r71481 = r71479 / r71480;
        double r71482 = r71476 - r71481;
        double r71483 = t;
        double r71484 = r71482 + r71483;
        return r71484;
}

↓

double f(double x, double y, double z, double t) {
        double r71485 = y;
        double r71486 = 2.0;
        double r71487 = r71485 / r71486;
        double r71488 = -r71487;
        double r71489 = z;
        double r71490 = x;
        double r71491 = 1.0;
        double r71492 = 8.0;
        double r71493 = r71491 / r71492;
        double r71494 = t;
        double r71495 = fma(r71490, r71493, r71494);
        double r71496 = fma(r71488, r71489, r71495);
        return r71496;
}

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 2019310 +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))