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

Average Error: 0.0 → 0.0

Time: 2.4s

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 r379369 = 1.0;
        double r379370 = 8.0;
        double r379371 = r379369 / r379370;
        double r379372 = x;
        double r379373 = r379371 * r379372;
        double r379374 = y;
        double r379375 = z;
        double r379376 = r379374 * r379375;
        double r379377 = 2.0;
        double r379378 = r379376 / r379377;
        double r379379 = r379373 - r379378;
        double r379380 = t;
        double r379381 = r379379 + r379380;
        return r379381;
}

↓

double f(double x, double y, double z, double t) {
        double r379382 = y;
        double r379383 = 2.0;
        double r379384 = r379382 / r379383;
        double r379385 = -r379384;
        double r379386 = z;
        double r379387 = x;
        double r379388 = 1.0;
        double r379389 = 8.0;
        double r379390 = r379388 / r379389;
        double r379391 = t;
        double r379392 = fma(r379387, r379390, r379391);
        double r379393 = fma(r379385, r379386, r379392);
        return r379393;
}

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 2019304 +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))