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

Average Error: 0.0 → 0.0

Time: 12.0s

Precision: 64

Math

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

↓

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

C

double f(double x, double y, double z, double t) {
        double r30717419 = 1.0;
        double r30717420 = 8.0;
        double r30717421 = r30717419 / r30717420;
        double r30717422 = x;
        double r30717423 = r30717421 * r30717422;
        double r30717424 = y;
        double r30717425 = z;
        double r30717426 = r30717424 * r30717425;
        double r30717427 = 2.0;
        double r30717428 = r30717426 / r30717427;
        double r30717429 = r30717423 - r30717428;
        double r30717430 = t;
        double r30717431 = r30717429 + r30717430;
        return r30717431;
}

↓

double f(double x, double y, double z, double t) {
        double r30717432 = x;
        double r30717433 = 8.0;
        double r30717434 = r30717432 / r30717433;
        double r30717435 = 1.0;
        double r30717436 = t;
        double r30717437 = fma(r30717434, r30717435, r30717436);
        double r30717438 = z;
        double r30717439 = y;
        double r30717440 = r30717438 * r30717439;
        double r30717441 = 2.0;
        double r30717442 = r30717440 / r30717441;
        double r30717443 = r30717437 - r30717442;
        return r30717443;
}

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

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

3. Final simplification 0.0

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

Reproduce

herbie shell --seed 2019172 +o rules:numerics
(FPCore (x y z t)
  :name "Diagrams.Solve.Polynomial:quartForm  from diagrams-solve-0.1, B"

  :herbie-target
  (- (+ (/ x 8.0) t) (* (/ z 2.0) y))

  (+ (- (* (/ 1.0 8.0) x) (/ (* y z) 2.0)) t))