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

Average Error: 0.0 → 0.0

Time: 2.1s

Precision: 64

• Falling back on racket egraph because egg-herbie package not installed

Math

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

↓

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

C

double f(double x, double y, double z, double t) {
        double r927754 = 1.0;
        double r927755 = 8.0;
        double r927756 = r927754 / r927755;
        double r927757 = x;
        double r927758 = r927756 * r927757;
        double r927759 = y;
        double r927760 = z;
        double r927761 = r927759 * r927760;
        double r927762 = 2.0;
        double r927763 = r927761 / r927762;
        double r927764 = r927758 - r927763;
        double r927765 = t;
        double r927766 = r927764 + r927765;
        return r927766;
}

↓

double f(double x, double y, double z, double t) {
        double r927767 = y;
        double r927768 = 2.0;
        double r927769 = r927767 / r927768;
        double r927770 = -r927769;
        double r927771 = z;
        double r927772 = 1.0;
        double r927773 = 8.0;
        double r927774 = r927772 / r927773;
        double r927775 = x;
        double r927776 = t;
        double r927777 = fma(r927774, r927775, r927776);
        double r927778 = fma(r927770, r927771, r927777);
        return r927778;
}

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

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

3. Final simplification 0.0

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

Reproduce

herbie shell --seed 2020042 +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))