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

Average Error: 0.0 → 0.0

Time: 1.1s

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 r787633 = 1.0;
        double r787634 = 8.0;
        double r787635 = r787633 / r787634;
        double r787636 = x;
        double r787637 = r787635 * r787636;
        double r787638 = y;
        double r787639 = z;
        double r787640 = r787638 * r787639;
        double r787641 = 2.0;
        double r787642 = r787640 / r787641;
        double r787643 = r787637 - r787642;
        double r787644 = t;
        double r787645 = r787643 + r787644;
        return r787645;
}

↓

double f(double x, double y, double z, double t) {
        double r787646 = y;
        double r787647 = 2.0;
        double r787648 = r787646 / r787647;
        double r787649 = -r787648;
        double r787650 = z;
        double r787651 = 1.0;
        double r787652 = 8.0;
        double r787653 = r787651 / r787652;
        double r787654 = x;
        double r787655 = t;
        double r787656 = fma(r787653, r787654, r787655);
        double r787657 = fma(r787649, r787650, r787656);
        return r787657;
}

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 2020045 +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))