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

Average Error: 0.0 → 0.0

Time: 1.0s

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 r774676 = 1.0;
        double r774677 = 8.0;
        double r774678 = r774676 / r774677;
        double r774679 = x;
        double r774680 = r774678 * r774679;
        double r774681 = y;
        double r774682 = z;
        double r774683 = r774681 * r774682;
        double r774684 = 2.0;
        double r774685 = r774683 / r774684;
        double r774686 = r774680 - r774685;
        double r774687 = t;
        double r774688 = r774686 + r774687;
        return r774688;
}

↓

double f(double x, double y, double z, double t) {
        double r774689 = y;
        double r774690 = -r774689;
        double r774691 = 2.0;
        double r774692 = r774690 / r774691;
        double r774693 = z;
        double r774694 = 1.0;
        double r774695 = 8.0;
        double r774696 = r774694 / r774695;
        double r774697 = x;
        double r774698 = t;
        double r774699 = fma(r774696, r774697, r774698);
        double r774700 = fma(r774692, r774693, r774699);
        return r774700;
}

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 2020047 +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))