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

Average Error: 0.0 → 0.0

Time: 1.6s

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 r732664 = 1.0;
        double r732665 = 8.0;
        double r732666 = r732664 / r732665;
        double r732667 = x;
        double r732668 = r732666 * r732667;
        double r732669 = y;
        double r732670 = z;
        double r732671 = r732669 * r732670;
        double r732672 = 2.0;
        double r732673 = r732671 / r732672;
        double r732674 = r732668 - r732673;
        double r732675 = t;
        double r732676 = r732674 + r732675;
        return r732676;
}

↓

double f(double x, double y, double z, double t) {
        double r732677 = y;
        double r732678 = -r732677;
        double r732679 = 2.0;
        double r732680 = r732678 / r732679;
        double r732681 = z;
        double r732682 = 1.0;
        double r732683 = 8.0;
        double r732684 = r732682 / r732683;
        double r732685 = x;
        double r732686 = t;
        double r732687 = fma(r732684, r732685, r732686);
        double r732688 = fma(r732680, r732681, r732687);
        return r732688;
}

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))