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

Average Error: 0.0 → 0.0

Time: 1.7s

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 r735725 = 1.0;
        double r735726 = 8.0;
        double r735727 = r735725 / r735726;
        double r735728 = x;
        double r735729 = r735727 * r735728;
        double r735730 = y;
        double r735731 = z;
        double r735732 = r735730 * r735731;
        double r735733 = 2.0;
        double r735734 = r735732 / r735733;
        double r735735 = r735729 - r735734;
        double r735736 = t;
        double r735737 = r735735 + r735736;
        return r735737;
}

↓

double f(double x, double y, double z, double t) {
        double r735738 = y;
        double r735739 = -r735738;
        double r735740 = 2.0;
        double r735741 = r735739 / r735740;
        double r735742 = z;
        double r735743 = 1.0;
        double r735744 = 8.0;
        double r735745 = r735743 / r735744;
        double r735746 = x;
        double r735747 = t;
        double r735748 = fma(r735745, r735746, r735747);
        double r735749 = fma(r735741, r735742, r735748);
        return r735749;
}

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 2020046 +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))