Diagrams.Solve.Tridiagonal:solveTriDiagonal from diagrams-solve-0.1, C

Average Error: 0.0 → 0

Time: 1.6s

Precision: 64

Math

\[x - y \cdot z\]

↓

\[\mathsf{fma}\left(-z, y, x\right)\]

C

double f(double x, double y, double z) {
        double r488340 = x;
        double r488341 = y;
        double r488342 = z;
        double r488343 = r488341 * r488342;
        double r488344 = r488340 - r488343;
        return r488344;
}

↓

double f(double x, double y, double z) {
        double r488345 = z;
        double r488346 = -r488345;
        double r488347 = y;
        double r488348 = x;
        double r488349 = fma(r488346, r488347, r488348);
        return r488349;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original	0.0
Target	0.0
Herbie	0

\[\frac{x + y \cdot z}{\frac{x + y \cdot z}{x - y \cdot z}}\]

Derivation

1. Initial program 0.0

   \[x - y \cdot z\]

2. Simplified 0

   \[\leadsto \color{blue}{\mathsf{fma}\left(-z, y, x\right)}\]

3. Final simplification 0

   \[\leadsto \mathsf{fma}\left(-z, y, x\right)\]

Reproduce

herbie shell --seed 2019179 +o rules:numerics
(FPCore (x y z)
  :name "Diagrams.Solve.Tridiagonal:solveTriDiagonal from diagrams-solve-0.1, C"

  :herbie-target
  (/ (+ x (* y z)) (/ (+ x (* y z)) (- x (* y z))))

  (- x (* y z)))