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

Average Error: 0.0 → 0

Time: 1.5s

Precision: 64

Math

\[x - y \cdot z\]

↓

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

C

double f(double x, double y, double z) {
        double r498822 = x;
        double r498823 = y;
        double r498824 = z;
        double r498825 = r498823 * r498824;
        double r498826 = r498822 - r498825;
        return r498826;
}

↓

double f(double x, double y, double z) {
        double r498827 = z;
        double r498828 = -r498827;
        double r498829 = y;
        double r498830 = x;
        double r498831 = fma(r498828, r498829, r498830);
        return r498831;
}

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 2019174 +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)))