Average Error: 0.0 → 0
Time: 4.2s
Precision: 64
\[x - y \cdot z\]
↓
\[\mathsf{fma}\left(y, -z, x\right)\]
x - y \cdot z
↓
\mathsf{fma}\left(y, -z, x\right)
double f(double x, double y, double z) {
        double r43278 = x;
        double r43279 = y;
        double r43280 = z;
        double r43281 = r43279 * r43280;
        double r43282 = r43278 - r43281;
        return r43282;
}
↓
double f(double x, double y, double z) {
        double r43283 = y;
        double r43284 = z;
        double r43285 = -r43284;
        double r43286 = x;
        double r43287 = fma(r43283, r43285, r43286);
        return r43287;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original0.0
Target0.0
Herbie0
\[\frac{x + y \cdot z}{\frac{x + y \cdot z}{x - y \cdot z}}\]

Derivation

  1. Initial program 0.0

    \[x - y \cdot z\]

  2. Taylor expanded around inf 0.0

    \[\leadsto \color{blue}{x - z \cdot y}\]

  3. Simplified0

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

  4. Final simplification0

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

Reproduce

herbie shell --seed 2019315 +o rules:numerics
(FPCore (x y z)
  :name "Diagrams.Solve.Tridiagonal:solveTriDiagonal from diagrams-solve-0.1, C"
  :precision binary64

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

  (- x (* y z)))