Numeric.Log:$cexpm1 from log-domain-0.10.2.1, B

Average Error: 0.0 → 0.0

Time: 441.0ms

Precision: 64

• Falling back on racket egraph because egg-herbie package not installed

Math

\[\left(x \cdot y + x\right) + y\]

↓

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

C

double f(double x, double y) {
        double r9827 = x;
        double r9828 = y;
        double r9829 = r9827 * r9828;
        double r9830 = r9829 + r9827;
        double r9831 = r9830 + r9828;
        return r9831;
}

↓

double f(double x, double y) {
        double r9832 = x;
        double r9833 = y;
        double r9834 = fma(r9832, r9833, r9832);
        double r9835 = r9834 + r9833;
        return r9835;
}

Error

Bits error versus x

Bits error versus y

Derivation

1. Initial program 0.0

   \[\left(x \cdot y + x\right) + y\]

2. Simplified 0.0

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

3. Final simplification 0.0

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

Reproduce

herbie shell --seed 2020045 +o rules:numerics
(FPCore (x y)
  :name "Numeric.Log:$cexpm1 from log-domain-0.10.2.1, B"
  :precision binary64
  (+ (+ (* x y) x) y))