FastMath dist

Average Error: 0.0 → 0.0

Time: 2.3s

Precision: 64

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

Math

\[d1 \cdot d2 + d1 \cdot d3\]

↓

\[\mathsf{fma}\left(d1, d2, d1 \cdot d3\right)\]

C

double f(double d1, double d2, double d3) {
        double r238236 = d1;
        double r238237 = d2;
        double r238238 = r238236 * r238237;
        double r238239 = d3;
        double r238240 = r238236 * r238239;
        double r238241 = r238238 + r238240;
        return r238241;
}

↓

double f(double d1, double d2, double d3) {
        double r238242 = d1;
        double r238243 = d2;
        double r238244 = d3;
        double r238245 = r238242 * r238244;
        double r238246 = fma(r238242, r238243, r238245);
        return r238246;
}

Error

Bits error versus d1

Bits error versus d2

Bits error versus d3

Target

Original	0.0
Target	0.0
Herbie	0.0

\[d1 \cdot \left(d2 + d3\right)\]

Derivation

1. Initial program 0.0

   \[d1 \cdot d2 + d1 \cdot d3\]
2. Using strategy rm

3. Applied fma-def 0.0

   \[\leadsto \color{blue}{\mathsf{fma}\left(d1, d2, d1 \cdot d3\right)}\]

4. Final simplification 0.0

   \[\leadsto \mathsf{fma}\left(d1, d2, d1 \cdot d3\right)\]

Reproduce

herbie shell --seed 2020046 +o rules:numerics
(FPCore (d1 d2 d3)
  :name "FastMath dist"
  :precision binary64

  :herbie-target
  (* d1 (+ d2 d3))

  (+ (* d1 d2) (* d1 d3)))