FastMath dist

Average Error: 0.0 → 0.0

Time: 4.1s

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 r300117 = d1;
        double r300118 = d2;
        double r300119 = r300117 * r300118;
        double r300120 = d3;
        double r300121 = r300117 * r300120;
        double r300122 = r300119 + r300121;
        return r300122;
}

↓

double f(double d1, double d2, double d3) {
        double r300123 = d1;
        double r300124 = d2;
        double r300125 = d3;
        double r300126 = r300123 * r300125;
        double r300127 = fma(r300123, r300124, r300126);
        return r300127;
}

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 2020047 +o rules:numerics
(FPCore (d1 d2 d3)
  :name "FastMath dist"
  :precision binary64

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

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