FastMath dist

Average Error: 0.0 → 0.0

Time: 26.5s

Precision: 64

Math

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

↓

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

C

double f(double d1, double d2, double d3) {
        double r5182431 = d1;
        double r5182432 = d2;
        double r5182433 = r5182431 * r5182432;
        double r5182434 = d3;
        double r5182435 = r5182431 * r5182434;
        double r5182436 = r5182433 + r5182435;
        return r5182436;
}

↓

double f(double d1, double d2, double d3) {
        double r5182437 = d1;
        double r5182438 = d2;
        double r5182439 = d3;
        double r5182440 = r5182437 * r5182439;
        double r5182441 = fma(r5182437, r5182438, r5182440);
        return r5182441;
}

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

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

4. Final simplification 0.0

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

Reproduce

herbie shell --seed 2019132 +o rules:numerics
(FPCore (d1 d2 d3)
  :name "FastMath dist"

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

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