FastMath dist

Average Error: 0.0 → 0.0

Time: 18.5s

Precision: 64

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 r8819292 = d1;
        double r8819293 = d2;
        double r8819294 = r8819292 * r8819293;
        double r8819295 = d3;
        double r8819296 = r8819292 * r8819295;
        double r8819297 = r8819294 + r8819296;
        return r8819297;
}

↓

double f(double d1, double d2, double d3) {
        double r8819298 = d1;
        double r8819299 = d2;
        double r8819300 = d3;
        double r8819301 = r8819298 * r8819300;
        double r8819302 = fma(r8819298, r8819299, r8819301);
        return r8819302;
}

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 2019200 +o rules:numerics
(FPCore (d1 d2 d3)
  :name "FastMath dist"

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

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