FastMath dist

Average Error: 0.0 → 0.0

Time: 2.2s

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 r256765 = d1;
        double r256766 = d2;
        double r256767 = r256765 * r256766;
        double r256768 = d3;
        double r256769 = r256765 * r256768;
        double r256770 = r256767 + r256769;
        return r256770;
}

↓

double f(double d1, double d2, double d3) {
        double r256771 = d1;
        double r256772 = d2;
        double r256773 = d3;
        double r256774 = r256771 * r256773;
        double r256775 = fma(r256771, r256772, r256774);
        return r256775;
}

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)))