FastMath test3

Average Error: 0.1 → 0.0

Time: 6.2s

Precision: 64

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

Math

\[\left(d1 \cdot 3 + d1 \cdot d2\right) + d1 \cdot d3\]

↓

\[\mathsf{fma}\left(d1, 3, d1 \cdot d2\right) + d1 \cdot d3\]

C

double f(double d1, double d2, double d3) {
        double r205658 = d1;
        double r205659 = 3.0;
        double r205660 = r205658 * r205659;
        double r205661 = d2;
        double r205662 = r205658 * r205661;
        double r205663 = r205660 + r205662;
        double r205664 = d3;
        double r205665 = r205658 * r205664;
        double r205666 = r205663 + r205665;
        return r205666;
}

↓

double f(double d1, double d2, double d3) {
        double r205667 = d1;
        double r205668 = 3.0;
        double r205669 = d2;
        double r205670 = r205667 * r205669;
        double r205671 = fma(r205667, r205668, r205670);
        double r205672 = d3;
        double r205673 = r205667 * r205672;
        double r205674 = r205671 + r205673;
        return r205674;
}

Error

Bits error versus d1

Bits error versus d2

Bits error versus d3

Target

Original	0.1
Target	0.1
Herbie	0.0

\[d1 \cdot \left(\left(3 + d2\right) + d3\right)\]

Derivation

1. Initial program 0.1

   \[\left(d1 \cdot 3 + d1 \cdot d2\right) + d1 \cdot d3\]
2. Using strategy rm

3. Applied fma-def 0.0

   \[\leadsto \color{blue}{\mathsf{fma}\left(d1, 3, d1 \cdot d2\right)} + d1 \cdot d3\]

4. Final simplification 0.0

   \[\leadsto \mathsf{fma}\left(d1, 3, d1 \cdot d2\right) + d1 \cdot d3\]

Reproduce

herbie shell --seed 2020047 +o rules:numerics
(FPCore (d1 d2 d3)
  :name "FastMath test3"
  :precision binary64

  :herbie-target
  (* d1 (+ (+ 3 d2) d3))

  (+ (+ (* d1 3) (* d1 d2)) (* d1 d3)))