FastMath test3

Average Error: 0.1 → 0.1

Time: 14.8s

Precision: 64

Math

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

↓

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

C

double f(double d1, double d2, double d3) {
        double r7199992 = d1;
        double r7199993 = 3.0;
        double r7199994 = r7199992 * r7199993;
        double r7199995 = d2;
        double r7199996 = r7199992 * r7199995;
        double r7199997 = r7199994 + r7199996;
        double r7199998 = d3;
        double r7199999 = r7199992 * r7199998;
        double r7200000 = r7199997 + r7199999;
        return r7200000;
}

↓

double f(double d1, double d2, double d3) {
        double r7200001 = d2;
        double r7200002 = d1;
        double r7200003 = r7200001 * r7200002;
        double r7200004 = 3.0;
        double r7200005 = d3;
        double r7200006 = r7200004 + r7200005;
        double r7200007 = r7200006 * r7200002;
        double r7200008 = r7200003 + r7200007;
        return r7200008;
}

Error

Bits error versus d1

Bits error versus d2

Bits error versus d3

Target

Original	0.1
Target	0.1
Herbie	0.1

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

Derivation

1. Initial program 0.1

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

2. Simplified 0.1

   \[\leadsto \color{blue}{\left(d2 + \left(3 + d3\right)\right) \cdot d1}\]
3. Using strategy rm

4. Applied *-commutative 0.1

   \[\leadsto \color{blue}{d1 \cdot \left(d2 + \left(3 + d3\right)\right)}\]
5. Using strategy rm

6. Applied distribute-rgt-in 0.1

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

7. Final simplification 0.1

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

Reproduce

herbie shell --seed 2019172 +o rules:numerics
(FPCore (d1 d2 d3)
  :name "FastMath test3"

  :herbie-target
  (* d1 (+ (+ 3.0 d2) d3))

  (+ (+ (* d1 3.0) (* d1 d2)) (* d1 d3)))