Average Error: 0.0 → 0.0
Time: 2.1s
Precision: 64
Internal Precision: 128
\[d1 \cdot d2 + d1 \cdot d3\]
↓
\[(d1 \cdot d2 + \left(d1 \cdot d3\right))_*\]

Error

Bits error versus d1

Bits error versus d2

Bits error versus d3

Target

Original0.0
Target0.0
Herbie0.0
\[d1 \cdot \left(d2 + d3\right)\]

Derivation

  1. Initial program 0.0

    \[d1 \cdot d2 + d1 \cdot d3\]
  2. Using strategy rm

  3. Applied fma-def0.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2019002 +o rules:numerics
(FPCore (d1 d2 d3)
  :name "FastMath dist"

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

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

Details

Time bar (total: 1.7s)Debug log

sample33.0ms

Algorithm
intervals

simplify11.0ms

Counts
1 → 1
Calls

1 calls. Slowest were:

11.0ms
(+ (* d1 d2) (* d1 d3))

prune20.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize7.0ms

Local error

Found 1 expressions with local error:

0.0b
(* (+ d2 d3) d1)

rewrite3.0ms

Algorithm
rewrite-expression-head
Counts
1 → 15
Calls

1 calls. Slowest were:

2.0ms
(* (+ d2 d3) d1)

series15.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

15.0ms
(* (+ d2 d3) d1)

simplify253.0ms

Counts
7 → 18
Calls

7 calls. Slowest were:

193.0ms
(* (- (* d2 d2) (* d3 d3)) d1)
41.0ms
(* (+ (pow d2 3) (pow d3 3)) d1)
7.0ms
(+ (* d3 d1) (* d2 d1))

prune151.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize11.0ms

Local error

Found 1 expressions with local error:

0.0b
(+ (* d1 d2) (* d1 d3))

rewrite5.0ms

Algorithm
rewrite-expression-head
Counts
1 → 15
Calls

1 calls. Slowest were:

4.0ms
(+ (* d1 d2) (* d1 d3))

series31.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

31.0ms
(+ (* d1 d2) (* d1 d3))

simplify41.0ms

Counts
5 → 18
Calls

5 calls. Slowest were:

20.0ms
(* (exp (* d1 d2)) (exp (* d1 d3)))
6.0ms
(+ (* d3 d1) (* d2 d1))
6.0ms
(+ (* d3 d1) (* d2 d1))

prune113.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize4.0ms

Local error

Found 0 expressions with local error:

rewrite0.0ms

Algorithm
rewrite-expression-head
Counts
0 → 0
Calls

0 calls. Slowest were:

series0.0ms

Counts
0 → 0
Calls

0 calls. Slowest were:

simplify0.0ms

Counts
0 → 0
Calls

0 calls. Slowest were:

prune3.0ms

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

end0.0ms

sample1.0s

Algorithm
intervals