Details

sample32.0ms

Algorithm

intervals

Results

12.0ms	200×	body	80	valid
4.0ms	18×	body	2560	valid
3.0ms	16×	body	1280	valid
2.0ms	14×	body	640	valid
2.0ms	6×	body	5120	valid
0.0ms	2×	body	320	valid

simplify6.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	22	8
1	24	8
2	24	8

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 39.7b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* re re) (* im im))
0.3b	(+ (sqrt (+ (* re re) (* im im))) re)
30.7b	(sqrt (+ (* re re) (* im im)))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

7×	`add-log-exp`
6×	`*-un-lft-identity`
5×	`add-sqr-sqrt`
4×	`pow1` `add-cube-cbrt`
3×	`add-exp-log` `flip3-+` `sqrt-prod` `add-cbrt-cube` `flip-+`
2×	`+-commutative` `sqrt-div` `sum-log`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `distribute-lft-out`

Counts

3 → 38

Calls

3 calls:

3.0ms	(+ (* re re) (* im im))
13.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))

series111.0ms

Counts

3 → 9

Calls

3 calls:

29.0ms	(+ (* re re) (* im im))
44.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
38.0ms	(sqrt (+ (* re re) (* im im)))

simplify64.0ms

Algorithm

egg-herbie

Counts

47 → 47

Iterations

Useful iterations: 3 (60.0ms)

Iter	Nodes	Cost
0	178	275
1	689	252
2	2017	248
3	5001	246

prune139.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 19.6b

localize12.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
7.3b	(+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
30.7b	(sqrt (+ (* re re) (* im im)))
30.7b	(sqrt (+ (* re re) (* im im)))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

72×	`sqrt-prod`
50×	`add-sqr-sqrt`
34×	`sqrt-pow1`
29×	`pow1`
28×	`sqrt-div`
18×	`add-cube-cbrt` `*-un-lft-identity` `pow1/2`
15×	`swap-sqr`
9×	`flip3-+` `associate-r` `associate-l` `pow-prod-up` `flip-+` `unswap-sqr`
6×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
5×	`pow-prod-down` `pow-sqr`
4×	`frac-times`
2×	`rem-sqrt-square` `associate-r/` `associate-l/`
1×	`+-commutative` `pow2` `pow-plus` `sqrt-unprod` `prod-exp` `sum-log` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 124

Calls

4 calls:

26.0ms	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
14.0ms	(+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
3.0ms	(sqrt (+ (* re re) (* im im)))
6.0ms	(sqrt (+ (* re re) (* im im)))

series156.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
47.0ms	(+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
35.0ms	(sqrt (+ (* re re) (* im im)))
38.0ms	(sqrt (+ (* re re) (* im im)))

simplify48.0ms

Algorithm

egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	267	1096
1	974	974
2	5001	950

prune289.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 19.6b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* re re) (* im im))
0.3b	(+ (sqrt (+ (* re re) (* im im))) re)
30.7b	(sqrt (+ (* re re) (* im im)))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

7×	`add-log-exp`
6×	`*-un-lft-identity`
5×	`add-sqr-sqrt`
4×	`pow1` `add-cube-cbrt`
3×	`add-exp-log` `flip3-+` `sqrt-prod` `add-cbrt-cube` `flip-+`
2×	`+-commutative` `sqrt-div` `sum-log`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `distribute-lft-out`

Counts

3 → 38

Calls

3 calls:

2.0ms	(+ (* re re) (* im im))
13.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))

series111.0ms

Counts

3 → 9

Calls

3 calls:

29.0ms	(+ (* re re) (* im im))
44.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
38.0ms	(sqrt (+ (* re re) (* im im)))

simplify65.0ms

Algorithm

egg-herbie

Counts

47 → 47

Iterations

Useful iterations: 3 (60.0ms)

Iter	Nodes	Cost
0	178	275
1	689	252
2	2017	248
3	5001	246

prune125.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 19.6b

localize18.0ms

Local error

Found 4 expressions with local error:

30.7b	(sqrt (+ (* re re) (* im im)))
30.7b	(sqrt (+ (* re re) (* im im)))
30.7b	(sqrt (+ (* re re) (* im im)))
30.7b	(sqrt (+ (* re re) (* im im)))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `sqrt-prod`
8×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `sqrt-div`
4×	`add-exp-log` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `add-cbrt-cube` `flip-+` `add-log-exp`

Counts

4 → 60

Calls

4 calls:

3.0ms	(sqrt (+ (* re re) (* im im)))
3.0ms	(sqrt (+ (* re re) (* im im)))
3.0ms	(sqrt (+ (* re re) (* im im)))
4.0ms	(sqrt (+ (* re re) (* im im)))

series146.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(sqrt (+ (* re re) (* im im)))
39.0ms	(sqrt (+ (* re re) (* im im)))
34.0ms	(sqrt (+ (* re re) (* im im)))
39.0ms	(sqrt (+ (* re re) (* im im)))

simplify143.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 5 (138.0ms)

Iter	Nodes	Cost
0	89	400
1	215	388
2	503	388
3	1265	388
4	4227	388
5	5002	384

prune307.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 19.6b

regimes347.0ms

Accuracy

56.1% (9.3b remaining)

Error of 27.0b against oracle of 17.8b and baseline of 38.9b

bsearch2.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	36
1	38	36

end0.0ms

sample1.1s

Algorithm

intervals

Results

376.0ms	6066×	body	80	valid
357.0ms	648×	body	2560	valid
100.0ms	482×	body	1280	valid
81.0ms	276×	body	5120	valid
47.0ms	287×	body	640	valid
18.0ms	142×	body	320	valid
9.0ms	99×	body	160	valid