Details

analyze360.0ms

Algorithm

Search

True	Other	False	Iter
0%	50%	50%	0
0%	50%	50%	1
25%	25%	50%	2
25%	25%	50%	3
31.2%	18.7%	50%	4
31.2%	18.7%	50%	5
34.3%	15.6%	50%	6
34.3%	15.6%	50%	7
35.9%	14%	50%	8
35.9%	14%	50%	9
36.7%	13.3%	50%	10
36.7%	13.3%	50%	11
37.1%	12.9%	50%	12
37.1%	12.9%	50%	13
37.3%	12.7%	50%	14

sample38.0ms

Algorithm

intervals

Results

9.0ms	193×	body	80	valid
7.0ms	25×	body	2560	valid
3.0ms	256×	pre	80	true
3.0ms	14×	body	1280	valid
3.0ms	8×	body	5120	valid
1.0ms	8×	body	640	valid
1.0ms	5×	body	320	valid
0.0ms	3×	body	160	valid

simplify16.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (15.0ms)

Iter	Nodes	Cost
0	265	15
1	265	15

prune6.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 38.2b

Counts

2 → 1

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
0.8b	(- (sqrt (+ (* re re) (* im im))) re)
28.2b	(sqrt (+ (* re re) (* im im)))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-sqr-sqrt`
7×	`pow1`
6×	`*-un-lft-identity`
5×	`sqrt-prod` `add-log-exp`
4×	`add-cube-cbrt` `sqrt-div`
3×	`add-exp-log` `sqrt-pow1` `add-cbrt-cube`
2×	`flip3--` `pow1/2` `associate-*r/` `flip--` `difference-of-squares`
1×	`sub-neg` `rem-sqrt-square` `flip3-+` `diff-log` `pow-prod-down` `flip-+` `distribute-lft-out--`

Counts

3 → 42

Calls

3 calls:

8.0ms	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
7.0ms	(- (sqrt (+ (* re re) (* im im))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))

series39.0ms

Counts

3 → 9

Calls

3 calls:

24.0ms	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
7.0ms	(- (sqrt (+ (* re re) (* im im))) re)
7.0ms	(sqrt (+ (* re re) (* im im)))

simplify25.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 0 (20.0ms)

Iter	Nodes	Cost
0	5010	608

prune123.0ms

Filtered

42 candidates to 51 candidates (-21.4%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	43	8	51
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	44	8	52

Merged error: 9.2b

Counts

52 → 8

localize6.0ms

Local error

Found 1 expressions with local error:

0.0b	(sqrt (* 2.0 (- im re)))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

4×	`pow1`
2×	`sqrt-pow1` `sqrt-div` `associate-*r/`
1×	`add-exp-log` `add-sqr-sqrt` `add-cube-cbrt` `flip3--` `*-un-lft-identity` `pow1/2` `pow-prod-down` `sqrt-prod` `add-cbrt-cube` `flip--` `add-log-exp`

Counts

1 → 13

Calls

1 calls:

4.0ms

(sqrt (* 2.0 (- im re)))

series17.0ms

Counts

1 → 3

Calls

1 calls:

17.0ms

(sqrt (* 2.0 (- im re)))

simplify40.0ms

Algorithm

egg-herbie

Counts

16 → 16

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5758	162

prune53.0ms

Filtered

13 candidates to 16 candidates (-23.1%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	14	2	16
Fresh	1	6	7
Picked	0	1	1
Done	0	0	0
Total	15	9	24

Merged error: 9.2b

Counts

24 → 9

localize12.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (cbrt (sqrt (* 2.0 (- im re)))) (cbrt (sqrt (* 2.0 (- im re)))))
0.4b	(cbrt (sqrt (* 2.0 (- im re))))
0.4b	(cbrt (sqrt (* 2.0 (- im re))))
0.4b	(cbrt (sqrt (* 2.0 (- im re))))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

32×	`cbrt-prod`
23×	`add-sqr-sqrt`
20×	`associate-*r/`
18×	`cbrt-div` `sqrt-div`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`flip3--` `pow1/3` `flip--`
7×	`swap-sqr` `associate-r` `associate-l` `sqrt-prod`
6×	`add-exp-log`
4×	`frac-times` `add-cbrt-cube` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `associate-*l/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 93

Calls

4 calls:

8.0ms	(* (cbrt (sqrt (* 2.0 (- im re)))) (cbrt (sqrt (* 2.0 (- im re)))))
5.0ms	(cbrt (sqrt (* 2.0 (- im re))))
5.0ms	(cbrt (sqrt (* 2.0 (- im re))))
5.0ms	(cbrt (sqrt (* 2.0 (- im re))))

series197.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(* (cbrt (sqrt (* 2.0 (- im re)))) (cbrt (sqrt (* 2.0 (- im re)))))
49.0ms	(cbrt (sqrt (* 2.0 (- im re))))
53.0ms	(cbrt (sqrt (* 2.0 (- im re))))
51.0ms	(cbrt (sqrt (* 2.0 (- im re))))

simplify50.0ms

Algorithm

egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	4885	1381
1	4885	1381

prune299.0ms

Filtered

82 candidates to 105 candidates (-28.0%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	104	1	105
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	104	10	114

Merged error: 9.2b

Counts

114 → 10

localize14.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (exp (* (log (cbrt (sqrt (* 2.0 (- im re))))) 2)) (cbrt (sqrt (* 2.0 (- im re)))))
0.4b	(cbrt (sqrt (* 2.0 (- im re))))
0.4b	(cbrt (sqrt (* 2.0 (- im re))))
3.2b	(exp (* (log (cbrt (sqrt (* 2.0 (- im re))))) 2))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt`
14×	`cbrt-prod`
9×	`add-cube-cbrt` `*-un-lft-identity`
8×	`associate-*r/`
7×	`pow1` `associate-r`
6×	`cbrt-div` `sqrt-div`
5×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
4×	`associate-l` `exp-lft-sqr` `unswap-sqr`
3×	`flip3--` `exp-to-pow` `sqrt-prod` `flip--`
2×	`pow1/3`
1×	`exp-prod` `pow-plus` `pow-prod-down` `prod-exp` `*-commutative` `pow-prod-up` `cbrt-unprod` `rem-exp-log`

Counts

4 → 69

Calls

4 calls:

8.0ms	(* (exp (* (log (cbrt (sqrt (* 2.0 (- im re))))) 2)) (cbrt (sqrt (* 2.0 (- im re)))))
5.0ms	(cbrt (sqrt (* 2.0 (- im re))))
5.0ms	(cbrt (sqrt (* 2.0 (- im re))))
3.0ms	(exp (* (log (cbrt (sqrt (* 2.0 (- im re))))) 2))

series200.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(* (exp (* (log (cbrt (sqrt (* 2.0 (- im re))))) 2)) (cbrt (sqrt (* 2.0 (- im re)))))
49.0ms	(cbrt (sqrt (* 2.0 (- im re))))
50.0ms	(cbrt (sqrt (* 2.0 (- im re))))
85.0ms	(exp (* (log (cbrt (sqrt (* 2.0 (- im re))))) 2))

simplify34.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	5318	1034

prune207.0ms

Filtered

65 candidates to 81 candidates (-24.6%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	80	1	81
Fresh	0	7	7
Picked	1	0	1
Done	0	2	2
Total	81	10	91

Merged error: 9.2b

Counts

91 → 10

regimes345.0ms

Accuracy

41.8% (11.2b remaining)

Error of 21.1b against oracle of 9.9b and baseline of 29.1b

bsearch125.0ms

Steps

Iters	Range		Point
8	1.0634574758951388e+176	2.9113785642110137e+179	8.594773102387256e+176
8	8.044368432194986e+105	2.3450186355547416e+110	2.301551743401769e+110
6	9.85587108249642e-76	1.2948029472325614e-74	3.6532567719110757e-75
8	-3.7709465126161785e-159	-3.630089800523016e-162	-5.686701427801653e-162
9	-4.571955507717494e+85	-9.644960619417434e+78	-1.6385368300839155e+81

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	69	84
1	69	84

end0.0ms

sample1.1s

Algorithm

intervals

Results

298.0ms	6061×	body	80	valid
204.0ms	716×	body	2560	valid
111.0ms	467×	body	1280	valid
111.0ms	8000×	pre	80	true
99.0ms	275×	body	5120	valid
47.0ms	241×	body	640	valid
21.0ms	150×	body	320	valid
8.0ms	90×	body	160	valid

Details

analyze360.0ms

sample38.0ms

simplify16.0ms

prune6.0ms

localize10.0ms

rewrite20.0ms

series39.0ms

simplify25.0ms

prune123.0ms

localize6.0ms

rewrite5.0ms

series17.0ms

simplify40.0ms

prune53.0ms

localize12.0ms

rewrite26.0ms

series197.0ms

simplify50.0ms

prune299.0ms

localize14.0ms

rewrite23.0ms

series200.0ms

simplify34.0ms

prune207.0ms

regimes345.0ms

bsearch125.0ms

simplify2.0ms

end0.0ms

sample1.1s

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