Details

analyze327.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
50%	50%	0.1%	3
50%	50%	0.1%	4
62.4%	37.5%	0.1%	5
62.4%	37.5%	0.1%	6
68.7%	31.2%	0.1%	7
68.7%	31.2%	0.1%	8
71.8%	28.1%	0.1%	9
71.8%	28.1%	0.1%	10
73.4%	26.5%	0.1%	11
73.4%	26.5%	0.1%	12
74.1%	25.8%	0.1%	13
74.1%	25.8%	0.1%	14

sample31.0ms

Algorithm

intervals

Results

9.0ms	197×	body	80	valid
4.0ms	15×	body	2560	valid
4.0ms	16×	body	1280	valid
3.0ms	9×	body	5120	valid
2.0ms	11×	body	640	valid
1.0ms	4×	body	320	valid
0.0ms	4×	body	160	valid

simplify3.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	22	15
1	22	15

prune8.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 38.9b

Counts

2 → 1

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
1.3b	(+ (sqrt (+ (* re re) (* im im))) re)
29.7b	(sqrt (+ (* re re) (* im im)))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 40

Calls

3 calls:

7.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
6.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))

series37.0ms

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)
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify33.0ms

Algorithm

egg-herbie

Counts

49 → 49

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	4949	551
1	4949	551

prune108.0ms

Filtered

42 candidates to 49 candidates (-16.7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	41	8	49
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	42	8	50

Merged error: 16.8b

Counts

50 → 8

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (cbrt (+ (* re re) (* im im)))))
6.0b	(+ (* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (cbrt (+ (* re re) (* im im))))) re)
30.8b	(cbrt (+ (* re re) (* im im)))
30.8b	(cbrt (+ (* re re) (* im im)))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
10×	`cbrt-prod` `add-cube-cbrt` `*-un-lft-identity`
9×	`associate-r`
8×	`sqrt-prod`
6×	`pow1` `add-exp-log` `cbrt-div` `add-cbrt-cube` `add-log-exp`
4×	`flip3-+` `flip-+`
3×	`associate-l` `unswap-sqr`
2×	`pow1/3` `sqrt-div` `associate-*r/`
1×	`+-commutative` `pow-prod-down` `prod-exp` `sum-log` `*-commutative` `cbrt-unprod`

Counts

4 → 65

Calls

4 calls:

10.0ms	(* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (cbrt (+ (* re re) (* im im)))))
8.0ms	(+ (* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (cbrt (+ (* re re) (* im im))))) re)
4.0ms	(cbrt (+ (* re re) (* im im)))
4.0ms	(cbrt (+ (* re re) (* im im)))

series108.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (cbrt (+ (* re re) (* im im)))))
29.0ms	(+ (* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (cbrt (+ (* re re) (* im im))))) re)
21.0ms	(cbrt (+ (* re re) (* im im)))
21.0ms	(cbrt (+ (* re re) (* im im)))

simplify46.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5235	1420

prune140.0ms

Filtered

65 candidates to 77 candidates (-18.5%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	74	3	77
Fresh	0	7	7
Picked	1	0	1
Done	0	0	0
Total	75	10	85

Merged error: 16.8b

Counts

85 → 10

localize12.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
7.7b	(+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
29.7b	(sqrt (+ (* re re) (* im im)))
29.7b	(sqrt (+ (* re re) (* im im)))

rewrite41.0ms

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:

14.0ms	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
13.0ms	(+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
5.0ms	(sqrt (+ (* re re) (* im im)))
4.0ms	(sqrt (+ (* re re) (* im im)))

series26.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
8.0ms	(+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
6.0ms	(sqrt (+ (* re re) (* im im)))
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify61.0ms

Algorithm

egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4998	1467
1	4998	1467

prune145.0ms

Filtered

71 candidates to 136 candidates (-91.5%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	136	0	136
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	136	10	146

Merged error: 16.8b

Counts

146 → 10

localize18.0ms

Local error

Found 4 expressions with local error:

5.1b	(exp (log (cbrt (+ (* re re) (* im im)))))
14.3b	(+ (* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (exp (log (cbrt (+ (* re re) (* im im))))))) re)
30.8b	(cbrt (+ (* re re) (* im im)))
30.8b	(cbrt (+ (* re re) (* im im)))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 58

Calls

4 calls:

5.0ms	(exp (log (cbrt (+ (* re re) (* im im)))))
10.0ms	(+ (* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (exp (log (cbrt (+ (* re re) (* im im))))))) re)
3.0ms	(cbrt (+ (* re re) (* im im)))
4.0ms	(cbrt (+ (* re re) (* im im)))

series94.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(exp (log (cbrt (+ (* re re) (* im im)))))
29.0ms	(+ (* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (exp (log (cbrt (+ (* re re) (* im im))))))) re)
23.0ms	(cbrt (+ (* re re) (* im im)))
21.0ms	(cbrt (+ (* re re) (* im im)))

simplify40.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	4876	1002
1	4876	1002

prune110.0ms

Filtered

58 candidates to 70 candidates (-20.7%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	68	2	70
Fresh	2	6	8
Picked	0	1	1
Done	0	1	1
Total	70	10	80

Merged error: 16.8b

Counts

80 → 10

regimes301.0ms

Accuracy

59.8% (8.8b remaining)

Error of 26.1b against oracle of 17.4b and baseline of 39.2b

bsearch43.0ms

Steps

Iters	Range		Point
6	1.5217820023232387e+115	6.317316159214062e+115	5.873768301992186e+115
6	-5.48614831849223e-301	-1.2520329910745253e-301	-1.2675488608054235e-301

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	62
1	38	62

end0.0ms

analyze326.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
50%	50%	0.1%	3
50%	50%	0.1%	4
62.4%	37.5%	0.1%	5
62.4%	37.5%	0.1%	6
68.7%	31.2%	0.1%	7
68.7%	31.2%	0.1%	8
71.8%	28.1%	0.1%	9
71.8%	28.1%	0.1%	10
73.4%	26.5%	0.1%	11
73.4%	26.5%	0.1%	12
74.1%	25.8%	0.1%	13
74.1%	25.8%	0.1%	14

sample935.0ms

Algorithm

intervals

Results

292.0ms	5980×	body	80	valid
200.0ms	701×	body	2560	valid
113.0ms	484×	body	1280	valid
107.0ms	318×	body	5120	valid
52.0ms	277×	body	640	valid
23.0ms	154×	body	320	valid
8.0ms	86×	body	160	valid

Details

analyze327.0ms

sample31.0ms

simplify3.0ms

prune8.0ms

localize11.0ms

rewrite18.0ms

series37.0ms

simplify33.0ms

prune108.0ms

localize14.0ms

rewrite27.0ms

series108.0ms

simplify46.0ms

prune140.0ms

localize12.0ms

rewrite41.0ms

series26.0ms

simplify61.0ms

prune145.0ms

localize18.0ms

rewrite24.0ms

series94.0ms

simplify40.0ms

prune110.0ms

regimes301.0ms

bsearch43.0ms

simplify1.0ms

end0.0ms

analyze326.0ms

sample935.0ms

Profiling