Details

analyze359.0ms

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

sample36.0ms

Algorithm

intervals

Results

9.0ms	188×	body	80	valid
6.0ms	20×	body	2560	valid
5.0ms	20×	body	1280	valid
4.0ms	12×	body	5120	valid
2.0ms	9×	body	640	valid
1.0ms	7×	body	320	valid

simplify3.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	22	15
1	22	15

prune7.0ms

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: 38.7b

Counts

2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* re re) (* im im))
0.0b	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
0.7b	(+ (sqrt (+ (* re re) (* im im))) re)
29.1b	(sqrt (+ (* re re) (* im im)))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 51

Calls

4 calls:

4.0ms	(+ (* re re) (* im im))
10.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
7.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))

series43.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(+ (* re re) (* im im))
23.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
7.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify28.0ms

Algorithm

egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 0 (22.0ms)

Iter	Nodes	Cost
0	5008	690

prune135.0ms

Filtered

53 candidates to 63 candidates (-18.9%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	56	7	63
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	56	8	64

Merged error: 16.2b

Counts

64 → 8

localize13.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
9.5b	(+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
29.1b	(sqrt (+ (* re re) (* im im)))
29.1b	(sqrt (+ (* re re) (* im im)))

rewrite46.0ms

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:

16.0ms	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
15.0ms	(+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
6.0ms	(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)))))
7.0ms	(+ (* (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)))

simplify70.0ms

Algorithm

egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4944	1470
1	4944	1470

prune154.0ms

Filtered

72 candidates to 136 candidates (-88.9%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	136	0	136
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	136	8	144

Merged error: 16.2b

Counts

144 → 8

localize13.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (sqrt (* (* im im) 2.0)) (sqrt (- (sqrt (+ (* re re) (* im im))) re)))
1.2b	(- (sqrt (+ (* re re) (* im im))) re)
29.1b	(sqrt (+ (* re re) (* im im)))
30.3b	(sqrt (* (* im im) 2.0))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

50×	`add-sqr-sqrt` `sqrt-prod`
37×	`*-un-lft-identity`
36×	`times-frac`
25×	`add-cube-cbrt`
12×	`difference-of-squares`
11×	`pow1`
9×	`associate-/r*`
6×	`add-exp-log` `add-cbrt-cube` `distribute-lft-out--` `add-log-exp`
4×	`sqrt-pow1` `sqrt-div` `associate-/l*`
3×	`pow-prod-down`
2×	`flip3--` `pow1/2` `associate-/r/` `flip--`
1×	`cbrt-undiv` `sub-neg` `rem-sqrt-square` `sqrt-undiv` `frac-2neg` `flip3-+` `diff-log` `div-exp` `clear-num` `flip-+` `div-inv`

Counts

4 → 105

Calls

4 calls:

14.0ms	(/ (sqrt (* (* im im) 2.0)) (sqrt (- (sqrt (+ (* re re) (* im im))) re)))
7.0ms	(- (sqrt (+ (* re re) (* im im))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))
4.0ms	(sqrt (* (* im im) 2.0))

series43.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(/ (sqrt (* (* im im) 2.0)) (sqrt (- (sqrt (+ (* re re) (* im im))) re)))
7.0ms	(- (sqrt (+ (* re re) (* im im))) re)
6.0ms	(sqrt (+ (* re re) (* im im)))
4.0ms	(sqrt (* (* im im) 2.0))

simplify44.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	4917	2308
1	4917	2308

prune209.0ms

Filtered

85 candidates to 117 candidates (-37.6%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	109	8	117
Fresh	3	2	5
Picked	1	0	1
Done	2	0	2
Total	115	10	125

Merged error: 9.5b

Counts

125 → 10

localize14.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (* (fabs im) (sqrt 2.0)) (sqrt (- (sqrt (+ (* re re) (* im im))) re)))
0.4b	(* (fabs im) (sqrt 2.0))
1.2b	(- (sqrt (+ (* re re) (* im im))) re)
29.1b	(sqrt (+ (* re re) (* im im)))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
22×	`sqrt-prod`
18×	`*-un-lft-identity`
12×	`add-cube-cbrt`
11×	`add-exp-log` `add-cbrt-cube`
9×	`times-frac` `associate-/r*`
7×	`pow1`
6×	`associate-r` `add-log-exp` `difference-of-squares`
4×	`sqrt-div`
3×	`associate-l` `distribute-lft-out--`
2×	`cbrt-undiv` `flip3--` `div-exp` `prod-exp` `associate-/r/` `flip--` `cbrt-unprod` `unswap-sqr`
1×	`sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `pow-prod-down` `clear-num` `-commutative` `flip-+` `div-inv` `associate-/l`

Counts

4 → 86

Calls

4 calls:

14.0ms	(/ (* (fabs im) (sqrt 2.0)) (sqrt (- (sqrt (+ (* re re) (* im im))) re)))
5.0ms	(* (fabs im) (sqrt 2.0))
7.0ms	(- (sqrt (+ (* re re) (* im im))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))

series44.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(/ (* (fabs im) (sqrt 2.0)) (sqrt (- (sqrt (+ (* re re) (* im im))) re)))
4.0ms	(* (fabs im) (sqrt 2.0))
7.0ms	(- (sqrt (+ (* re re) (* im im))) re)
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify40.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	4996	1352
1	4996	1352

prune137.0ms

Filtered

67 candidates to 98 candidates (-46.3%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	95	3	98
Fresh	3	6	9
Picked	1	0	1
Done	0	0	0
Total	99	9	108

Merged error: 5.9b

Counts

108 → 9

regimes315.0ms

Accuracy

53.4% (13.4b remaining)

Error of 20.9b against oracle of 7.5b and baseline of 36.3b

bsearch46.0ms

Steps

Iters	Range		Point
8	1.0077236321707987e-103	4.550154514735237e-99	1.0928277540347782e-101
8	-1.3392279029411704e+18	-64505185206752.0	-1.306963558091192e+18

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	50	49
1	50	49

end0.0ms

sample961.0ms

Algorithm

intervals

Results

310.0ms	6059×	body	80	valid
193.0ms	656×	body	2560	valid
117.0ms	480×	body	1280	valid
97.0ms	274×	body	5120	valid
58.0ms	307×	body	640	valid
21.0ms	148×	body	320	valid
7.0ms	76×	body	160	valid

Details

analyze359.0ms

sample36.0ms

simplify3.0ms

prune7.0ms

localize11.0ms

rewrite27.0ms

series43.0ms

simplify28.0ms

prune135.0ms

localize13.0ms

rewrite46.0ms

series26.0ms

simplify70.0ms

prune154.0ms

localize13.0ms

rewrite33.0ms

series43.0ms

simplify44.0ms

prune209.0ms

localize14.0ms

rewrite32.0ms

series44.0ms

simplify40.0ms

prune137.0ms

regimes315.0ms

bsearch46.0ms

simplify2.0ms

end0.0ms

sample961.0ms

Profiling