Details

analyze372.0ms

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

sample34.0ms

Algorithm

intervals

Results

10.0ms	200×	body	80	valid
6.0ms	20×	body	2560	valid
3.0ms	7×	body	5120	valid
2.0ms	12×	body	640	valid
2.0ms	9×	body	1280	valid
1.0ms	6×	body	320	valid
0.0ms	2×	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: 38.1b

Counts

2 → 1

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
0.4b	(+ (sqrt (+ (* re re) (* im im))) re)
29.9b	(sqrt (+ (* re re) (* im im)))

rewrite20.0ms

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:

8.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
7.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
5.0ms	(sqrt (+ (* re re) (* im im)))

series38.0ms

Counts

3 → 9

Calls

3 calls:

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

simplify56.0ms

Algorithm

egg-herbie

Counts

49 → 49

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4936	551
1	4936	551

prune113.0ms

Filtered

42 candidates to 49 candidates (-16.7%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	43	6	49
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	44	6	50

Merged error: 15.8b

Counts

50 → 6

localize16.0ms

Local error

Found 4 expressions with local error:

8.4b	(+ (* (* (cbrt (sqrt (+ (* re re) (* im im)))) (cbrt (sqrt (+ (* re re) (* im im))))) (cbrt (sqrt (+ (* re re) (* im im))))) re)
29.9b	(sqrt (+ (* re re) (* im im)))
29.9b	(sqrt (+ (* re re) (* im im)))
29.9b	(sqrt (+ (* re re) (* im im)))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 56

Calls

4 calls:

23.0ms	(+ (* (* (cbrt (sqrt (+ (* re re) (* im im)))) (cbrt (sqrt (+ (* re re) (* im im))))) (cbrt (sqrt (+ (* re re) (* im im))))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))
4.0ms	(sqrt (+ (* re re) (* im im)))
4.0ms	(sqrt (+ (* re re) (* im im)))

series25.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify57.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5310	612

prune114.0ms

Filtered

56 candidates to 68 candidates (-21.4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	68	0	68
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	68	6	74

Merged error: 15.8b

Counts

74 → 6

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sqrt (* (* im im) 2.0)) (sqrt (- (sqrt (+ (* re re) (* im im))) re)))
1.3b	(- (sqrt (+ (* re re) (* im im))) re)
29.9b	(sqrt (+ (* re re) (* im im)))
30.6b	(sqrt (* (* im im) 2.0))

rewrite36.0ms

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:

17.0ms	(/ (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))

series39.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(/ (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))

simplify49.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	4917	2308
1	4917	2308

prune203.0ms

Filtered

85 candidates to 117 candidates (-37.6%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	110	7	117
Fresh	2	2	4
Picked	1	0	1
Done	1	0	1
Total	114	9	123

Merged error: 11.0b

Counts

123 → 9

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (fabs im) (/ (sqrt 2.0) (sqrt (- (sqrt (+ (* im im) (* re re))) re))))
0.3b	(/ (sqrt 2.0) (sqrt (- (sqrt (+ (* im im) (* re re))) re)))
1.3b	(- (sqrt (+ (* im im) (* re re))) re)
29.9b	(sqrt (+ (* im im) (* re re)))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 195

Calls

4 calls:

24.0ms	(* (fabs im) (/ (sqrt 2.0) (sqrt (- (sqrt (+ (* im im) (* re re))) re))))
12.0ms	(/ (sqrt 2.0) (sqrt (- (sqrt (+ (* im im) (* re re))) re)))
8.0ms	(- (sqrt (+ (* im im) (* re re))) re)
4.0ms	(sqrt (+ (* im im) (* re re)))

series63.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(* (fabs im) (/ (sqrt 2.0) (sqrt (- (sqrt (+ (* im im) (* re re))) re))))
21.0ms	(/ (sqrt 2.0) (sqrt (- (sqrt (+ (* im im) (* re re))) re)))
11.0ms	(- (sqrt (+ (* im im) (* re re))) re)
6.0ms	(sqrt (+ (* im im) (* re re)))

simplify63.0ms

Algorithm

egg-herbie

Counts

207 → 207

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	4992	4007
1	4992	4007

prune235.0ms

Filtered

111 candidates to 207 candidates (-86.5%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	202	5	207
Fresh	3	5	8
Picked	1	0	1
Done	0	0	0
Total	206	10	216

Merged error: 2.5b

Counts

216 → 10

regimes357.0ms

Accuracy

36.7% (22.3b remaining)

Error of 24.7b against oracle of 2.4b and baseline of 37.6b

bsearch224.0ms

Steps

Iters	Range		Point
8	1.6073451226672565e-53	8.146918205299875e-51	1.6256659982008955e-53
5	4.4335198511299244e-256	1.5394121772547398e-255	9.31958241418903e-256
7	4.90167134011844e-303	5.420240690527463e-301	4.5315791895923296e-301
4	-5.847481117529312e-203	-3.862281142630397e-203	-5.343399453899552e-203
9	-2.052157511824163e-165	-4.2598212817702325e-171	-5.246210656301982e-170
10	-9.938224781261647e-136	-5.604297157085938e-150	-6.581642780549371e-136
10	-2.870042175967054e-91	-5.943908579670495e-104	-8.123931497249956e-104
6	-6.11877097291748e+79	-1.2351617950470747e+79	-6.009215179797225e+79
9	-4.695560266516465e+97	-1.731216653249741e+88	-1.7798394941061263e+88

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	103	158
1	103	158

end0.0ms

sample1.0s

Algorithm

intervals

Results

320.0ms	6030×	body	80	valid
206.0ms	655×	body	2560	valid
129.0ms	491×	body	1280	valid
110.0ms	298×	body	5120	valid
58.0ms	296×	body	640	valid
23.0ms	159×	body	320	valid
7.0ms	71×	body	160	valid

Details

analyze372.0ms

sample34.0ms

simplify3.0ms

prune8.0ms

localize11.0ms

rewrite20.0ms

series38.0ms

simplify56.0ms

prune113.0ms

localize16.0ms

rewrite37.0ms

series25.0ms

simplify57.0ms

prune114.0ms

localize14.0ms

rewrite36.0ms

series39.0ms

simplify49.0ms

prune203.0ms

localize17.0ms

rewrite58.0ms

series63.0ms

simplify63.0ms

prune235.0ms

regimes357.0ms

bsearch224.0ms

simplify2.0ms

end0.0ms

sample1.0s

Profiling