Details

analyze364.0ms (2.9%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
6.2%	93.6%	0.2%	5
6.2%	68.6%	25.1%	6
6.2%	49.9%	43.9%	7
6.2%	35.9%	57.9%	8
6.2%	25.3%	68.4%	9
6.2%	20.1%	73.7%	10
6.2%	15.7%	78.1%	11
6.2%	12%	81.7%	12
6.2%	9%	84.8%	13
6.2%	7.5%	86.3%	14

Compiler

Compiled 32 to 28 computations (12.5% saved)

sample138.0ms (1.1%)

Algorithm

1×

intervals

Results

46.0ms	133×	body	512	valid
37.0ms	314×	body	128	nan
23.0ms	50×	body	1024	valid
8.0ms	37×	body	256	valid
4.0ms	36×	body	128	valid

Compiler

Compiled 63 to 59 computations (6.3% saved)

simplify237.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5168	50

prune4.0ms (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: 5.5b

Counts

2 → 1

Compiler

Compiled 62 to 54 computations (12.9% saved)

localize26.0ms (0.2%)

Local error

Found 4 expressions with local error:

2.8b	(-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t))
3.0b	(-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))
3.5b	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
3.7b	(-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))

rewrite81.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

44×	`sqrt-prod_binary64_15098` `add-sqr-sqrt_binary64_15104`
40×	`*-un-lft-identity_binary64_15082`
24×	`cancel-sign-sub-inv_binary64_15048`
16×	`difference-of-squares_binary64_15051`
12×	`distribute-lft-out--_binary64_15034` `add-cube-cbrt_binary64_15117` `add-log-exp_binary64_15121`
4×	`flip3--_binary64_15086` `add-cbrt-cube_binary64_15118` `sub-neg_binary64_15075` `pow1_binary64_15143` `distribute-lft-out_binary64_15033` `add-exp-log_binary64_15120` `diff-log_binary64_15174` `flip--_binary64_15057`

Counts

4 → 96

Calls

4 calls:

18.0ms	(-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))
14.0ms	(-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t))
14.0ms	(-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))
11.0ms	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

series349.0ms (2.8%)

Counts

4 → 12

Calls

4 calls:

104.0ms	(-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))
99.0ms	(-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))
78.0ms	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
66.0ms	(-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t))

simplify105.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 0 (75.0ms)

Iter	Nodes	Cost
0	5136	2211

prune251.0ms (2%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	99	9	108
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	100	9	109

Merged error: 1.1b

Counts

109 → 9

Compiler

Compiled 4586 to 2976 computations (35.1% saved)

localize27.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z)))
2.8b	(-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t))
3.0b	(-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))
3.5b	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

rewrite75.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

70×	`*-un-lft-identity_binary64_15082`
49×	`sqrt-prod_binary64_15098`
45×	`add-sqr-sqrt_binary64_15104`
21×	`add-cube-cbrt_binary64_15117`
19×	`distribute-lft-out_binary64_15033`
18×	`times-frac_binary64_15088` `cancel-sign-sub-inv_binary64_15048`
12×	`difference-of-squares_binary64_15051`
10×	`add-log-exp_binary64_15121`
9×	`distribute-lft-out--_binary64_15034`
8×	`add-exp-log_binary64_15120`
6×	`add-cbrt-cube_binary64_15118` `associate-/r*_binary64_15026`
5×	`pow1_binary64_15143`
3×	`flip3--_binary64_15086` `sub-neg_binary64_15075` `diff-log_binary64_15174` `flip--_binary64_15057` `associate-/l*_binary64_15027`
2×	`div-exp_binary64_15133` `associate-/r/_binary64_15028`
1×	`inv-pow_binary64_15167` `frac-2neg_binary64_15093` `clear-num_binary64_15081` `flip-+_binary64_15056` `cbrt-undiv_binary64_15116` `div-inv_binary64_15079` `1-exp_binary64_15126` `rec-exp_binary64_15132` `flip3-+_binary64_15085` `pow-flip_binary64_15156`

Counts

4 → 117

Calls

4 calls:

19.0ms	(-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))
14.0ms	(-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t))
12.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z)))
11.0ms	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

series295.0ms (2.3%)

Counts

4 → 12

Calls

4 calls:

84.0ms	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
72.0ms	(-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t))
70.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z)))
69.0ms	(-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))

simplify101.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	5112	2622

prune401.0ms (3.2%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	125	4	129
Fresh	3	5	8
Picked	1	0	1
Done	0	0	0
Total	129	9	138

Merged error: 0.6b

Counts

138 → 9

Compiler

Compiled 5615 to 3738 computations (33.4% saved)

localize55.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z)))
0.1b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 t)) (sqrt.f64 t)))
3.0b	(-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))
3.5b	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

rewrite122.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

100×	`*-un-lft-identity_binary64_15082`
54×	`sqrt-prod_binary64_15098`
46×	`add-sqr-sqrt_binary64_15104`
36×	`times-frac_binary64_15088`
34×	`distribute-lft-out_binary64_15033`
30×	`add-cube-cbrt_binary64_15117`
12×	`cancel-sign-sub-inv_binary64_15048` `associate-/r*_binary64_15026` `add-exp-log_binary64_15120`
8×	`difference-of-squares_binary64_15051` `add-cbrt-cube_binary64_15118` `add-log-exp_binary64_15121`
6×	`distribute-lft-out--_binary64_15034` `pow1_binary64_15143` `associate-/l*_binary64_15027`
4×	`div-exp_binary64_15133` `associate-/r/_binary64_15028`
2×	`inv-pow_binary64_15167` `frac-2neg_binary64_15093` `flip3--_binary64_15086` `clear-num_binary64_15081` `flip-+_binary64_15056` `cbrt-undiv_binary64_15116` `sub-neg_binary64_15075` `div-inv_binary64_15079` `diff-log_binary64_15174` `flip--_binary64_15057` `1-exp_binary64_15126` `rec-exp_binary64_15132` `flip3-+_binary64_15085` `pow-flip_binary64_15156`

Counts

4 → 138

Calls

4 calls:

23.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z)))
22.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 t)) (sqrt.f64 t)))
20.0ms	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
19.0ms	(-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))

series325.0ms (2.6%)

Counts

4 → 12

Calls

4 calls:

94.0ms	(-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))
91.0ms	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
83.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z)))
57.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 t)) (sqrt.f64 t)))

simplify117.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

150 → 150

Iterations

Useful iterations: 0 (76.0ms)

Iter	Nodes	Cost
0	4887	3026
1	4887	3026

prune430.0ms (3.4%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	148	2	150
Fresh	3	5	8
Picked	1	0	1
Done	0	0	0
Total	152	7	159

Merged error: 0.1b

Counts

159 → 7

Compiler

Compiled 6637 to 4507 computations (32.1% saved)

localize33.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z)))
0.1b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 t)) (sqrt.f64 t)))
0.2b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y)))
3.5b	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

rewrite80.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

130×	`*-un-lft-identity_binary64_15082`
59×	`sqrt-prod_binary64_15098`
54×	`times-frac_binary64_15088`
49×	`distribute-lft-out_binary64_15033`
47×	`add-sqr-sqrt_binary64_15104`
39×	`add-cube-cbrt_binary64_15117`
18×	`associate-/r*_binary64_15026`
16×	`add-exp-log_binary64_15120`
10×	`add-cbrt-cube_binary64_15118`
9×	`associate-/l*_binary64_15027`
7×	`pow1_binary64_15143`
6×	`div-exp_binary64_15133` `cancel-sign-sub-inv_binary64_15048` `add-log-exp_binary64_15121` `associate-/r/_binary64_15028`
4×	`difference-of-squares_binary64_15051`
3×	`inv-pow_binary64_15167` `frac-2neg_binary64_15093` `distribute-lft-out--_binary64_15034` `clear-num_binary64_15081` `flip-+_binary64_15056` `cbrt-undiv_binary64_15116` `div-inv_binary64_15079` `1-exp_binary64_15126` `rec-exp_binary64_15132` `flip3-+_binary64_15085` `pow-flip_binary64_15156`
1×	`flip3--_binary64_15086` `sub-neg_binary64_15075` `diff-log_binary64_15174` `flip--_binary64_15057`

Counts

4 → 159

Calls

4 calls:

20.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z)))
15.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 t)) (sqrt.f64 t)))
12.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y)))
11.0ms	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

series286.0ms (2.3%)

Counts

4 → 12

Calls

4 calls:

110.0ms	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
62.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z)))
58.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y)))
55.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 t)) (sqrt.f64 t)))

simplify126.0ms (1%)

Algorithm

1×	egg-herbie

Counts

171 → 171

Iterations

Useful iterations: 0 (70.0ms)

Iter	Nodes	Cost
0	4904	3440
1	4904	3440

prune580.0ms (4.6%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	167	4	171
Fresh	3	3	6
Picked	1	0	1
Done	0	0	0
Total	171	7	178

Merged error: 0.0b

Counts

178 → 7

Compiler

Compiled 7563 to 5199 computations (31.3% saved)

regimes1.5s (12.1%)

Compiler: Compiled 18741 to 16050 computations (14.4% saved)

bsearch0.0ms (0%)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	41	62
1	41	62

end0.0ms (0%)

sample6.4s (51.2%)

Algorithm

1×

intervals

Results

1.8s	4396×	body	512	valid
1.3s	9331×	body	128	nan
902.0ms	1690×	body	1024	valid
282.0ms	1031×	body	256	valid
119.0ms	883×	body	128	valid

Compiler

Compiled 1450 to 1243 computations (14.3% saved)

Details

analyze364.0ms (2.9%)

sample138.0ms (1.1%)

simplify237.0ms (1.9%)

prune4.0ms (0%)

localize26.0ms (0.2%)

rewrite81.0ms (0.6%)

series349.0ms (2.8%)

simplify105.0ms (0.8%)

prune251.0ms (2%)

localize27.0ms (0.2%)

rewrite75.0ms (0.6%)

series295.0ms (2.3%)

simplify101.0ms (0.8%)

prune401.0ms (3.2%)

localize55.0ms (0.4%)

rewrite122.0ms (1%)

series325.0ms (2.6%)

simplify117.0ms (0.9%)

prune430.0ms (3.4%)

localize33.0ms (0.3%)

rewrite80.0ms (0.6%)

series286.0ms (2.3%)

simplify126.0ms (1%)

prune580.0ms (4.6%)

regimes1.5s (12.1%)

bsearch0.0ms (0%)

simplify5.0ms (0%)

end0.0ms (0%)

sample6.4s (51.2%)

Profiling