Details

analyze522.0ms (0.9%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
25%	75%	0%	3
25%	50%	25%	4
25%	37.5%	37.5%	5
25%	31.2%	43.8%	6
25%	28.1%	46.9%	7
25%	26.5%	48.5%	8
25%	25.8%	49.2%	9
25%	25.4%	49.6%	10
25%	25.2%	49.8%	11
25%	25.1%	49.9%	12
25%	25%	50%	13
25%	25%	50%	14

Compiler

Compiled 10 to 8 computations (20% saved)

sample111.0ms (0.2%)

Algorithm

1×

intervals

Results

43.0ms	140×	body	2048	nan
21.0ms	256×	body	128	valid
18.0ms	75×	body	1024	nan
6.0ms	32×	body	512	nan
2.0ms	18×	body	256	nan
1.0ms	16×	body	128	nan

Compiler

Compiled 19 to 16 computations (15.8% saved)

simplify567.0ms (1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (340.0ms)

Iter	Nodes	Cost
0	4922	14
1	4922	14

prune14.0ms (0%)

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: 33.1b

Counts

2 → 1

Compiler

Compiled 18 to 14 computations (22.2% saved)

localize29.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1))))
0.0b	(-.f64 (*.f64 x x) 1)
30.8b	(sqrt.f64 (-.f64 (*.f64 x x) 1))

rewrite53.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`*-un-lft-identity_binary64_760`
9×	`add-sqr-sqrt_binary64_782`
6×	`sqrt-prod_binary64_776` `add-cube-cbrt_binary64_795`
5×	`add-log-exp_binary64_799` `pow1_binary64_821`
4×	`add-exp-log_binary64_798` `difference-of-squares_binary64_729` `log-prod_binary64_846`
3×	`cancel-sign-sub-inv_binary64_726` `add-cbrt-cube_binary64_796`
2×	`log-div_binary64_847` `sqrt-div_binary64_777` `difference-of-sqr-1_binary64_730` `flip--_binary64_735` `flip3--_binary64_764`
1×	`diff-log_binary64_852` `rem-sqrt-square_binary64_773` `distribute-lft-out_binary64_711` `flip3-+_binary64_763` `sqrt-pow1_binary64_778` `flip-+_binary64_734` `log-pow_binary64_849` `rem-log-exp_binary64_801` `pow1/2_binary64_840` `sub-neg_binary64_753`

Counts

3 → 50

Calls

3 calls:

25.0ms	(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1))))
11.0ms	(sqrt.f64 (-.f64 (*.f64 x x) 1))
10.0ms	(-.f64 (*.f64 x x) 1)

series390.0ms (0.7%)

Counts

3 → 9

Calls

3 calls:

232.0ms	(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1))))
106.0ms	(-.f64 (*.f64 x x) 1)
51.0ms	(sqrt.f64 (-.f64 (*.f64 x x) 1))

simplify135.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

59 → 59

Iterations

Useful iterations: 0 (107.0ms)

Iter	Nodes	Cost
0	5119	839

prune577.0ms (1%)

Pruning

20 alts after pruning (19 fresh and 1 done)

	Pruned	Kept	Total
New	40	19	59
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	40	20	60

Merged error: 0b

Counts

60 → 20

Compiler

Compiled 1188 to 808 computations (32% saved)

localize40.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.0b	(log.f64 (+.f64 x (*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (-.f64 x 1)))))
0.5b	(*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (-.f64 x 1)))

rewrite86.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`add-sqr-sqrt_binary64_782`
15×	`sqrt-prod_binary64_776`
12×	`*-un-lft-identity_binary64_760` `sqrt-div_binary64_777`
10×	`associate-r_binary64_700`
7×	`add-cube-cbrt_binary64_795` `associate-l_binary64_701` `pow1_binary64_821`
5×	`add-exp-log_binary64_798`
4×	`unswap-sqr_binary64_728` `flip3-+_binary64_763` `flip-+_binary64_734` `add-cbrt-cube_binary64_796` `frac-times_binary64_770`
3×	`pow-prod-down_binary64_831` `flip--_binary64_735` `log-prod_binary64_846` `flip3--_binary64_764`
2×	`log-div_binary64_847` `associate-l/_binary64_703` `sqrt-pow1_binary64_778` `add-log-exp_binary64_799` `difference-of-squares_binary64_729` `associate-r/_binary64_702` `pow1/2_binary64_840`
1×	`distribute-lft-out_binary64_711` `prod-exp_binary64_809` `difference-of-sqr-1_binary64_730` `sqrt-unprod_binary64_780` `log-pow_binary64_849` `distribute-lft-out--_binary64_712` `rem-log-exp_binary64_801` `cbrt-unprod_binary64_793` `*-commutative_binary64_691`

Counts

2 → 57

Calls

2 calls:

53.0ms	(*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (-.f64 x 1)))
12.0ms	(log.f64 (+.f64 x (*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (-.f64 x 1)))))

series201.0ms (0.4%)

Counts

2 → 6

Calls

2 calls:

119.0ms	(*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (-.f64 x 1)))
81.0ms	(log.f64 (+.f64 x (*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (-.f64 x 1)))))

simplify138.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 0 (105.0ms)

Iter	Nodes	Cost
0	5079	1377

prune907.0ms (1.6%)

Pruning

34 alts after pruning (32 fresh and 2 done)

	Pruned	Kept	Total
New	44	19	63
Fresh	5	13	18
Picked	0	1	1
Done	0	1	1
Total	49	34	83

Merged error: 0b

Counts

83 → 34

Compiler

Compiled 2005 to 1539 computations (23.2% saved)

localize33.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(sqrt.f64 (sqrt.f64 (+.f64 x 1)))
0.1b	(sqrt.f64 (sqrt.f64 (+.f64 x 1)))
0.3b	(.f64 (sqrt.f64 (sqrt.f64 (+.f64 x 1))) (.f64 (sqrt.f64 (-.f64 x 1)) (sqrt.f64 (sqrt.f64 (+.f64 x 1)))))
0.4b	(*.f64 (sqrt.f64 (-.f64 x 1)) (sqrt.f64 (sqrt.f64 (+.f64 x 1))))

rewrite134.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

116×	`sqrt-div_binary64_777`
62×	`sqrt-prod_binary64_776`
36×	`add-sqr-sqrt_binary64_782`
32×	`frac-times_binary64_770`
27×	`*-un-lft-identity_binary64_760`
23×	`flip3-+_binary64_763` `flip-+_binary64_734`
20×	`associate-l_binary64_701` `pow1_binary64_821`
16×	`add-cube-cbrt_binary64_795` `associate-*r/_binary64_702`
13×	`sqrt-pow1_binary64_778`
12×	`flip--_binary64_735` `flip3--_binary64_764`
11×	`add-exp-log_binary64_798` `add-cbrt-cube_binary64_796` `associate-r_binary64_700`
10×	`associate-*l/_binary64_703` `pow-prod-down_binary64_831`
9×	`pow1/2_binary64_840`
6×	`unswap-sqr_binary64_728`
4×	`rem-sqrt-square_binary64_773` `distribute-lft-out_binary64_711` `prod-exp_binary64_809` `add-log-exp_binary64_799` `cbrt-unprod_binary64_793`
3×	`sqrt-unprod_binary64_780`
2×	`difference-of-squares_binary64_729` `*-commutative_binary64_691`
1×	`difference-of-sqr-1_binary64_730` `distribute-lft-out--_binary64_712`

Counts

4 → 146

Calls

4 calls:

45.0ms	(.f64 (sqrt.f64 (sqrt.f64 (+.f64 x 1))) (.f64 (sqrt.f64 (-.f64 x 1)) (sqrt.f64 (sqrt.f64 (+.f64 x 1)))))
34.0ms	(*.f64 (sqrt.f64 (-.f64 x 1)) (sqrt.f64 (sqrt.f64 (+.f64 x 1))))
10.0ms	(sqrt.f64 (sqrt.f64 (+.f64 x 1)))
9.0ms	(sqrt.f64 (sqrt.f64 (+.f64 x 1)))

series303.0ms (0.5%)

Counts

4 → 12

Calls

4 calls:

130.0ms	(*.f64 (sqrt.f64 (-.f64 x 1)) (sqrt.f64 (sqrt.f64 (+.f64 x 1))))
88.0ms	(.f64 (sqrt.f64 (sqrt.f64 (+.f64 x 1))) (.f64 (sqrt.f64 (-.f64 x 1)) (sqrt.f64 (sqrt.f64 (+.f64 x 1)))))
45.0ms	(sqrt.f64 (sqrt.f64 (+.f64 x 1)))
39.0ms	(sqrt.f64 (sqrt.f64 (+.f64 x 1)))

simplify251.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

158 → 158

Iterations

Useful iterations: 0 (179.0ms)

Iter	Nodes	Cost
0	4897	3529
1	4897	3529

prune6.2s (11%)

Pruning

49 alts after pruning (46 fresh and 3 done)

	Pruned	Kept	Total
New	127	31	158
Fresh	16	15	31
Picked	0	1	1
Done	0	2	2
Total	143	49	192

Merged error: 0b

Counts

192 → 49

Compiler

Compiled 5551 to 4362 computations (21.4% saved)

localize66.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.5b	(*.f64 (cbrt.f64 (-.f64 x 1)) (cbrt.f64 (-.f64 x 1)))
0.6b	(cbrt.f64 (-.f64 x 1))
0.6b	(cbrt.f64 (-.f64 x 1))
0.6b	(cbrt.f64 (-.f64 x 1))

rewrite160.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

61×	`cbrt-prod_binary64_791`
55×	`add-sqr-sqrt_binary64_782`
44×	`*-un-lft-identity_binary64_760`
18×	`cbrt-div_binary64_792`
16×	`difference-of-squares_binary64_729`
15×	`add-cube-cbrt_binary64_795`
14×	`swap-sqr_binary64_727`
11×	`pow1_binary64_821`
10×	`associate-r_binary64_700` `associate-l_binary64_701`
9×	`pow1/3_binary64_842` `difference-of-sqr-1_binary64_730` `distribute-lft-out--_binary64_712` `flip--_binary64_735` `flip3--_binary64_764`
6×	`add-exp-log_binary64_798`
4×	`unswap-sqr_binary64_728` `add-log-exp_binary64_799` `add-cbrt-cube_binary64_796` `frac-times_binary64_770`
2×	`associate-l/_binary64_703` `pow-sqr_binary64_733` `associate-r/_binary64_702` `pow-prod-up_binary64_830` `pow-prod-down_binary64_831`
1×	`pow2_binary64_841` `prod-exp_binary64_809` `pow-plus_binary64_823` `cbrt-unprod_binary64_793` `*-commutative_binary64_691`

Counts

4 → 115

Calls

4 calls:

61.0ms	(*.f64 (cbrt.f64 (-.f64 x 1)) (cbrt.f64 (-.f64 x 1)))
16.0ms	(cbrt.f64 (-.f64 x 1))
15.0ms	(cbrt.f64 (-.f64 x 1))
11.0ms	(cbrt.f64 (-.f64 x 1))

series520.0ms (0.9%)

Counts

4 → 12

Calls

4 calls:

147.0ms	(*.f64 (cbrt.f64 (-.f64 x 1)) (cbrt.f64 (-.f64 x 1)))
131.0ms	(cbrt.f64 (-.f64 x 1))
125.0ms	(cbrt.f64 (-.f64 x 1))
117.0ms	(cbrt.f64 (-.f64 x 1))

simplify196.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 0 (121.0ms)

Iter	Nodes	Cost
0	5099	2112

prune4.4s (7.7%)

Pruning

62 alts after pruning (58 fresh and 4 done)

	Pruned	Kept	Total
New	104	23	127
Fresh	10	35	45
Picked	0	1	1
Done	0	3	3
Total	114	62	176

Merged error: 0b

Counts

176 → 62

Compiler

Compiled 4778 to 3829 computations (19.9% saved)

regimes5.3s (9.3%)

Compiler: Compiled 23092 to 19015 computations (17.7% saved)

bsearch4.7s (8.2%)

simplify70.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (6.0ms)

Iter	Nodes	Cost
0	33	51
1	33	51

end0.0ms (0%)

sample30.7s (54.1%)

Algorithm

1×

intervals

Results

1.8s	4014×	body	2048	nan
827.0ms	8000×	body	128	valid
631.0ms	2014×	body	1024	nan
240.0ms	1046×	body	512	nan
74.0ms	495×	body	256	nan
33.0ms	496×	body	128	nan
2.0ms	6×	body	4096	nan

Compiler

Compiled 7836 to 6458 computations (17.6% saved)

Pareto

2.527889426227442e-05

Details

analyze522.0ms (0.9%)

sample111.0ms (0.2%)

simplify567.0ms (1%)

prune14.0ms (0%)

localize29.0ms (0.1%)

rewrite53.0ms (0.1%)

series390.0ms (0.7%)

simplify135.0ms (0.2%)

prune577.0ms (1%)

localize40.0ms (0.1%)

rewrite86.0ms (0.2%)

series201.0ms (0.4%)

simplify138.0ms (0.2%)

prune907.0ms (1.6%)

localize33.0ms (0.1%)

rewrite134.0ms (0.2%)

series303.0ms (0.5%)

simplify251.0ms (0.4%)

prune6.2s (11%)

localize66.0ms (0.1%)

rewrite160.0ms (0.3%)

series520.0ms (0.9%)

simplify196.0ms (0.3%)

prune4.4s (7.7%)

regimes5.3s (9.3%)

bsearch4.7s (8.2%)

simplify70.0ms (0.1%)

end0.0ms (0%)

sample30.7s (54.1%)

Profiling