Details

analyze3.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	74.6%	25.4%	0
0%	74.6%	25.4%	1
37.3%	37.3%	25.4%	2
37.3%	18.7%	44%	3
46.7%	9.3%	44%	4
46.7%	4.7%	48.7%	5
49%	2.3%	48.7%	6
49%	1.2%	49.8%	7
49.6%	0.6%	49.8%	8
49.9%	0.3%	49.8%	9
49.9%	0.1%	50%	10
49.9%	0.1%	50.1%	11
49.9%	0%	50.1%	12
49.9%	0%	50.1%	13
49.9%	0%	50.1%	14

Compiler

Compiled 7 to 6 computations (14.3% saved)

sample41.0ms (1.3%)

Algorithm

1×

intervals

Results

22.0ms	135×	body	1024	valid
5.0ms	64×	body	512	valid
3.0ms	256×	pre	128	true
3.0ms	15×	body	2048	valid
1.0ms	24×	body	256	valid
0.0ms	18×	body	128	valid

Compiler

Compiled 11 to 11 computations (0% saved)

simplify166.0ms (5.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	9	6
1	9	6

prune2.0ms (0.1%)

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: 58.8b

Counts

2 → 1

Compiler

Compiled 8 to 8 computations (0% saved)

localize3.0ms (0.1%)

Local error

Found 1 expressions with local error:

6.0b	(-.f64 (exp.f64 x) 1)

rewrite7.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`add-sqr-sqrt_binary64_1123`
5×	`*-un-lft-identity_binary64_1101`
3×	`add-log-exp_binary64_1140` `cancel-sign-sub-inv_binary64_1067`
2×	`difference-of-squares_binary64_1070` `add-cube-cbrt_binary64_1136`
1×	`diff-log_binary64_1193` `add-exp-log_binary64_1139` `pow1_binary64_1162` `sub-neg_binary64_1094` `difference-of-sqr-1_binary64_1071` `distribute-lft-out--_binary64_1053` `flip--_binary64_1076` `flip3--_binary64_1105` `add-cbrt-cube_binary64_1137`

Counts

1 → 18

Calls

1 calls:

6.0ms

(-.f64 (exp.f64 x) 1)

series20.0ms (0.7%)

Counts

1 → 3

Calls

1 calls:

20.0ms

(-.f64 (exp.f64 x) 1)

simplify102.0ms (3.4%)

Algorithm

1×	egg-herbie

Counts

21 → 21

Iterations

Useful iterations: 0 (95.0ms)

Iter	Nodes	Cost
0	4841	199
1	4841	199

prune23.0ms (0.8%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	19	2	21
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	20	2	22

Merged error: 0.0b

Counts

22 → 2

Compiler

Compiled 188 to 117 computations (37.8% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(.f64 x (.f64 x (+.f64 1/2 (*.f64 x 1/6))))
0.0b	(.f64 x (+.f64 1/2 (.f64 x 1/6)))
0.4b	(*.f64 x 1/6)

rewrite24.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`add-sqr-sqrt_binary64_1123` `add-exp-log_binary64_1139` `pow1_binary64_1162` `add-cbrt-cube_binary64_1137`
9×	`associate-l_binary64_1042`
8×	`*-un-lft-identity_binary64_1101` `add-cube-cbrt_binary64_1136`
7×	`associate-r_binary64_1041`
6×	`associate-*r/_binary64_1043`
5×	`cbrt-unprod_binary64_1134` `prod-exp_binary64_1150` `distribute-lft-in_binary64_1050` `pow-prod-down_binary64_1172` `distribute-rgt-in_binary64_1051`
3×	`*-commutative_binary64_1032` `add-log-exp_binary64_1140`
2×	`flip3-+_binary64_1104` `flip-+_binary64_1075` `unswap-sqr_binary64_1069`

Counts

3 → 64

Calls

3 calls:

8.0ms	(.f64 x (.f64 x (+.f64 1/2 (*.f64 x 1/6))))
6.0ms	(.f64 x (+.f64 1/2 (.f64 x 1/6)))
5.0ms	(*.f64 x 1/6)

series192.0ms (6.3%)

Counts

3 → 9

Calls

3 calls:

87.0ms	(.f64 x (.f64 x (+.f64 1/2 (*.f64 x 1/6))))
83.0ms	(.f64 x (+.f64 1/2 (.f64 x 1/6)))
21.0ms	(*.f64 x 1/6)

simplify70.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4998	823
1	4998	823

prune59.0ms (1.9%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	73	0	73
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	73	2	75

Merged error: 0.0b

Counts

75 → 2

Compiler

Compiled 1116 to 760 computations (31.9% saved)

localize8.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (exp.f64 x))
0.0b	(sqrt.f64 (exp.f64 x))
0.0b	(*.f64 (+.f64 1 (sqrt.f64 (exp.f64 x))) (+.f64 -1 (sqrt.f64 (exp.f64 x))))
6.0b	(+.f64 -1 (sqrt.f64 (exp.f64 x)))

rewrite29.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`*-un-lft-identity_binary64_1101`
15×	`add-sqr-sqrt_binary64_1123`
10×	`add-cube-cbrt_binary64_1136`
8×	`pow1_binary64_1162` `sqrt-pow1_binary64_1119`
7×	`flip3-+_binary64_1104` `sqrt-prod_binary64_1117` `flip-+_binary64_1075`
6×	`add-log-exp_binary64_1140` `add-exp-log_binary64_1139` `exp-prod_binary64_1153` `add-cbrt-cube_binary64_1137`
5×	`associate-l_binary64_1042`
4×	`frac-times_binary64_1111` `distribute-lft-out_binary64_1052` `associate-r_binary64_1041`
2×	`rem-sqrt-square_binary64_1114` `associate-r/_binary64_1043` `associate-l/_binary64_1044` `pow1/2_binary64_1181`
1×	`*-commutative_binary64_1032` `cbrt-unprod_binary64_1134` `prod-exp_binary64_1150` `sum-log_binary64_1192` `distribute-lft-in_binary64_1050` `+-commutative_binary64_1031` `pow-prod-down_binary64_1172` `unswap-sqr_binary64_1069` `distribute-rgt-in_binary64_1051`

Counts

4 → 75

Calls

4 calls:

13.0ms	(*.f64 (+.f64 1 (sqrt.f64 (exp.f64 x))) (+.f64 -1 (sqrt.f64 (exp.f64 x))))
5.0ms	(+.f64 -1 (sqrt.f64 (exp.f64 x)))
2.0ms	(sqrt.f64 (exp.f64 x))
2.0ms	(sqrt.f64 (exp.f64 x))

series178.0ms (5.9%)

Counts

4 → 12

Calls

4 calls:

93.0ms	(*.f64 (+.f64 1 (sqrt.f64 (exp.f64 x))) (+.f64 -1 (sqrt.f64 (exp.f64 x))))
33.0ms	(+.f64 -1 (sqrt.f64 (exp.f64 x)))
29.0ms	(sqrt.f64 (exp.f64 x))
22.0ms	(sqrt.f64 (exp.f64 x))

simplify67.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5168	990

prune71.0ms (2.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	84	3	87
Fresh	0	0	0
Picked	1	0	1
Done	0	1	1
Total	85	4	89

Merged error: 0.0b

Counts

89 → 4

Compiler

Compiled 1330 to 694 computations (47.8% saved)

localize12.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (exp.f64 x))
0.0b	(.f64 (.f64 x x) (+.f64 1/8 (*.f64 x 1/48)))
0.0b	(.f64 (+.f64 1 (sqrt.f64 (exp.f64 x))) (+.f64 (.f64 x 1/2) (.f64 (.f64 x x) (+.f64 1/8 (*.f64 x 1/48)))))
0.4b	(*.f64 x 1/48)

rewrite38.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-sqr-sqrt_binary64_1123`
14×	`*-un-lft-identity_binary64_1101` `pow1_binary64_1162`
13×	`add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137`
11×	`add-cube-cbrt_binary64_1136`
9×	`associate-r_binary64_1041` `associate-l_binary64_1042`
7×	`flip3-+_binary64_1104` `flip-+_binary64_1075`
5×	`cbrt-unprod_binary64_1134` `prod-exp_binary64_1150` `pow-prod-down_binary64_1172`
4×	`frac-times_binary64_1111` `add-log-exp_binary64_1140` `sqrt-pow1_binary64_1119` `sqrt-prod_binary64_1117` `associate-*r/_binary64_1043`
3×	`*-commutative_binary64_1032` `exp-prod_binary64_1153` `unswap-sqr_binary64_1069`
2×	`distribute-lft-out_binary64_1052` `distribute-lft-in_binary64_1050` `associate-*l/_binary64_1044` `distribute-rgt-in_binary64_1051`
1×	`rem-sqrt-square_binary64_1114` `pow1/2_binary64_1181`

Counts

4 → 87

Calls

4 calls:

13.0ms	(.f64 (+.f64 1 (sqrt.f64 (exp.f64 x))) (+.f64 (.f64 x 1/2) (.f64 (.f64 x x) (+.f64 1/8 (*.f64 x 1/48)))))
9.0ms	(.f64 (.f64 x x) (+.f64 1/8 (*.f64 x 1/48)))
4.0ms	(*.f64 x 1/48)
2.0ms	(sqrt.f64 (exp.f64 x))

series202.0ms (6.7%)

Counts

4 → 12

Calls

4 calls:

86.0ms	(.f64 (.f64 x x) (+.f64 1/8 (*.f64 x 1/48)))
72.0ms	(.f64 (+.f64 1 (sqrt.f64 (exp.f64 x))) (+.f64 (.f64 x 1/2) (.f64 (.f64 x x) (+.f64 1/8 (*.f64 x 1/48)))))
23.0ms	(sqrt.f64 (exp.f64 x))
22.0ms	(*.f64 x 1/48)

simplify64.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4953	1806
1	4953	1806

prune117.0ms (3.9%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	98	1	99
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	99	4	103

Merged error: 0.0b

Counts

103 → 4

Compiler

Compiled 2491 to 1575 computations (36.8% saved)

regimes107.0ms (3.5%)

Compiler: Compiled 1018 to 774 computations (24% saved)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	24	29
1	24	29

end0.0ms (0%)

sample1.4s (46.6%)

Algorithm

1×

intervals

Results

575.0ms	4103×	body	1024	valid
147.0ms	1956×	body	512	valid
100.0ms	8000×	pre	128	true
59.0ms	389×	body	2048	valid
47.0ms	985×	body	256	valid
14.0ms	567×	body	128	valid

Compiler

Compiled 310 to 235 computations (24.2% saved)

Details

analyze3.0ms (0.1%)

sample41.0ms (1.3%)

simplify166.0ms (5.5%)

prune2.0ms (0.1%)

localize3.0ms (0.1%)

rewrite7.0ms (0.2%)

series20.0ms (0.7%)

simplify102.0ms (3.4%)

prune23.0ms (0.8%)

localize7.0ms (0.2%)

rewrite24.0ms (0.8%)

series192.0ms (6.3%)

simplify70.0ms (2.3%)

prune59.0ms (1.9%)

localize8.0ms (0.3%)

rewrite29.0ms (0.9%)

series178.0ms (5.9%)

simplify67.0ms (2.2%)

prune71.0ms (2.3%)

localize12.0ms (0.4%)

rewrite38.0ms (1.3%)

series202.0ms (6.7%)

simplify64.0ms (2.1%)

prune117.0ms (3.9%)

regimes107.0ms (3.5%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample1.4s (46.6%)

Profiling