Details

analyze312.0ms (11.4%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
25%	75%	0%	3
25%	62.5%	12.5%	4
25%	56.2%	18.8%	5
28.1%	50%	21.9%	6
29.7%	46.9%	23.5%	7
30.5%	45.3%	24.3%	8
30.8%	44.9%	24.3%	9
31.2%	44.5%	24.3%	10
31.3%	44.4%	24.3%	11
31.4%	44.3%	24.3%	12
31.4%	44.2%	24.3%	13
31.5%	44.2%	24.3%	14

Compiler

Compiled 8 to 6 computations (25% saved)

sample30.0ms (1.1%)

Algorithm

1×

intervals

Results

15.0ms	94×	body	1024	valid
4.0ms	44×	body	512	valid
2.0ms	89×	body	128	valid
1.0ms	8×	body	2048	valid
1.0ms	21×	body	256	valid
0.0ms	1×	body	2048	invalid

Compiler

Compiled 15 to 12 computations (20% saved)

simplify164.0ms (6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	10	11
1	10	11

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: 43.3b

Counts

2 → 1

Compiler

Compiled 14 to 10 computations (28.6% saved)

localize4.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.7b	(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
1.8b	(-.f64 (exp.f64 x) 1)

rewrite18.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

34×	`add-sqr-sqrt_binary64_772`
29×	`*-un-lft-identity_binary64_751`
21×	`times-frac_binary64_757`
14×	`add-cube-cbrt_binary64_783`
10×	`difference-of-squares_binary64_720`
7×	`associate-/r*_binary64_697`
5×	`distribute-lft-out--_binary64_705` `difference-of-sqr-1_binary64_721`
4×	`add-log-exp_binary64_787` `add-cbrt-cube_binary64_784`
3×	`add-exp-log_binary64_786` `associate-/l*_binary64_698`
2×	`pow1_binary64_809` `flip--_binary64_726` `associate-/r/_binary64_699` `flip3--_binary64_755`
1×	`div-inv_binary64_748` `diff-log_binary64_840` `cbrt-undiv_binary64_782` `frac-2neg_binary64_762` `clear-num_binary64_750` `sub-neg_binary64_744` `div-exp_binary64_799`

Counts

2 → 60

Calls

2 calls:

8.0ms	(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
5.0ms	(-.f64 (exp.f64 x) 1)

series95.0ms (3.5%)

Counts

2 → 6

Calls

2 calls:

77.0ms	(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
18.0ms	(-.f64 (exp.f64 x) 1)

simplify47.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	4932	1126
1	4932	1126

prune64.0ms (2.3%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	63	3	66
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	64	3	67

Merged error: 0b

Counts

67 → 3

Compiler

Compiled 938 to 466 computations (50.3% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b	(+.f64 (*.f64 x 1/12) (+.f64 1/2 (/.f64 1 x)))
0.3b	(*.f64 x 1/12)

rewrite16.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`add-log-exp_binary64_787`
6×	`add-sqr-sqrt_binary64_772`
4×	`add-cube-cbrt_binary64_783` `pow1_binary64_809` `add-cbrt-cube_binary64_784` `*-un-lft-identity_binary64_751` `add-exp-log_binary64_786`
3×	`sum-log_binary64_839` `associate-l_binary64_694` `associate-r_binary64_693`
1×	`prod-exp_binary64_797` `+-commutative_binary64_683` `unswap-sqr_binary64_719` `flip3-+_binary64_754` `pow-prod-down_binary64_819` `*-commutative_binary64_684` `associate-+r+_binary64_685` `cbrt-unprod_binary64_781` `flip-+_binary64_725`

Counts

2 → 31

Calls

2 calls:

10.0ms	(+.f64 (*.f64 x 1/12) (+.f64 1/2 (/.f64 1 x)))
4.0ms	(*.f64 x 1/12)

series42.0ms (1.5%)

Counts

2 → 6

Calls

2 calls:

23.0ms	(*.f64 x 1/12)
19.0ms	(+.f64 (*.f64 x 1/12) (+.f64 1/2 (/.f64 1 x)))

simplify73.0ms (2.7%)

Algorithm

1×	egg-herbie

Counts

37 → 37

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	4895	417
1	4895	417

prune33.0ms (1.2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	37	0	37
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	37	3	40

Merged error: 0b

Counts

40 → 3

Compiler

Compiled 517 to 412 computations (20.3% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b	(/.f64 1 (-.f64 1 (exp.f64 (neg.f64 x))))
1.8b	(-.f64 1 (exp.f64 (neg.f64 x)))

rewrite17.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`*-un-lft-identity_binary64_751` `add-sqr-sqrt_binary64_772`
18×	`times-frac_binary64_757`
13×	`add-cube-cbrt_binary64_783`
10×	`difference-of-squares_binary64_720`
6×	`associate-/r*_binary64_697` `add-exp-log_binary64_786`
5×	`distribute-lft-out--_binary64_705`
4×	`add-log-exp_binary64_787` `add-cbrt-cube_binary64_784`
3×	`pow1_binary64_809` `associate-/l*_binary64_698`
2×	`flip--_binary64_726` `associate-/r/_binary64_699` `flip3--_binary64_755` `div-exp_binary64_799`
1×	`1-exp_binary64_792` `rec-exp_binary64_798` `inv-pow_binary64_833` `div-inv_binary64_748` `diff-log_binary64_840` `cbrt-undiv_binary64_782` `frac-2neg_binary64_762` `clear-num_binary64_750` `sub-neg_binary64_744` `pow-flip_binary64_822`

Counts

2 → 59

Calls

2 calls:

8.0ms	(/.f64 1 (-.f64 1 (exp.f64 (neg.f64 x))))
5.0ms	(-.f64 1 (exp.f64 (neg.f64 x)))

series91.0ms (3.3%)

Counts

2 → 6

Calls

2 calls:

69.0ms	(/.f64 1 (-.f64 1 (exp.f64 (neg.f64 x))))
22.0ms	(-.f64 1 (exp.f64 (neg.f64 x)))

simplify71.0ms (2.6%)

Algorithm

1×	egg-herbie

Counts

65 → 65

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	5267	1034

prune48.0ms (1.8%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	65	0	65
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	65	3	68

Merged error: 0b

Counts

68 → 3

Compiler

Compiled 857 to 544 computations (36.5% saved)

localize11.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 1 (sqrt.f64 (exp.f64 x)))
0.6b	(/.f64 (exp.f64 x) (+.f64 -1 (sqrt.f64 (exp.f64 x))))
0.7b	(*.f64 (/.f64 1 (+.f64 1 (sqrt.f64 (exp.f64 x)))) (/.f64 (exp.f64 x) (+.f64 -1 (sqrt.f64 (exp.f64 x)))))
1.8b	(+.f64 -1 (sqrt.f64 (exp.f64 x)))

rewrite57.0ms (2.1%)

Algorithm

1×	rewrite-expression-head

Rules

60×	`*-un-lft-identity_binary64_751`
51×	`add-sqr-sqrt_binary64_772`
46×	`times-frac_binary64_757`
30×	`add-cube-cbrt_binary64_783`
23×	`add-exp-log_binary64_786`
21×	`associate-l_binary64_694`
18×	`add-cbrt-cube_binary64_784` `associate-r_binary64_693`
16×	`distribute-lft-out_binary64_704`
9×	`div-exp_binary64_799`
8×	`prod-exp_binary64_797` `add-log-exp_binary64_787`
6×	`unswap-sqr_binary64_719` `pow1_binary64_809` `associate-/r/_binary64_699`
5×	`flip3-+_binary64_754` `cbrt-undiv_binary64_782` `flip-+_binary64_725`
4×	`associate-/r*_binary64_697` `sqrt-prod_binary64_766` `cbrt-unprod_binary64_781`
3×	`div-inv_binary64_748` `associate-/l*_binary64_698`
2×	`1-exp_binary64_792` `+-commutative_binary64_683` `rec-exp_binary64_798` `sum-log_binary64_839`
1×	`frac-times_binary64_761` `pow-prod-down_binary64_819` `-commutative_binary64_684` `associate-r/_binary64_695` `frac-2neg_binary64_762` `clear-num_binary64_750` `associate-*l/_binary64_696`

Counts

4 → 127

Calls

4 calls:

25.0ms	(*.f64 (/.f64 1 (+.f64 1 (sqrt.f64 (exp.f64 x)))) (/.f64 (exp.f64 x) (+.f64 -1 (sqrt.f64 (exp.f64 x)))))
8.0ms	(/.f64 (exp.f64 x) (+.f64 -1 (sqrt.f64 (exp.f64 x))))
5.0ms	(+.f64 -1 (sqrt.f64 (exp.f64 x)))
5.0ms	(+.f64 1 (sqrt.f64 (exp.f64 x)))

series348.0ms (12.7%)

Counts

4 → 12

Calls

4 calls:

190.0ms	(*.f64 (/.f64 1 (+.f64 1 (sqrt.f64 (exp.f64 x)))) (/.f64 (exp.f64 x) (+.f64 -1 (sqrt.f64 (exp.f64 x)))))
97.0ms	(/.f64 (exp.f64 x) (+.f64 -1 (sqrt.f64 (exp.f64 x))))
32.0ms	(+.f64 -1 (sqrt.f64 (exp.f64 x)))
28.0ms	(+.f64 1 (sqrt.f64 (exp.f64 x)))

simplify86.0ms (3.1%)

Algorithm

1×	egg-herbie

Counts

139 → 139

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4945	2987
1	4945	2987

prune146.0ms (5.3%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	139	0	139
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	139	3	142

Merged error: 0b

Counts

142 → 3

Compiler

Compiled 3081 to 1632 computations (47% saved)

regimes24.0ms (0.9%)

Compiler: Compiled 70 to 58 computations (17.1% saved)

bsearch1.0ms (0%)

Compiler: Compiled 2 to 2 computations (0% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	28	47
1	28	47

end0.0ms (0%)

sample925.0ms (33.8%)

Algorithm

1×

intervals

Results

413.0ms	2644×	body	1024	valid
115.0ms	1319×	body	512	valid
75.0ms	3068×	body	128	valid
52.0ms	301×	body	2048	valid
38.0ms	668×	body	256	valid
0.0ms	2×	body	2048	invalid

Compiler

Compiled 77 to 61 computations (20.8% saved)

Details

analyze312.0ms (11.4%)

sample30.0ms (1.1%)

simplify164.0ms (6%)

prune2.0ms (0.1%)

localize4.0ms (0.1%)

rewrite18.0ms (0.6%)

series95.0ms (3.5%)

simplify47.0ms (1.7%)

prune64.0ms (2.3%)

localize6.0ms (0.2%)

rewrite16.0ms (0.6%)

series42.0ms (1.5%)

simplify73.0ms (2.7%)

prune33.0ms (1.2%)

localize5.0ms (0.2%)

rewrite17.0ms (0.6%)

series91.0ms (3.3%)

simplify71.0ms (2.6%)

prune48.0ms (1.8%)

localize11.0ms (0.4%)

rewrite57.0ms (2.1%)

series348.0ms (12.7%)

simplify86.0ms (3.1%)

prune146.0ms (5.3%)

regimes24.0ms (0.9%)

bsearch1.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample925.0ms (33.8%)

Profiling