Details

analyze2.2s (23.9%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.7%	0.3%	0
0%	99.7%	0.3%	1
0%	99.7%	0.3%	2
0%	99.7%	0.3%	3
0%	99.7%	0.3%	4
0%	99.7%	0.3%	5
0%	99.7%	0.3%	6
0%	99.7%	0.3%	7
0%	99.7%	0.3%	8
0%	99.7%	0.3%	9
0%	99.7%	0.3%	10
0%	99.7%	0.3%	11
0%	99.7%	0.3%	12
5.1%	94.6%	0.3%	13
7%	92.7%	0.3%	14

Compiler

Compiled 19 to 19 computations (0% saved)

sample52.0ms (0.6%)

Algorithm

1×

intervals

Results

19.0ms	256×	body	128	valid
8.0ms	102×	body	128	nan
3.0ms	38×	body	128	invalid

Compiler

Compiled 37 to 43 computations (-16.2% saved)

simplify202.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	6100	27

prune3.0ms (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: 14.1b

Counts

2 → 1

Compiler

Compiled 36 to 36 computations (0% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

2.9b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
3.5b	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))
5.8b	(/.f64 (.f64 M D) (.f64 2 d))
11.0b	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))

rewrite45.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

67×	`add-exp-log_binary64_798`
38×	`add-sqr-sqrt_binary64_782`
27×	`prod-exp_binary64_809`
23×	`add-cbrt-cube_binary64_796`
19×	`associate-r_binary64_700` `div-exp_binary64_811`
17×	`*-un-lft-identity_binary64_760` `add-cube-cbrt_binary64_795`
15×	`times-frac_binary64_766`
13×	`associate-l_binary64_701`
10×	`unswap-sqr_binary64_728` `pow-exp_binary64_828`
7×	`sqrt-prod_binary64_776` `cbrt-unprod_binary64_793` `pow1_binary64_821` `unpow-prod-down_binary64_839`
5×	`cbrt-undiv_binary64_794`
4×	`add-log-exp_binary64_799` `sqrt-div_binary64_777`
3×	`unpow2_binary64_825` `div-inv_binary64_757` `associate-*r/_binary64_702` `sqr-pow_binary64_732`
2×	`pow-to-exp_binary64_829` `*-commutative_binary64_691` `flip--_binary64_735` `flip3--_binary64_764`
1×	`rem-sqrt-square_binary64_773` `frac-2neg_binary64_771` `sqrt-pow1_binary64_778` `associate-/r_binary64_704` `associate-/l_binary64_705` `pow1/2_binary64_840` `clear-num_binary64_759` `pow-prod-down_binary64_831`

Counts

4 → 116

Calls

4 calls:

13.0ms	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))
9.0ms	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
6.0ms	(/.f64 (.f64 M D) (.f64 2 d))
4.0ms	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))

series1.0s (11%)

Counts

4 → 12

Calls

4 calls:

506.0ms	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
308.0ms	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))
151.0ms	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))
40.0ms	(/.f64 (.f64 M D) (.f64 2 d))

simplify55.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	5599	2845

prune180.0ms (2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	120	8	128
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	121	8	129

Merged error: 8.0b

Counts

129 → 8

Compiler

Compiled 3311 to 1923 computations (41.9% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

3.5b	(sqrt.f64 (-.f64 1 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (/.f64 h l)))))
5.8b	(/.f64 (.f64 M D) (.f64 2 d))
5.8b	(/.f64 (.f64 M D) (.f64 2 d))
9.6b	(.f64 (/.f64 (.f64 M D) (*.f64 2 d)) (/.f64 h l))

rewrite46.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

69×	`add-exp-log_binary64_798` `add-cbrt-cube_binary64_796`
26×	`prod-exp_binary64_809` `cbrt-unprod_binary64_793`
21×	`cbrt-undiv_binary64_794` `div-exp_binary64_811`
19×	`add-sqr-sqrt_binary64_782`
13×	`-un-lft-identity_binary64_760` `add-cube-cbrt_binary64_795` `associate-r*_binary64_700` `times-frac_binary64_766`
7×	`pow1_binary64_821`
5×	`associate-l_binary64_701`
4×	`add-log-exp_binary64_799` `div-inv_binary64_757`
3×	`sqrt-prod_binary64_776`
2×	`unswap-sqr_binary64_728` `frac-2neg_binary64_771` `associate-/r_binary64_704` `sqrt-div_binary64_777` `associate-/l_binary64_705` `clear-num_binary64_759`
1×	`rem-sqrt-square_binary64_773` `associate-l/_binary64_703` `sqrt-pow1_binary64_778` `frac-times_binary64_770` `associate-r/_binary64_702` `pow1/2_binary64_840` `pow-prod-down_binary64_831` `*-commutative_binary64_691` `flip--_binary64_735` `flip3--_binary64_764`

Counts

4 → 109

Calls

4 calls:

14.0ms	(.f64 (/.f64 (.f64 M D) (*.f64 2 d)) (/.f64 h l))
6.0ms	(/.f64 (.f64 M D) (.f64 2 d))
6.0ms	(/.f64 (.f64 M D) (.f64 2 d))
6.0ms	(sqrt.f64 (-.f64 1 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (/.f64 h l)))))

series510.0ms (5.6%)

Counts

4 → 12

Calls

4 calls:

303.0ms	(sqrt.f64 (-.f64 1 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (/.f64 h l)))))
121.0ms	(.f64 (/.f64 (.f64 M D) (*.f64 2 d)) (/.f64 h l))
43.0ms	(/.f64 (.f64 M D) (.f64 2 d))
42.0ms	(/.f64 (.f64 M D) (.f64 2 d))

simplify71.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5011	2149

prune160.0ms (1.8%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	117	4	121
Fresh	1	6	7
Picked	1	0	1
Done	0	0	0
Total	119	10	129

Merged error: 7.3b

Counts

129 → 10

Compiler

Compiled 3661 to 1921 computations (47.5% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

4.8b	(/.f64 (.f64 (/.f64 (.f64 M D) (*.f64 2 d)) h) l)
5.8b	(/.f64 (.f64 M D) (.f64 2 d))
5.8b	(/.f64 (.f64 M D) (.f64 2 d))
6.2b	(.f64 (/.f64 (.f64 M D) (*.f64 2 d)) h)

rewrite45.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

71×	`add-exp-log_binary64_798` `add-cbrt-cube_binary64_796`
26×	`prod-exp_binary64_809` `cbrt-unprod_binary64_793`
22×	`cbrt-undiv_binary64_794` `div-exp_binary64_811`
10×	`add-sqr-sqrt_binary64_782`
8×	`*-un-lft-identity_binary64_760` `add-cube-cbrt_binary64_795`
6×	`pow1_binary64_821` `times-frac_binary64_766`
5×	`associate-/r_binary64_704` `associate-l*_binary64_701`
4×	`add-log-exp_binary64_799` `div-inv_binary64_757`
3×	`frac-2neg_binary64_771` `associate-/l_binary64_705` `associate-r*_binary64_700` `clear-num_binary64_759`
2×	`associate-*l/_binary64_703`
1×	`unswap-sqr_binary64_728` `associate-/l/_binary64_707` `pow-prod-down_binary64_831` `*-commutative_binary64_691`

Counts

4 → 101

Calls

4 calls:

11.0ms	(/.f64 (.f64 (/.f64 (.f64 M D) (*.f64 2 d)) h) l)
9.0ms	(.f64 (/.f64 (.f64 M D) (*.f64 2 d)) h)
6.0ms	(/.f64 (.f64 M D) (.f64 2 d))
6.0ms	(/.f64 (.f64 M D) (.f64 2 d))

series299.0ms (3.3%)

Counts

4 → 12

Calls

4 calls:

114.0ms	(/.f64 (.f64 (/.f64 (.f64 M D) (*.f64 2 d)) h) l)
96.0ms	(.f64 (/.f64 (.f64 M D) (*.f64 2 d)) h)
47.0ms	(/.f64 (.f64 M D) (.f64 2 d))
42.0ms	(/.f64 (.f64 M D) (.f64 2 d))

simplify72.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4977	1599
1	4977	1599

prune148.0ms (1.6%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	112	1	113
Fresh	1	8	9
Picked	1	0	1
Done	0	0	0
Total	114	9	123

Merged error: 7.3b

Counts

123 → 9

Compiler

Compiled 3305 to 1896 computations (42.6% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

4.8b	(/.f64 (.f64 (/.f64 1 (/.f64 (.f64 2 d) (*.f64 M D))) h) l)
5.6b	(/.f64 (.f64 2 d) (.f64 M D))
5.8b	(/.f64 (.f64 M D) (.f64 2 d))
6.2b	(.f64 (/.f64 1 (/.f64 (.f64 2 d) (*.f64 M D))) h)

rewrite66.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

168×	`add-exp-log_binary64_798`
86×	`add-cbrt-cube_binary64_796`
69×	`div-exp_binary64_811`
64×	`prod-exp_binary64_809`
33×	`cbrt-undiv_binary64_794`
28×	`cbrt-unprod_binary64_793`
25×	`times-frac_binary64_766`
23×	`add-sqr-sqrt_binary64_782`
20×	`associate-l_binary64_701`
17×	`*-un-lft-identity_binary64_760`
16×	`add-cube-cbrt_binary64_795`
10×	`rec-exp_binary64_810` `1-exp_binary64_804`
7×	`div-inv_binary64_757`
6×	`pow1_binary64_821`
5×	`associate-/r*_binary64_704`
4×	`add-log-exp_binary64_799`
3×	`unswap-sqr_binary64_728` `frac-2neg_binary64_771` `associate-/l_binary64_705` `associate-r*_binary64_700` `clear-num_binary64_759`
2×	`associate-*l/_binary64_703`
1×	`associate-/r/_binary64_706` `associate-/l/_binary64_707` `pow-prod-down_binary64_831` `*-commutative_binary64_691`

Counts

4 → 142

Calls

4 calls:

18.0ms	(.f64 (/.f64 1 (/.f64 (.f64 2 d) (*.f64 M D))) h)
15.0ms	(/.f64 (.f64 (/.f64 1 (/.f64 (.f64 2 d) (*.f64 M D))) h) l)
7.0ms	(/.f64 (.f64 2 d) (.f64 M D))
6.0ms	(/.f64 (.f64 M D) (.f64 2 d))

series306.0ms (3.3%)

Counts

4 → 12

Calls

4 calls:

116.0ms	(/.f64 (.f64 (/.f64 1 (/.f64 (.f64 2 d) (*.f64 M D))) h) l)
100.0ms	(.f64 (/.f64 1 (/.f64 (.f64 2 d) (*.f64 M D))) h)
48.0ms	(/.f64 (.f64 M D) (.f64 2 d))
41.0ms	(/.f64 (.f64 2 d) (.f64 M D))

simplify104.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

154 → 154

Iterations

Useful iterations: 0 (74.0ms)

Iter	Nodes	Cost
0	4964	2271
1	4964	2271

prune208.0ms (2.3%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	154	0	154
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	154	9	163

Merged error: 7.3b

Counts

163 → 9

Compiler

Compiled 4423 to 2550 computations (42.3% saved)

regimes1.1s (12.3%)

Compiler: Compiled 14330 to 12359 computations (13.8% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	89	36
1	89	36

end0.0ms (0%)

sample2.2s (24.1%)

Algorithm

1×

intervals

Results

620.0ms	8000×	body	128	valid
253.0ms	3096×	body	128	nan
112.0ms	1341×	body	128	invalid

Compiler

Compiled 914 to 782 computations (14.4% saved)

Details

analyze2.2s (23.9%)

sample52.0ms (0.6%)

simplify202.0ms (2.2%)

prune3.0ms (0%)

localize14.0ms (0.1%)

rewrite45.0ms (0.5%)

series1.0s (11%)

simplify55.0ms (0.6%)

prune180.0ms (2%)

localize16.0ms (0.2%)

rewrite46.0ms (0.5%)

series510.0ms (5.6%)

simplify71.0ms (0.8%)

prune160.0ms (1.8%)

localize17.0ms (0.2%)

rewrite45.0ms (0.5%)

series299.0ms (3.3%)

simplify72.0ms (0.8%)

prune148.0ms (1.6%)

localize16.0ms (0.2%)

rewrite66.0ms (0.7%)

series306.0ms (3.3%)

simplify104.0ms (1.1%)

prune208.0ms (2.3%)

regimes1.1s (12.3%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample2.2s (24.1%)

Profiling