Details

analyze2.5s (6.9%)

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%	98.1%	1.9%	7
0%	98.1%	1.9%	8
0%	97.8%	2.2%	9
0%	96.8%	3.2%	10
0%	96.3%	3.7%	11
0%	94.3%	5.7%	12
0.4%	92.1%	7.5%	13
0.6%	90.8%	8.6%	14

Compiler

Compiled 29 to 24 computations (17.2% saved)

sample98.0ms (0.3%)

Algorithm

1×

intervals

Results

37.0ms	381×	body	128	nan
28.0ms	256×	body	128	valid
5.0ms	47×	body	128	invalid

Compiler

Compiled 57 to 53 computations (7% saved)

simplify214.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	5453	39

prune6.0ms (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: 31.2b

Counts

2 → 2

Compiler

Compiled 80 to 63 computations (21.3% saved)

localize16.0ms (0%)

Local error

Found 4 expressions with local error:

4.8b	(.f64 n (.f64 (/.f64 l Om) (-.f64 U* U)))
7.8b	(.f64 (/.f64 l Om) (-.f64 U U))
10.6b	(.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U)))))))
19.1b	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U))))))))

rewrite57.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`pow1_binary64_135`
27×	`add-exp-log_binary64_112` `add-cbrt-cube_binary64_110`
21×	`add-sqr-sqrt_binary64_98`
17×	`associate-l_binary64_20`
16×	`pow-prod-down_binary64_145` `*-un-lft-identity_binary64_77`
14×	`add-cube-cbrt_binary64_109`
13×	`cbrt-unprod_binary64_107` `associate-*r/_binary64_21` `prod-exp_binary64_123`
10×	`times-frac_binary64_83`
9×	`associate-r_binary64_19`
6×	`sub-neg_binary64_70` `distribute-lft-in_binary64_28` `distribute-rgt-in_binary64_29`
4×	`add-log-exp_binary64_113` `sqrt-pow1_binary64_94` `frac-times_binary64_87` `flip--_binary64_52` `flip3--_binary64_81`
3×	`*-commutative_binary64_10`
2×	`flip-+_binary64_51` `cbrt-undiv_binary64_108` `sqrt-div_binary64_93` `flip3-+_binary64_80` `associate-*l/_binary64_22` `div-exp_binary64_125` `unswap-sqr_binary64_45`
1×	`sqrt-prod_binary64_92` `distribute-lft-out--_binary64_31` `difference-of-squares_binary64_46` `pow1/2_binary64_154` `div-inv_binary64_74`

Counts

4 → 109

Calls

4 calls:

14.0ms	(.f64 n (.f64 (/.f64 l Om) (-.f64 U* U)))
11.0ms	(.f64 (/.f64 l Om) (-.f64 U U))
10.0ms	(.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U)))))))
8.0ms	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U))))))))

series4.7s (12.9%)

Counts

4 → 12

Calls

4 calls:

3.6s	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U))))))))
781.0ms	(.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U)))))))
199.0ms	(.f64 n (.f64 (/.f64 l Om) (-.f64 U* U)))
129.0ms	(.f64 (/.f64 l Om) (-.f64 U U))

simplify75.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4961	2903
1	4961	2903

prune192.0ms (0.5%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	111	10	121
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	112	11	123

Merged error: 20.9b

Counts

123 → 11

Compiler

Compiled 4574 to 2001 computations (56.3% saved)

localize17.0ms (0%)

Local error

Found 4 expressions with local error:

4.9b	(.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U))))))))
5.1b	(.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U)))))))
7.8b	(.f64 (/.f64 l Om) (-.f64 U U))
19.1b	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U)))))))))

rewrite50.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

33×	`pow1_binary64_135`
23×	`add-exp-log_binary64_112` `add-cbrt-cube_binary64_110` `add-sqr-sqrt_binary64_98`
18×	`pow-prod-down_binary64_145`
17×	`associate-l_binary64_20`
16×	`*-un-lft-identity_binary64_77`
14×	`add-cube-cbrt_binary64_109`
12×	`associate-*r/_binary64_21`
11×	`cbrt-unprod_binary64_107` `prod-exp_binary64_123`
10×	`times-frac_binary64_83`
9×	`associate-r_binary64_19`
6×	`distribute-lft-in_binary64_28` `distribute-rgt-in_binary64_29`
5×	`sqrt-pow1_binary64_94`
4×	`add-log-exp_binary64_113`
3×	`flip-+_binary64_51` `flip3-+_binary64_80` `unswap-sqr_binary64_45` `*-commutative_binary64_10`
2×	`sqrt-div_binary64_93` `frac-times_binary64_87` `sub-neg_binary64_70` `flip--_binary64_52` `flip3--_binary64_81`
1×	`sqrt-prod_binary64_92` `cbrt-undiv_binary64_108` `distribute-lft-out--_binary64_31` `associate-*l/_binary64_22` `div-exp_binary64_125` `difference-of-squares_binary64_46` `pow1/2_binary64_154` `div-inv_binary64_74`

Counts

4 → 106

Calls

4 calls:

11.0ms	(.f64 (/.f64 l Om) (-.f64 U U))
10.0ms	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U)))))))))
9.0ms	(.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U))))))))
6.0ms	(.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U)))))))

series5.2s (14.2%)

Counts

4 → 12

Calls

4 calls:

3.7s	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U)))))))))
798.0ms	(.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U))))))))
622.0ms	(.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U)))))))
110.0ms	(.f64 (/.f64 l Om) (-.f64 U U))

simplify112.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 0 (80.0ms)

Iter	Nodes	Cost
0	4957	3388
1	4957	3388

prune167.0ms (0.5%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	113	5	118
Fresh	4	6	10
Picked	0	1	1
Done	0	0	0
Total	117	12	129

Merged error: 16.7b

Counts

129 → 12

Compiler

Compiled 4561 to 1988 computations (56.4% saved)

localize21.0ms (0.1%)

Local error

Found 4 expressions with local error:

7.8b	(.f64 (/.f64 l Om) (-.f64 U U))
7.8b	(.f64 (/.f64 l Om) (-.f64 U U))
19.1b	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U)))))))))
19.1b	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U)))))))))

rewrite62.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

34×	`pow1_binary64_135` `add-sqr-sqrt_binary64_98`
26×	`associate-l_binary64_20`
24×	`*-un-lft-identity_binary64_77`
20×	`times-frac_binary64_83` `add-cube-cbrt_binary64_109`
18×	`pow-prod-down_binary64_145`
14×	`add-exp-log_binary64_112` `add-cbrt-cube_binary64_110`
12×	`associate-*r/_binary64_21`
10×	`sqrt-pow1_binary64_94` `associate-r_binary64_19`
4×	`add-log-exp_binary64_113` `cbrt-unprod_binary64_107` `sqrt-div_binary64_93` `frac-times_binary64_87` `sub-neg_binary64_70` `flip--_binary64_52` `unswap-sqr_binary64_45` `prod-exp_binary64_123` `flip3--_binary64_81`
2×	`sqrt-prod_binary64_92` `flip-+_binary64_51` `cbrt-undiv_binary64_108` `distribute-lft-out--_binary64_31` `flip3-+_binary64_80` `distribute-lft-in_binary64_28` `associate-l/_binary64_22` `div-exp_binary64_125` `difference-of-squares_binary64_46` `-commutative_binary64_10` `pow1/2_binary64_154` `distribute-rgt-in_binary64_29` `div-inv_binary64_74`

Counts

4 → 112

Calls

4 calls:

11.0ms	(.f64 (/.f64 l Om) (-.f64 U U))
11.0ms	(.f64 (/.f64 l Om) (-.f64 U U))
8.0ms	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U)))))))))
8.0ms	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U)))))))))

series7.5s (20.7%)

Counts

4 → 12

Calls

4 calls:

3.7s	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U)))))))))
3.6s	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U)))))))))
132.0ms	(.f64 (/.f64 l Om) (-.f64 U U))
131.0ms	(.f64 (/.f64 l Om) (-.f64 U U))

simplify63.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5321	2558

prune275.0ms (0.8%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	124	0	124
Fresh	0	10	10
Picked	0	1	1
Done	0	1	1
Total	124	12	136

Merged error: 16.7b

Counts

136 → 12

Compiler

Compiled 8150 to 3580 computations (56.1% saved)

localize25.0ms (0.1%)

Local error

Found 4 expressions with local error:

7.8b	(.f64 (/.f64 l Om) (-.f64 U U))
19.1b	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U)))))))))
19.1b	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U)))))))))
19.1b	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U)))))))))

rewrite59.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

45×	`pow1_binary64_135`
25×	`pow-prod-down_binary64_145`
19×	`add-sqr-sqrt_binary64_98`
15×	`sqrt-pow1_binary64_94`
14×	`associate-r/_binary64_21` `-un-lft-identity_binary64_77`
13×	`associate-l_binary64_20`
12×	`add-cube-cbrt_binary64_109`
10×	`times-frac_binary64_83`
9×	`add-exp-log_binary64_112` `add-cbrt-cube_binary64_110`
6×	`sqrt-div_binary64_93`
5×	`associate-r_binary64_19`
4×	`add-log-exp_binary64_113`
3×	`sqrt-prod_binary64_92` `flip-+_binary64_51` `flip3-+_binary64_80` `pow1/2_binary64_154`
2×	`cbrt-unprod_binary64_107` `frac-times_binary64_87` `sub-neg_binary64_70` `flip--_binary64_52` `unswap-sqr_binary64_45` `prod-exp_binary64_123` `flip3--_binary64_81`
1×	`cbrt-undiv_binary64_108` `distribute-lft-out--_binary64_31` `distribute-lft-in_binary64_28` `associate-l/_binary64_22` `div-exp_binary64_125` `difference-of-squares_binary64_46` `-commutative_binary64_10` `distribute-rgt-in_binary64_29` `div-inv_binary64_74`

Counts

4 → 88

Calls

4 calls:

11.0ms	(.f64 (/.f64 l Om) (-.f64 U U))
8.0ms	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U)))))))))
8.0ms	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U)))))))))
8.0ms	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U)))))))))

series10.9s (29.8%)

Counts

4 → 12

Calls

4 calls:

3.6s	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U)))))))))
3.6s	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U)))))))))
3.5s	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U)))))))))
140.0ms	(.f64 (/.f64 l Om) (-.f64 U U))

simplify64.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5321	2681

prune301.0ms (0.8%)

Pruning

12 alts after pruning (9 fresh and 3 done)

	Pruned	Kept	Total
New	100	0	100
Fresh	0	9	9
Picked	0	1	1
Done	0	2	2
Total	100	12	112

Merged error: 16.7b

Counts

112 → 12

Compiler

Compiled 9129 to 4000 computations (56.2% saved)

regimes406.0ms (1.1%)

Compiler: Compiled 4426 to 2920 computations (34% saved)

bsearch59.0ms (0.2%)

Steps

Iters	Range		Point
7	-8.225744292457765e-305	-2.917558284702512e-306	-2.9707454333495456e-306

Compiler

Compiled 1 to 6 computations (-500% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	48	86
1	48	86

end0.0ms (0%)

sample3.3s (9.1%)

Algorithm

1×

intervals

Results

1.3s	12877×	body	128	nan
780.0ms	8000×	body	128	valid
122.0ms	1239×	body	128	invalid

Compiler

Compiled 603 to 390 computations (35.3% saved)

Details

analyze2.5s (6.9%)

sample98.0ms (0.3%)

simplify214.0ms (0.6%)

prune6.0ms (0%)

localize16.0ms (0%)

rewrite57.0ms (0.2%)

series4.7s (12.9%)

simplify75.0ms (0.2%)

prune192.0ms (0.5%)

localize17.0ms (0%)

rewrite50.0ms (0.1%)

series5.2s (14.2%)

simplify112.0ms (0.3%)

prune167.0ms (0.5%)

localize21.0ms (0.1%)

rewrite62.0ms (0.2%)

series7.5s (20.7%)

simplify63.0ms (0.2%)

prune275.0ms (0.8%)

localize25.0ms (0.1%)

rewrite59.0ms (0.2%)

series10.9s (29.8%)

simplify64.0ms (0.2%)

prune301.0ms (0.8%)

regimes406.0ms (1.1%)

bsearch59.0ms (0.2%)

simplify3.0ms (0%)

end0.0ms (0%)

sample3.3s (9.1%)

Profiling