Details

analyze2.2s (11.3%)

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)

sample100.0ms (0.5%)

Algorithm

1×

intervals

Results

39.0ms	439×	body	128	nan
23.0ms	256×	body	128	valid
4.0ms	40×	body	128	invalid

Compiler

Compiled 57 to 53 computations (7% saved)

simplify136.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5178	39

prune5.0ms (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: 30.4b

Counts

2 → 2

Compiler

Compiled 80 to 63 computations (21.3% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

1.3b	(.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))))
10.8b	(.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))
11.4b	(.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U U)))))))
17.6b	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U U))))))))

rewrite60.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`add-cbrt-cube_binary64_455` `add-exp-log_binary64_457` `pow1_binary64_480`
29×	`add-sqr-sqrt_binary64_441`
27×	`associate-l_binary64_360`
24×	`*-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454`
19×	`times-frac_binary64_425`
18×	`distribute-rgt-in_binary64_369` `distribute-lft-in_binary64_368`
16×	`pow-prod-down_binary64_490`
14×	`prod-exp_binary64_468` `cbrt-unprod_binary64_452`
12×	`associate-*r/_binary64_361` `cancel-sign-sub-inv_binary64_385`
7×	`associate-r_binary64_359`
4×	`flip3-+_binary64_422` `sub-neg_binary64_412` `add-log-exp_binary64_458` `frac-times_binary64_429` `flip-+_binary64_393` `sqrt-pow1_binary64_437`
3×	`*-commutative_binary64_350` `div-exp_binary64_470` `cbrt-undiv_binary64_453`
2×	`associate-*l/_binary64_362` `sqrt-div_binary64_436` `div-inv_binary64_416` `unswap-sqr_binary64_387` `flip3--_binary64_423` `flip--_binary64_394`
1×	`pow1/2_binary64_499` `sqrt-prod_binary64_435`

Counts

4 → 131

Calls

4 calls:

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

series2.7s (13.8%)

Counts

4 → 12

Calls

4 calls:

2.0s	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U U))))))))
432.0ms	(.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U U)))))))
147.0ms	(.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))))
91.0ms	(.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))

simplify89.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

143 → 143

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5099	4107

prune220.0ms (1.1%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	130	13	143
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	132	13	145

Merged error: 22.2b

Counts

145 → 13

Compiler

Compiled 5477 to 2280 computations (58.4% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

6.1b	(*.f64 n (/.f64 l Om))
6.8b	(.f64 (.f64 n (/.f64 l Om)) (-.f64 U* U))
11.4b	(.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (.f64 n (/.f64 l Om)) (-.f64 U U))))))
17.6b	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (.f64 n (/.f64 l Om)) (-.f64 U U)))))))

rewrite46.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`pow1_binary64_480`
27×	`add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
23×	`add-sqr-sqrt_binary64_441`
21×	`associate-r_binary64_359`
18×	`*-un-lft-identity_binary64_419`
16×	`pow-prod-down_binary64_490` `add-cube-cbrt_binary64_454`
13×	`prod-exp_binary64_468` `cbrt-unprod_binary64_452`
10×	`times-frac_binary64_425` `associate-*r/_binary64_361`
6×	`cancel-sign-sub-inv_binary64_385`
5×	`distribute-rgt-in_binary64_369` `distribute-lft-in_binary64_368` `associate-l_binary64_360`
4×	`add-log-exp_binary64_458` `sqrt-pow1_binary64_437`
3×	`*-commutative_binary64_350`
2×	`flip3-+_binary64_422` `sqrt-div_binary64_436` `sub-neg_binary64_412` `unswap-sqr_binary64_387` `frac-times_binary64_429` `flip3--_binary64_423` `flip-+_binary64_393` `flip--_binary64_394` `div-exp_binary64_470` `cbrt-undiv_binary64_453`
1×	`associate-*l/_binary64_362` `difference-of-squares_binary64_388` `pow1/2_binary64_499` `div-inv_binary64_416` `distribute-lft-out--_binary64_371` `sqrt-prod_binary64_435`

Counts

4 → 107

Calls

4 calls:

11.0ms	(.f64 (.f64 n (/.f64 l Om)) (-.f64 U* U))
9.0ms	(.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (.f64 n (/.f64 l Om)) (-.f64 U U))))))
7.0ms	(*.f64 n (/.f64 l Om))
7.0ms	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (.f64 n (/.f64 l Om)) (-.f64 U U)))))))

series2.6s (13.4%)

Counts

4 → 12

Calls

4 calls:

2.1s	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (.f64 n (/.f64 l Om)) (-.f64 U U)))))))
432.0ms	(.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (.f64 n (/.f64 l Om)) (-.f64 U U))))))
96.0ms	(.f64 (.f64 n (/.f64 l Om)) (-.f64 U* U))
18.0ms	(*.f64 n (/.f64 l Om))

simplify71.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5059	2829

prune154.0ms (0.8%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	117	2	119
Fresh	2	10	12
Picked	1	0	1
Done	0	0	0
Total	120	12	132

Merged error: 21.3b

Counts

132 → 12

Compiler

Compiled 4430 to 1935 computations (56.3% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

6.1b	(*.f64 n (/.f64 l Om))
6.5b	(.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (.f64 n (/.f64 l Om)) (-.f64 U U)))))))
6.8b	(.f64 (.f64 n (/.f64 l Om)) (-.f64 U* U))
17.6b	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (.f64 n (/.f64 l Om)) (-.f64 U U))))))))

rewrite48.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`pow1_binary64_480`
30×	`add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
22×	`add-sqr-sqrt_binary64_441`
20×	`pow-prod-down_binary64_490`
19×	`associate-r_binary64_359`
17×	`*-un-lft-identity_binary64_419`
15×	`add-cube-cbrt_binary64_454` `prod-exp_binary64_468` `cbrt-unprod_binary64_452`
14×	`associate-*r/_binary64_361`
10×	`times-frac_binary64_425`
8×	`distribute-rgt-in_binary64_369` `distribute-lft-in_binary64_368`
6×	`cancel-sign-sub-inv_binary64_385`
5×	`associate-l_binary64_360` `sqrt-pow1_binary64_437`
4×	`add-log-exp_binary64_458`
3×	`*-commutative_binary64_350`
2×	`flip3-+_binary64_422` `sqrt-div_binary64_436` `sub-neg_binary64_412` `unswap-sqr_binary64_387` `frac-times_binary64_429` `flip3--_binary64_423` `flip-+_binary64_393` `flip--_binary64_394` `div-exp_binary64_470` `cbrt-undiv_binary64_453`
1×	`associate-*l/_binary64_362` `difference-of-squares_binary64_388` `pow1/2_binary64_499` `div-inv_binary64_416` `distribute-lft-out--_binary64_371` `sqrt-prod_binary64_435`

Counts

4 → 111

Calls

4 calls:

13.0ms	(.f64 (.f64 n (/.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 (.f64 n (/.f64 l Om)) (-.f64 U U)))))))
7.0ms	(*.f64 n (/.f64 l Om))
7.0ms	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (.f64 n (/.f64 l Om)) (-.f64 U U))))))))

series2.6s (13.3%)

Counts

4 → 12

Calls

4 calls:

2.1s	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (.f64 n (/.f64 l Om)) (-.f64 U U))))))))
426.0ms	(.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (.f64 n (/.f64 l Om)) (-.f64 U U)))))))
94.0ms	(.f64 (.f64 n (/.f64 l Om)) (-.f64 U* U))
17.0ms	(*.f64 n (/.f64 l Om))

simplify73.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5016	2927

prune169.0ms (0.9%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	116	7	123
Fresh	3	8	11
Picked	1	0	1
Done	0	0	0
Total	120	15	135

Merged error: 18.3b

Counts

135 → 15

Compiler

Compiled 4622 to 2047 computations (55.7% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

4.4b	(.f64 (-.f64 U U) (*.f64 n l))
5.7b	(/.f64 (.f64 (-.f64 U U) (*.f64 n l)) Om)
6.5b	(.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (/.f64 (.f64 (-.f64 U* U) (*.f64 n l)) Om))))))
17.6b	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (/.f64 (.f64 (-.f64 U* U) (*.f64 n l)) Om)))))))

rewrite47.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

34×	`pow1_binary64_480`
30×	`add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
19×	`pow-prod-down_binary64_490`
14×	`prod-exp_binary64_468` `cbrt-unprod_binary64_452`
9×	`*-un-lft-identity_binary64_419` `add-sqr-sqrt_binary64_441`
8×	`associate-*r/_binary64_361`
7×	`add-cube-cbrt_binary64_454`
6×	`associate-l_binary64_360`
5×	`sqrt-pow1_binary64_437`
4×	`associate-*l/_binary64_362` `add-log-exp_binary64_458` `distribute-rgt-in_binary64_369` `distribute-lft-in_binary64_368`
3×	`times-frac_binary64_425` `associate-/r*_binary64_363` `div-exp_binary64_470` `cbrt-undiv_binary64_453`
2×	`flip3-+_binary64_422` `sqrt-div_binary64_436` `associate-r_binary64_359` `flip3--_binary64_423` `*-commutative_binary64_350` `flip-+_binary64_393` `flip--_binary64_394` `associate-/l/_binary64_366`
1×	`clear-num_binary64_418` `difference-of-squares_binary64_388` `pow1/2_binary64_499` `div-inv_binary64_416` `distribute-lft-out--_binary64_371` `frac-2neg_binary64_430` `sqrt-prod_binary64_435` `associate-/l*_binary64_364`

Counts

4 → 91

Calls

4 calls:

10.0ms	(/.f64 (.f64 (-.f64 U U) (*.f64 n l)) Om)
9.0ms	(.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (/.f64 (.f64 (-.f64 U* U) (*.f64 n l)) Om))))))
8.0ms	(.f64 (-.f64 U U) (*.f64 n l))
7.0ms	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (/.f64 (.f64 (-.f64 U* U) (*.f64 n l)) Om)))))))

series2.6s (13.4%)

Counts

4 → 12

Calls

4 calls:

2.1s	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (/.f64 (.f64 (-.f64 U* U) (*.f64 n l)) Om)))))))
430.0ms	(.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (/.f64 (.f64 (-.f64 U* U) (*.f64 n l)) Om))))))
79.0ms	(/.f64 (.f64 (-.f64 U U) (*.f64 n l)) Om)
45.0ms	(.f64 (-.f64 U U) (*.f64 n l))

simplify54.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	5428	2496

prune122.0ms (0.6%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	100	3	103
Fresh	2	12	14
Picked	1	0	1
Done	0	0	0
Total	103	15	118

Merged error: 17.8b

Counts

118 → 15

Compiler

Compiled 3249 to 1407 computations (56.7% saved)

regimes1.3s (6.4%)

Compiler: Compiled 17658 to 11680 computations (33.9% saved)

bsearch72.0ms (0.4%)

Steps

Iters	Range		Point
9	-4.037286196172629e-305	1.1451514437376966e-305	1.63844295675637e-309

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	50	86
1	50	86

end0.0ms (0%)

sample4.0s (20.4%)

Algorithm

1×

intervals

Results

1.1s	12627×	body	128	nan
736.0ms	8000×	body	128	valid
103.0ms	1118×	body	128	invalid

Compiler

Compiled 2257 to 1485 computations (34.2% saved)

Details

analyze2.2s (11.3%)

sample100.0ms (0.5%)

simplify136.0ms (0.7%)

prune5.0ms (0%)

localize16.0ms (0.1%)

rewrite60.0ms (0.3%)

series2.7s (13.8%)

simplify89.0ms (0.5%)

prune220.0ms (1.1%)

localize16.0ms (0.1%)

rewrite46.0ms (0.2%)

series2.6s (13.4%)

simplify71.0ms (0.4%)

prune154.0ms (0.8%)

localize17.0ms (0.1%)

rewrite48.0ms (0.2%)

series2.6s (13.3%)

simplify73.0ms (0.4%)

prune169.0ms (0.9%)

localize17.0ms (0.1%)

rewrite47.0ms (0.2%)

series2.6s (13.4%)

simplify54.0ms (0.3%)

prune122.0ms (0.6%)

regimes1.3s (6.4%)

bsearch72.0ms (0.4%)

simplify3.0ms (0%)

end0.0ms (0%)

sample4.0s (20.4%)

Profiling