Details

analyze2.3s (7.9%)

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)

sample300.0ms (1%)

Algorithm

1×

intervals

Results

243.0ms	392×	body	128	nan
23.0ms	256×	body	128	valid
5.0ms	49×	body	128	invalid

Compiler

Compiled 57 to 53 computations (7% saved)

simplify52.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4990	39
1	4990	39

prune8.0ms (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: 29.8b

Counts

2 → 2

Compiler

Compiled 134 to 106 computations (20.9% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

1.1b	(.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))))
8.7b	(.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))
9.8b	(.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)))))))
19.1b	(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))))))))

rewrite63.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
29×	`add-sqr-sqrt_binary64`
27×	`associate-l_binary64`
24×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
19×	`times-frac_binary64`
18×	`distribute-lft-in_binary64` `distribute-rgt-in_binary64`
16×	`pow-prod-down_binary64`
14×	`cbrt-unprod_binary64` `prod-exp_binary64`
12×	`associate-*r/_binary64` `cancel-sign-sub-inv_binary64`
7×	`associate-r_binary64`
4×	`flip3-+_binary64` `add-log-exp_binary64` `sub-neg_binary64` `sqrt-pow1_binary64` `flip-+_binary64` `frac-times_binary64`
3×	`cbrt-undiv_binary64` `div-exp_binary64` `*-commutative_binary64`
2×	`flip3--_binary64` `unswap-sqr_binary64` `div-inv_binary64` `flip--_binary64` `sqrt-div_binary64` `associate-*l/_binary64`
1×	`pow1/2_binary64` `sqrt-prod_binary64`

Counts

4 → 131

Calls

4 calls:

13.0ms	(.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)))))))
13.0ms	(.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))
12.0ms	(.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))))))))

series4.9s (16.9%)

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 (/.f64 l Om) (.f64 n (-.f64 U U))))))))
785.0ms	(.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)))))))
319.0ms	(.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))))
206.0ms	(.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))

simplify110.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

143 → 143

Iterations

Useful iterations: 0 (75.0ms)

Iter	Nodes	Cost
0	5016	4107

prune710.0ms (2.5%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	131	12	143
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	133	12	145

Merged error: 20.1b

Counts

145 → 12

Compiler

Compiled 18630 to 10283 computations (44.8% saved)

localize20.0ms (0.1%)

Local error

Found 4 expressions with local error:

4.7b	(*.f64 n (/.f64 l Om))
9.8b	(.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))))))
10.1b	(.f64 (.f64 n (/.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 (.f64 n (/.f64 l Om)) (-.f64 U U)))))))

rewrite51.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`pow1_binary64`
27×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
23×	`add-sqr-sqrt_binary64`
21×	`associate-r_binary64`
18×	`*-un-lft-identity_binary64`
16×	`pow-prod-down_binary64` `add-cube-cbrt_binary64`
13×	`cbrt-unprod_binary64` `prod-exp_binary64`
10×	`associate-*r/_binary64` `times-frac_binary64`
6×	`cancel-sign-sub-inv_binary64`
5×	`distribute-lft-in_binary64` `associate-l_binary64` `distribute-rgt-in_binary64`
4×	`add-log-exp_binary64` `sqrt-pow1_binary64`
3×	`*-commutative_binary64`
2×	`flip3-+_binary64` `sub-neg_binary64` `flip3--_binary64` `cbrt-undiv_binary64` `unswap-sqr_binary64` `div-exp_binary64` `flip--_binary64` `flip-+_binary64` `frac-times_binary64` `sqrt-div_binary64`
1×	`pow1/2_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `div-inv_binary64` `sqrt-prod_binary64` `associate-*l/_binary64`

Counts

4 → 107

Calls

4 calls:

12.0ms	(.f64 (.f64 n (/.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 (.f64 n (/.f64 l Om)) (-.f64 U U))))))
8.0ms	(*.f64 n (/.f64 l Om))
8.0ms	(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)))))))

series4.6s (16.1%)

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 (.f64 n (/.f64 l Om)) (-.f64 U U)))))))
796.0ms	(.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))))))
211.0ms	(.f64 (.f64 n (/.f64 l Om)) (-.f64 U* U))
33.0ms	(*.f64 n (/.f64 l Om))

simplify60.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5296	2813

prune237.0ms (0.8%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	117	2	119
Fresh	2	9	11
Picked	0	1	1
Done	0	0	0
Total	119	12	131

Merged error: 19.9b

Counts

131 → 12

Compiler

Compiled 6496 to 3209 computations (50.6% saved)

localize21.0ms (0.1%)

Local error

Found 4 expressions with local error:

16.6b	(cbrt.f64 (.f64 (/.f64 l Om) (.f64 n (-.f64 U* U))))
16.6b	(cbrt.f64 (.f64 (/.f64 l Om) (.f64 n (-.f64 U* U))))
16.6b	(cbrt.f64 (.f64 (/.f64 l Om) (.f64 n (-.f64 U* U))))
19.1b	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (.f64 (cbrt.f64 (.f64 (/.f64 l Om) (.f64 n (-.f64 U U)))) (cbrt.f64 (.f64 (/.f64 l Om) (.f64 n (-.f64 U* U))))) (cbrt.f64 (.f64 (/.f64 l Om) (.f64 n (-.f64 U* U))))))))))

rewrite47.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`associate-*r/_binary64`
15×	`cbrt-div_binary64`
14×	`pow1_binary64`
6×	`pow-prod-down_binary64` `flip3--_binary64` `flip--_binary64` `frac-times_binary64`
4×	`*-un-lft-identity_binary64` `add-log-exp_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `sqrt-pow1_binary64` `add-sqr-sqrt_binary64`
3×	`pow1/3_binary64` `cbrt-prod_binary64` `associate-*l/_binary64`
2×	`sqrt-div_binary64`
1×	`flip3-+_binary64` `pow1/2_binary64` `sqrt-prod_binary64` `flip-+_binary64`

Counts

4 → 57

Calls

4 calls:

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

series6.0s (20.8%)

Counts

4 → 12

Calls

4 calls:

4.7s	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (.f64 (cbrt.f64 (.f64 (/.f64 l Om) (.f64 n (-.f64 U U)))) (cbrt.f64 (.f64 (/.f64 l Om) (.f64 n (-.f64 U* U))))) (cbrt.f64 (.f64 (/.f64 l Om) (.f64 n (-.f64 U* U))))))))))
450.0ms	(cbrt.f64 (.f64 (/.f64 l Om) (.f64 n (-.f64 U* U))))
437.0ms	(cbrt.f64 (.f64 (/.f64 l Om) (.f64 n (-.f64 U* U))))
435.0ms	(cbrt.f64 (.f64 (/.f64 l Om) (.f64 n (-.f64 U* U))))

simplify62.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5055	1846

prune118.0ms (0.4%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	69	0	69
Fresh	0	10	10
Picked	0	1	1
Done	0	1	1
Total	69	12	81

Merged error: 19.9b

Counts

81 → 12

Compiler

Compiled 4088 to 1348 computations (67% saved)

localize25.0ms (0.1%)

Local error

Found 4 expressions with local error:

19.1b	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (.f64 (cbrt.f64 (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U U)))))) (cbrt.f64 (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U* U))))))) (cbrt.f64 (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U* U))))))))))
27.0b	(cbrt.f64 (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U* U))))))
27.0b	(cbrt.f64 (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U* U))))))
27.0b	(cbrt.f64 (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U* U))))))

rewrite45.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`cbrt-div_binary64`
14×	`pow1_binary64`
8×	`associate-*r/_binary64`
7×	`flip3-+_binary64` `flip-+_binary64`
6×	`pow-prod-down_binary64` `frac-times_binary64`
4×	`*-un-lft-identity_binary64` `add-log-exp_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `sqrt-pow1_binary64` `add-sqr-sqrt_binary64`
3×	`pow1/3_binary64` `cbrt-prod_binary64` `associate-*l/_binary64`
2×	`sqrt-div_binary64`
1×	`pow1/2_binary64` `sqrt-prod_binary64`

Counts

4 → 57

Calls

4 calls:

8.0ms	(cbrt.f64 (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U* U))))))
8.0ms	(cbrt.f64 (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U* U))))))
8.0ms	(cbrt.f64 (.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 (cbrt.f64 (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U U)))))) (cbrt.f64 (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U* U))))))) (cbrt.f64 (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U* U))))))))))

series5.2s (18.1%)

Counts

4 → 12

Calls

4 calls:

3.5s	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (.f64 (cbrt.f64 (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U U)))))) (cbrt.f64 (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U* U))))))) (cbrt.f64 (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U* U))))))))))
575.0ms	(cbrt.f64 (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U* U))))))
565.0ms	(cbrt.f64 (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U* U))))))
565.0ms	(cbrt.f64 (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U* U))))))

simplify50.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 0 (21.0ms)

Iter	Nodes	Cost
0	5331	2631

prune145.0ms (0.5%)

Pruning

12 alts after pruning (9 fresh and 3 done)

	Pruned	Kept	Total
New	69	0	69
Fresh	0	9	9
Picked	0	1	1
Done	0	2	2
Total	69	12	81

Merged error: 19.9b

Counts

81 → 12

Compiler

Compiled 4804 to 1856 computations (61.4% saved)

regimes267.0ms (0.9%)

Compiler: Compiled 2874 to 1818 computations (36.7% saved)

bsearch153.0ms (0.5%)

Steps

Iters	Range		Point
7	8911176908316.242	234144438038497.38	12906022861238.295
9	-8.2681152677167635e-25	-9.475190713632262e-30	-1.6254006010445829e-28

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	59	114
1	59	114

end0.0ms (0%)

sample3.3s (11.3%)

Algorithm

1×

intervals

Results

1.3s	13234×	body	128	nan
750.0ms	8000×	body	128	valid
120.0ms	1195×	body	128	invalid

Compiler

Compiled 582 to 366 computations (37.1% saved)

Details

analyze2.3s (7.9%)

sample300.0ms (1%)

simplify52.0ms (0.2%)

prune8.0ms (0%)

localize16.0ms (0.1%)

rewrite63.0ms (0.2%)

series4.9s (16.9%)

simplify110.0ms (0.4%)

prune710.0ms (2.5%)

localize20.0ms (0.1%)

rewrite51.0ms (0.2%)

series4.6s (16.1%)

simplify60.0ms (0.2%)

prune237.0ms (0.8%)

localize21.0ms (0.1%)

rewrite47.0ms (0.2%)

series6.0s (20.8%)

simplify62.0ms (0.2%)

prune118.0ms (0.4%)

localize25.0ms (0.1%)

rewrite45.0ms (0.2%)

series5.2s (18.1%)

simplify50.0ms (0.2%)

prune145.0ms (0.5%)

regimes267.0ms (0.9%)

bsearch153.0ms (0.5%)

simplify3.0ms (0%)

end0.0ms (0%)

sample3.3s (11.3%)

Profiling