Details

analyze2.5s (8.6%)

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)

sample94.0ms (0.3%)

Algorithm

1×

intervals

Results

39.0ms	377×	body	128	nan
24.0ms	256×	body	128	valid
3.0ms	33×	body	128	invalid

Compiler

Compiled 57 to 53 computations (7% saved)

simplify199.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4990	39
1	4990	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: 29.6b

Counts

2 → 2

Compiler

Compiled 80 to 63 computations (21.3% saved)

localize20.0ms (0.1%)

Local error

Found 4 expressions with local error:

2.1b	(.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))))
10.3b	(.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)))))))
11.5b	(.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))
17.8b	(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))))))))

rewrite59.0ms (0.2%)

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)))
11.0ms	(.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.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)))))))
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))))))))

series4.8s (16.5%)

Counts

4 → 12

Calls

4 calls:

3.5s	(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))))))))
783.0ms	(.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)))))))
313.0ms	(.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))))
210.0ms	(.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))

simplify106.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

143 → 143

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	5017	4107

prune220.0ms (0.8%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	133	10	143
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	133	12	145

Merged error: 20.5b

Counts

145 → 12

Compiler

Compiled 5325 to 2210 computations (58.5% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

6.4b	(*.f64 n (/.f64 l Om))
9.5b	(.f64 (.f64 n (/.f64 l Om)) (-.f64 U* U))
10.3b	(.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))))))
17.8b	(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)))))))

rewrite53.0ms (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))
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))
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)))))))

series4.6s (15.9%)

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 n (/.f64 l Om)) (-.f64 U U)))))))
809.0ms	(.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))))))
205.0ms	(.f64 (.f64 n (/.f64 l Om)) (-.f64 U* U))
36.0ms	(*.f64 n (/.f64 l Om))

simplify60.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5297	2813

prune168.0ms (0.6%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	115	4	119
Fresh	3	7	10
Picked	1	0	1
Done	1	0	1
Total	120	11	131

Merged error: 19.8b

Counts

131 → 11

Compiler

Compiled 4294 to 1874 computations (56.4% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

6.4b	(*.f64 n (/.f64 l Om))
6.4b	(.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)))))))
9.5b	(.f64 (.f64 n (/.f64 l Om)) (-.f64 U* U))
17.8b	(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))))))))

rewrite54.0ms (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:

12.0ms	(.f64 (.f64 n (/.f64 l Om)) (-.f64 U* U))
10.0ms	(.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)))))))
8.0ms	(*.f64 n (/.f64 l Om))
8.0ms	(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))))))))

series4.7s (16.1%)

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 (.f64 n (/.f64 l Om)) (-.f64 U U))))))))
803.0ms	(.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)))))))
203.0ms	(.f64 (.f64 n (/.f64 l Om)) (-.f64 U* U))
33.0ms	(*.f64 n (/.f64 l Om))

simplify59.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	5160	2911

prune164.0ms (0.6%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	120	3	123
Fresh	2	8	10
Picked	1	0	1
Done	0	0	0
Total	123	11	134

Merged error: 16.9b

Counts

134 → 11

Compiler

Compiled 4363 to 1901 computations (56.4% saved)

localize22.0ms (0.1%)

Local error

Found 4 expressions with local error:

4.9b	(.f64 (/.f64 n (.f64 (cbrt.f64 Om) (cbrt.f64 Om))) (/.f64 l (cbrt.f64 Om)))
6.4b	(.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (.f64 (/.f64 n (.f64 (cbrt.f64 Om) (cbrt.f64 Om))) (/.f64 l (cbrt.f64 Om))) (-.f64 U* U)))))))
9.5b	(.f64 (.f64 (/.f64 n (.f64 (cbrt.f64 Om) (cbrt.f64 Om))) (/.f64 l (cbrt.f64 Om))) (-.f64 U U))
17.8b	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (.f64 (/.f64 n (.f64 (cbrt.f64 Om) (cbrt.f64 Om))) (/.f64 l (cbrt.f64 Om))) (-.f64 U* U))))))))

rewrite82.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

66×	`add-exp-log_binary64_457`
52×	`add-cbrt-cube_binary64_455`
40×	`add-sqr-sqrt_binary64_441`
36×	`pow1_binary64_480`
31×	`prod-exp_binary64_468` `cbrt-unprod_binary64_452`
28×	`times-frac_binary64_425` `associate-r_binary64_359`
24×	`*-un-lft-identity_binary64_419`
22×	`add-cube-cbrt_binary64_454`
20×	`pow-prod-down_binary64_490`
14×	`associate-*r/_binary64_361` `div-exp_binary64_470` `cbrt-undiv_binary64_453`
11×	`cbrt-prod_binary64_450`
10×	`frac-times_binary64_429`
9×	`associate-l_binary64_360`
8×	`distribute-rgt-in_binary64_369` `distribute-lft-in_binary64_368`
7×	`associate-*l/_binary64_362`
6×	`unswap-sqr_binary64_387` `cancel-sign-sub-inv_binary64_385`
5×	`sqrt-pow1_binary64_437`
4×	`add-log-exp_binary64_458` `flip3--_binary64_423` `flip--_binary64_394`
3×	`*-commutative_binary64_350`
2×	`flip3-+_binary64_422` `sqrt-div_binary64_436` `sub-neg_binary64_412` `div-inv_binary64_416` `flip-+_binary64_393`
1×	`difference-of-squares_binary64_388` `pow1/2_binary64_499` `distribute-lft-out--_binary64_371` `sqrt-prod_binary64_435`

Counts

4 → 152

Calls

4 calls:

22.0ms	(.f64 (.f64 (/.f64 n (.f64 (cbrt.f64 Om) (cbrt.f64 Om))) (/.f64 l (cbrt.f64 Om))) (-.f64 U U))
18.0ms	(.f64 (/.f64 n (.f64 (cbrt.f64 Om) (cbrt.f64 Om))) (/.f64 l (cbrt.f64 Om)))
10.0ms	(.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (.f64 (/.f64 n (.f64 (cbrt.f64 Om) (cbrt.f64 Om))) (/.f64 l (cbrt.f64 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 (.f64 (/.f64 n (.f64 (cbrt.f64 Om) (cbrt.f64 Om))) (/.f64 l (cbrt.f64 Om))) (-.f64 U* U))))))))

series5.9s (20.1%)

Counts

4 → 12

Calls

4 calls:

4.4s	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (.f64 (/.f64 n (.f64 (cbrt.f64 Om) (cbrt.f64 Om))) (/.f64 l (cbrt.f64 Om))) (-.f64 U* U))))))))
1.1s	(.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (.f64 (/.f64 n (.f64 (cbrt.f64 Om) (cbrt.f64 Om))) (/.f64 l (cbrt.f64 Om))) (-.f64 U* U)))))))
312.0ms	(.f64 (.f64 (/.f64 n (.f64 (cbrt.f64 Om) (cbrt.f64 Om))) (/.f64 l (cbrt.f64 Om))) (-.f64 U U))
95.0ms	(.f64 (/.f64 n (.f64 (cbrt.f64 Om) (cbrt.f64 Om))) (/.f64 l (cbrt.f64 Om)))

simplify64.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

164 → 164

Iterations

Useful iterations: 0 (19.0ms)

Iter	Nodes	Cost
0	5130	4112

prune207.0ms (0.7%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	163	1	164
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	163	12	175

Merged error: 16.9b

Counts

175 → 12

Compiler

Compiled 5880 to 2266 computations (61.5% saved)

regimes1.1s (3.7%)

Compiler: Compiled 12730 to 8648 computations (32.1% saved)

bsearch62.0ms (0.2%)

Steps

Iters	Range		Point
8	-7.259013970289198e-303	-9.248743860364985e-307	-9.428773996481168e-307

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%)

sample3.8s (13.2%)

Algorithm

1×

intervals

Results

1.2s	12602×	body	128	nan
767.0ms	8000×	body	128	valid
121.0ms	1162×	body	128	invalid

Compiler

Compiled 1641 to 1106 computations (32.6% saved)

Details

analyze2.5s (8.6%)

sample94.0ms (0.3%)

simplify199.0ms (0.7%)

prune5.0ms (0%)

localize20.0ms (0.1%)

rewrite59.0ms (0.2%)

series4.8s (16.5%)

simplify106.0ms (0.4%)

prune220.0ms (0.8%)

localize17.0ms (0.1%)

rewrite53.0ms (0.2%)

series4.6s (15.9%)

simplify60.0ms (0.2%)

prune168.0ms (0.6%)

localize17.0ms (0.1%)

rewrite54.0ms (0.2%)

series4.7s (16.1%)

simplify59.0ms (0.2%)

prune164.0ms (0.6%)

localize22.0ms (0.1%)

rewrite82.0ms (0.3%)

series5.9s (20.1%)

simplify64.0ms (0.2%)

prune207.0ms (0.7%)

regimes1.1s (3.7%)

bsearch62.0ms (0.2%)

simplify3.0ms (0%)

end0.0ms (0%)

sample3.8s (13.2%)

Profiling