Details

analyze2.6s (10.4%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5820	672
0	6	6
1	6	6

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)

sample92.0ms (0.4%)

Algorithm

1×

intervals

Results

32.0ms	358×	body	128	nan
23.0ms	256×	body	128	valid
4.0ms	46×	body	128	invalid

Compiler

Compiled 57 to 53 computations (7% saved)

simplify54.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (49.0ms)

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: 32.1b

Counts

2 → 2

Compiler

Compiled 80 to 63 computations (21.3% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.6b	(.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))))
8.5b	(.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)))))))
20.8b	(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))))))))

rewrite53.0ms (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:

12.0ms	(.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)))))
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)))))))
7.0ms	(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 (11%)

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))))))))
424.0ms	(.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)))))))
141.0ms	(.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))))
96.0ms	(.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))

simplify94.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

143 → 143

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	5099	4107

prune219.0ms (0.9%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	130	13	143
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	131	14	145

Merged error: 24.0b

Counts

145 → 14

Compiler

Compiled 5503 to 2301 computations (58.2% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

3.3b	(*.f64 n (/.f64 l Om))
6.7b	(.f64 (.f64 n (/.f64 l Om)) (-.f64 U* U))
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))))))
20.8b	(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)))))))

rewrite48.0ms (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:

12.0ms	(.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))))))
10.0ms	(.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 (10.7%)

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)))))))
436.0ms	(.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))))))
100.0ms	(.f64 (.f64 n (/.f64 l Om)) (-.f64 U* U))
20.0ms	(*.f64 n (/.f64 l Om))

simplify77.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5059	2829

prune162.0ms (0.7%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	114	5	119
Fresh	5	8	13
Picked	1	0	1
Done	0	0	0
Total	120	13	133

Merged error: 23.0b

Counts

133 → 13

Compiler

Compiled 4456 to 1956 computations (56.1% saved)

localize20.0ms (0.1%)

Local error

Found 4 expressions with local error:

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))))))
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))))))
20.8b	(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)))))))
20.8b	(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)))))))

rewrite50.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

42×	`pow1_binary64_480`
24×	`pow-prod-down_binary64_490`
22×	`add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
12×	`prod-exp_binary64_468` `cbrt-unprod_binary64_452`
8×	`associate-*r/_binary64_361` `sqrt-pow1_binary64_437`
6×	`-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454` `associate-r*_binary64_359` `add-sqr-sqrt_binary64_441`
4×	`flip3-+_binary64_422` `sqrt-div_binary64_436` `add-log-exp_binary64_458` `flip-+_binary64_393`
2×	`distribute-rgt-in_binary64_369` `pow1/2_binary64_499` `distribute-lft-in_binary64_368` `-commutative_binary64_350` `associate-l*_binary64_360` `sqrt-prod_binary64_435`

Counts

4 → 80

Calls

4 calls:

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))))))
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	(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)))))))
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)))))))

series5.0s (20.3%)

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)))))))
2.0s	(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)))))))
433.0ms	(.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))))))
430.0ms	(.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))))))

simplify80.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5083	3652

prune213.0ms (0.9%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	91	1	92
Fresh	1	11	12
Picked	0	1	1
Done	0	0	0
Total	92	13	105

Merged error: 23.0b

Counts

105 → 13

Compiler

Compiled 6538 to 2886 computations (55.9% saved)

localize33.0ms (0.1%)

Local error

Found 4 expressions with local error:

12.4b	(cbrt.f64 (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (.f64 n (/.f64 l Om)) (-.f64 U* U))))))
12.4b	(cbrt.f64 (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (.f64 n (/.f64 l Om)) (-.f64 U* U))))))
20.8b	(sqrt.f64 (.f64 (.f64 (.f64 (.f64 2 n) U) (.f64 (cbrt.f64 (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (.f64 n (/.f64 l Om)) (-.f64 U U)))))) (cbrt.f64 (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (.f64 n (/.f64 l Om)) (-.f64 U* U)))))))) (cbrt.f64 (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (.f64 n (/.f64 l Om)) (-.f64 U* U))))))))
20.8b	(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)))))))

rewrite66.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

58×	`cbrt-div_binary64_451`
44×	`pow1_binary64_480`
34×	`associate-*r/_binary64_361`
30×	`flip3-+_binary64_422` `flip-+_binary64_393`
28×	`pow-prod-down_binary64_490` `sqrt-div_binary64_436` `frac-times_binary64_429`
14×	`associate-*l/_binary64_362`
12×	`sqrt-pow1_binary64_437`
6×	`*-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454` `cbrt-prod_binary64_450` `add-sqr-sqrt_binary64_441`
4×	`add-log-exp_binary64_458` `add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
2×	`pow1/3_binary64_501` `pow1/2_binary64_499` `sqrt-prod_binary64_435`

Counts

4 → 84

Calls

4 calls:

21.0ms	(sqrt.f64 (.f64 (.f64 (.f64 (.f64 2 n) U) (.f64 (cbrt.f64 (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (.f64 n (/.f64 l Om)) (-.f64 U U)))))) (cbrt.f64 (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (.f64 n (/.f64 l Om)) (-.f64 U* U)))))))) (cbrt.f64 (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (.f64 n (/.f64 l Om)) (-.f64 U* U))))))))
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)))))))
3.0ms	(cbrt.f64 (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (.f64 n (/.f64 l Om)) (-.f64 U* U))))))
3.0ms	(cbrt.f64 (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (.f64 n (/.f64 l Om)) (-.f64 U* U))))))

series5.1s (20.7%)

Counts

4 → 12

Calls

4 calls:

2.1s	(sqrt.f64 (.f64 (.f64 (.f64 (.f64 2 n) U) (.f64 (cbrt.f64 (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (.f64 n (/.f64 l Om)) (-.f64 U U)))))) (cbrt.f64 (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (.f64 n (/.f64 l Om)) (-.f64 U* U)))))))) (cbrt.f64 (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (.f64 n (/.f64 l Om)) (-.f64 U* U))))))))
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)))))))
436.0ms	(cbrt.f64 (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (.f64 n (/.f64 l Om)) (-.f64 U* U))))))
422.0ms	(cbrt.f64 (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (.f64 n (/.f64 l Om)) (-.f64 U* U))))))

simplify112.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4974	8423
1	4974	8423

prune403.0ms (1.6%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	96	0	96
Fresh	0	11	11
Picked	0	1	1
Done	0	1	1
Total	96	13	109

Merged error: 23.0b

Counts

109 → 13

Compiler

Compiled 11818 to 4638 computations (60.8% saved)

regimes859.0ms (3.5%)

Compiler: Compiled 11562 to 7672 computations (33.6% saved)

bsearch255.0ms (1%)

Steps

Iters	Range		Point
7	7.10304474095806e+86	1.1948959672748551e+89	2.4193320928135134e+88
10	6.950861664549911e-121	3.4766977942432025e-109	2.1618040063167887e-119
10	4.3573758723865983e-218	4.563447769303649e-207	7.111121743805023e-210

Compiler

Compiled 1 to 6 computations (-500% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	66	100
1	66	100

end0.0ms (0%)

sample3.6s (14.9%)

Algorithm

1×

intervals

Results

1.1s	12443×	body	128	nan
742.0ms	8000×	body	128	valid
109.0ms	1191×	body	128	invalid

Compiler

Compiled 1504 to 991 computations (34.1% saved)

Details

analyze2.6s (10.4%)

sample92.0ms (0.4%)

simplify54.0ms (0.2%)

prune5.0ms (0%)

localize18.0ms (0.1%)

rewrite53.0ms (0.2%)

series2.7s (11%)

simplify94.0ms (0.4%)

prune219.0ms (0.9%)

localize17.0ms (0.1%)

rewrite48.0ms (0.2%)

series2.6s (10.7%)

simplify77.0ms (0.3%)

prune162.0ms (0.7%)

localize20.0ms (0.1%)

rewrite50.0ms (0.2%)

series5.0s (20.3%)

simplify80.0ms (0.3%)

prune213.0ms (0.9%)

localize33.0ms (0.1%)

rewrite66.0ms (0.3%)

series5.1s (20.7%)

simplify112.0ms (0.5%)

prune403.0ms (1.6%)

regimes859.0ms (3.5%)

bsearch255.0ms (1%)

simplify4.0ms (0%)

end0.0ms (0%)

sample3.6s (14.9%)

Profiling