Details

analyze2.3s (11.5%)

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)

sample96.0ms (0.5%)

Algorithm

1×

intervals

Results

40.0ms	395×	body	128	nan
24.0ms	256×	body	128	valid
4.0ms	39×	body	128	invalid

Compiler

Compiled 57 to 53 computations (7% saved)

simplify147.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (46.0ms)

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

Error

30.8b

Counts

2 → 2

Compiler

Compiled 80 to 63 computations (21.3% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

1.6b	(.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))))
10.1b	(.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))
13.0b	(.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)))))))
16.7b	(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 (0.3%)

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:

13.0ms	(.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)))))
9.0ms	(.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 (13.8%)

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 l Om) (.f64 n (-.f64 U U))))))))
428.0ms	(.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)))))))
146.0ms	(.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))))
92.0ms	(.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))

simplify91.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

143 → 143

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	5099	4107

prune208.0ms (1.1%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	135	8	143
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	136	9	145

Error

20.9b

Counts

145 → 9

Compiler

Compiled 5250 to 2154 computations (59% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

5.4b	(*.f64 n (/.f64 l Om))
6.1b	(.f64 (.f64 n (/.f64 l Om)) (-.f64 U* U))
13.0b	(.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))))))
16.7b	(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)))))))

rewrite49.0ms (0.3%)

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:

13.0ms	(.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)))))))

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)))))))
441.0ms	(.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))))))
102.0ms	(.f64 (.f64 n (/.f64 l Om)) (-.f64 U* U))
19.0ms	(*.f64 n (/.f64 l Om))

simplify78.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5059	2829

prune150.0ms (0.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	117	2	119
Fresh	2	6	8
Picked	1	0	1
Done	0	0	0
Total	120	8	128

Error

19.7b

Counts

128 → 8

Compiler

Compiled 4203 to 1809 computations (57% saved)

localize20.0ms (0.1%)

Local error

Found 4 expressions with local error:

5.4b	(*.f64 n (/.f64 l Om))
6.1b	(.f64 (.f64 n (/.f64 l Om)) (-.f64 U* U))
7.7b	(.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)))))))
16.7b	(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))))))))

rewrite47.0ms (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:

11.0ms	(.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)))))))
8.0ms	(*.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))))))))
428.0ms	(.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)))))))
95.0ms	(.f64 (.f64 n (/.f64 l Om)) (-.f64 U* U))
18.0ms	(*.f64 n (/.f64 l Om))

simplify75.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5016	2927

prune164.0ms (0.8%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	117	6	123
Fresh	1	6	7
Picked	0	1	1
Done	0	0	0
Total	118	13	131

Error

16.3b

Counts

131 → 13

Compiler

Compiled 4472 to 1955 computations (56.3% saved)

localize20.0ms (0.1%)

Local error

Found 4 expressions with local error:

6.1b	(.f64 (cbrt.f64 (pow.f64 (.f64 n (/.f64 l Om)) 3)) (-.f64 U* U))
7.7b	(.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (cbrt.f64 (pow.f64 (.f64 n (/.f64 l Om)) 3)) (-.f64 U U)))))))
16.7b	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (cbrt.f64 (pow.f64 (.f64 n (/.f64 l Om)) 3)) (-.f64 U U))))))))
25.4b	(cbrt.f64 (pow.f64 (*.f64 n (/.f64 l Om)) 3))

rewrite45.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

31×	`pow1_binary64_480`
18×	`cbrt-prod_binary64_450` `add-exp-log_binary64_457`
17×	`pow-prod-down_binary64_490` `add-sqr-sqrt_binary64_441` `add-cbrt-cube_binary64_455`
14×	`associate-*r/_binary64_361`
12×	`-un-lft-identity_binary64_419` `associate-l*_binary64_360`
10×	`add-cube-cbrt_binary64_454`
9×	`prod-exp_binary64_468` `cbrt-unprod_binary64_452`
8×	`distribute-rgt-in_binary64_369` `distribute-lft-in_binary64_368`
6×	`associate-r_binary64_359` `cancel-sign-sub-inv_binary64_385`
5×	`sqrt-pow1_binary64_437`
4×	`add-log-exp_binary64_458` `cbrt-div_binary64_451` `cube-div_binary64_448`
3×	`unswap-sqr_binary64_387` `sqr-pow_binary64_391`
2×	`flip3-+_binary64_422` `sqrt-div_binary64_436` `sub-neg_binary64_412` `unpow-prod-down_binary64_498` `unpow3_binary64_485` `cube-mult_binary64_449` `frac-times_binary64_429` `flip3--_binary64_423` `*-commutative_binary64_350` `cube-prod_binary64_447` `flip-+_binary64_393` `flip--_binary64_394`
1×	`associate-*l/_binary64_362` `pow1/3_binary64_501` `difference-of-squares_binary64_388` `pow1/2_binary64_499` `distribute-lft-out--_binary64_371` `rem-cbrt-cube_binary64_443` `sqrt-prod_binary64_435`

Counts

4 → 105

Calls

4 calls:

11.0ms	(.f64 (cbrt.f64 (pow.f64 (.f64 n (/.f64 l Om)) 3)) (-.f64 U* U))
10.0ms	(.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (cbrt.f64 (pow.f64 (.f64 n (/.f64 l Om)) 3)) (-.f64 U U)))))))
7.0ms	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (cbrt.f64 (pow.f64 (.f64 n (/.f64 l Om)) 3)) (-.f64 U U))))))))
2.0ms	(cbrt.f64 (pow.f64 (*.f64 n (/.f64 l Om)) 3))

series3.2s (16.5%)

Counts

4 → 12

Calls

4 calls:

2.6s	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (cbrt.f64 (pow.f64 (.f64 n (/.f64 l Om)) 3)) (-.f64 U U))))))))
521.0ms	(.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (cbrt.f64 (pow.f64 (.f64 n (/.f64 l Om)) 3)) (-.f64 U U)))))))
116.0ms	(.f64 (cbrt.f64 (pow.f64 (.f64 n (/.f64 l Om)) 3)) (-.f64 U* U))
25.0ms	(cbrt.f64 (pow.f64 (*.f64 n (/.f64 l Om)) 3))

simplify80.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5145	3064

prune140.0ms (0.7%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	117	0	117
Fresh	0	11	11
Picked	0	1	1
Done	0	1	1
Total	117	13	130

Error

16.3b

Counts

130 → 13

Compiler

Compiled 4041 to 1719 computations (57.5% saved)

regimes851.0ms (4.3%)

Accuracy

Total 8.3b remaining (31.6%)

Threshold costs 0b (0%)

Compiler

Compiled 11114 to 7344 computations (33.9% saved)

bsearch4.0ms (0%)

Compiler: Compiled 27 to 22 computations (18.5% saved)

simplify25.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (21.0ms)

Iter	Nodes	Cost
0	755	303
1	755	303

end0.0ms (0%)

sample3.8s (19.3%)

Algorithm

1×

intervals

Results

1.2s	12912×	body	128	nan
753.0ms	8000×	body	128	valid
116.0ms	1244×	body	128	invalid

Compiler

Compiled 1583 to 1016 computations (35.8% saved)

Details

analyze2.3s (11.5%)

sample96.0ms (0.5%)

simplify147.0ms (0.7%)

prune5.0ms (0%)

localize17.0ms (0.1%)

rewrite59.0ms (0.3%)

series2.7s (13.8%)

simplify91.0ms (0.5%)

prune208.0ms (1.1%)

localize17.0ms (0.1%)

rewrite49.0ms (0.3%)

series2.6s (13.4%)

simplify78.0ms (0.4%)

prune150.0ms (0.8%)

localize20.0ms (0.1%)

rewrite47.0ms (0.2%)

series2.6s (13.3%)

simplify75.0ms (0.4%)

prune164.0ms (0.8%)

localize20.0ms (0.1%)

rewrite45.0ms (0.2%)

series3.2s (16.5%)

simplify80.0ms (0.4%)

prune140.0ms (0.7%)

regimes851.0ms (4.3%)

bsearch4.0ms (0%)

simplify25.0ms (0.1%)

end0.0ms (0%)

sample3.8s (19.3%)

Profiling