Details

analyze2.2s (10.1%)

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)

sample92.0ms (0.4%)

Algorithm

1×

intervals

Results

38.0ms	396×	body	128	nan
22.0ms	256×	body	128	valid
3.0ms	30×	body	128	invalid

Compiler

Compiled 57 to 53 computations (7% saved)

simplify141.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5178	39

prune10.0ms (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

31.8b

Counts

2 → 2

Compiler

Compiled 80 to 63 computations (21.3% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

1.0b	(.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))))
9.5b	(.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)))))))
10.4b	(.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))
20.5b	(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))))))))

rewrite54.0ms (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:

12.0ms	(.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)))))
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))))))))

series2.8s (12.9%)

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))))))))
435.0ms	(.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)))))))
160.0ms	(.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)))

simplify91.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

143 → 143

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	5099	4107

prune224.0ms (1%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	132	11	143
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	133	12	145

Error

22.1b

Counts

145 → 12

Compiler

Compiled 5418 to 2255 computations (58.4% saved)

localize20.0ms (0.1%)

Local error

Found 4 expressions with local error:

4.1b	(*.f64 n (/.f64 l Om))
9.1b	(.f64 (.f64 n (/.f64 l Om)) (-.f64 U* U))
9.5b	(.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))))))
20.5b	(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)))))))

rewrite47.0ms (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 (12.2%)

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)))))))
426.0ms	(.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))))))
97.0ms	(.f64 (.f64 n (/.f64 l Om)) (-.f64 U* U))
19.0ms	(*.f64 n (/.f64 l Om))

simplify76.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5059	2829

prune153.0ms (0.7%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	117	2	119
Fresh	2	9	11
Picked	1	0	1
Done	0	0	0
Total	120	11	131

Error

21.8b

Counts

131 → 11

Compiler

Compiled 4371 to 1910 computations (56.3% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

4.5b	(.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (.f64 n (/.f64 l Om)) (-.f64 U U))))))
7.2b	(.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)))))))
9.1b	(.f64 (.f64 n (/.f64 l Om)) (-.f64 U* U))
20.5b	(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))))))))

rewrite45.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`pow1_binary64_480`
27×	`add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
20×	`pow-prod-down_binary64_490`
15×	`associate-*r/_binary64_361`
14×	`prod-exp_binary64_468` `cbrt-unprod_binary64_452`
13×	`add-sqr-sqrt_binary64_441`
11×	`*-un-lft-identity_binary64_419`
9×	`distribute-rgt-in_binary64_369` `add-cube-cbrt_binary64_454` `associate-r_binary64_359` `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×	`flip3-+_binary64_422` `*-commutative_binary64_350` `flip-+_binary64_393`
2×	`sqrt-div_binary64_436` `sub-neg_binary64_412` `frac-times_binary64_429` `flip3--_binary64_423` `flip--_binary64_394`
1×	`associate-*l/_binary64_362` `difference-of-squares_binary64_388` `pow1/2_binary64_499` `unswap-sqr_binary64_387` `distribute-lft-out--_binary64_371` `sqrt-prod_binary64_435` `div-exp_binary64_470` `cbrt-undiv_binary64_453`

Counts

4 → 101

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)))))))
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))))))))
6.0ms	(.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (.f64 n (/.f64 l Om)) (-.f64 U U))))))

series2.9s (13.5%)

Counts

4 → 12

Calls

4 calls:

2.0s	(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))))))))
430.0ms	(.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)))))))
336.0ms	(.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (.f64 n (/.f64 l Om)) (-.f64 U U))))))
91.0ms	(.f64 (.f64 n (/.f64 l Om)) (-.f64 U* U))

simplify67.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5368	3449

prune157.0ms (0.7%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	108	5	113
Fresh	3	7	10
Picked	0	1	1
Done	0	0	0
Total	111	13	124

Error

17.4b

Counts

124 → 13

Compiler

Compiled 4311 to 1839 computations (57.3% saved)

localize20.0ms (0.1%)

Local error

Found 4 expressions with local error:

9.1b	(.f64 (.f64 n (/.f64 l Om)) (-.f64 U* U))
9.1b	(.f64 (.f64 n (/.f64 l Om)) (-.f64 U* U))
20.5b	(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))))))))
20.5b	(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))))))))

rewrite56.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

40×	`pow1_binary64_480`
22×	`pow-prod-down_binary64_490` `add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
18×	`associate-*r/_binary64_361`
14×	`*-un-lft-identity_binary64_419` `add-sqr-sqrt_binary64_441`
12×	`cancel-sign-sub-inv_binary64_385`
10×	`add-cube-cbrt_binary64_454` `associate-r_binary64_359` `prod-exp_binary64_468` `cbrt-unprod_binary64_452` `sqrt-pow1_binary64_437`
8×	`distribute-rgt-in_binary64_369` `distribute-lft-in_binary64_368`
4×	`sqrt-div_binary64_436` `sub-neg_binary64_412` `add-log-exp_binary64_458` `frac-times_binary64_429` `flip3--_binary64_423` `flip--_binary64_394`
2×	`flip3-+_binary64_422` `associate-l/_binary64_362` `difference-of-squares_binary64_388` `pow1/2_binary64_499` `distribute-lft-out--_binary64_371` `-commutative_binary64_350` `associate-l_binary64_360` `flip-+_binary64_393` `sqrt-prod_binary64_435` `div-exp_binary64_470` `cbrt-undiv_binary64_453`

Counts

4 → 102

Calls

4 calls:

13.0ms	(.f64 (.f64 n (/.f64 l Om)) (-.f64 U* U))
11.0ms	(.f64 (.f64 n (/.f64 l Om)) (-.f64 U* U))
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))))))))
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))))))))

series4.3s (20%)

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))))))))
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))))))))
96.0ms	(.f64 (.f64 n (/.f64 l Om)) (-.f64 U* U))
96.0ms	(.f64 (.f64 n (/.f64 l Om)) (-.f64 U* U))

simplify52.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	5130	2680

prune226.0ms (1.1%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	113	1	114
Fresh	0	11	11
Picked	1	0	1
Done	0	1	1
Total	114	13	127

Error

17.4b

Counts

127 → 13

Compiler

Compiled 7036 to 2962 computations (57.9% saved)

regimes1.2s (5.5%)

Accuracy

Total 8.9b remaining (33.1%)

Threshold costs 0b (0%)

Compiler

Compiled 15130 to 9752 computations (35.5% saved)

bsearch5.0ms (0%)

Compiler: Compiled 28 to 23 computations (17.9% saved)

simplify28.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	765	301
1	765	301

end0.0ms (0%)

sample4.0s (18.4%)

Algorithm

1×

intervals

Results

1.2s	13192×	body	128	nan
714.0ms	8000×	body	128	valid
105.0ms	1220×	body	128	invalid

Compiler

Compiled 2083 to 1315 computations (36.9% saved)

Details

analyze2.2s (10.1%)

sample92.0ms (0.4%)

simplify141.0ms (0.7%)

prune10.0ms (0%)

localize16.0ms (0.1%)

rewrite54.0ms (0.3%)

series2.8s (12.9%)

simplify91.0ms (0.4%)

prune224.0ms (1%)

localize20.0ms (0.1%)

rewrite47.0ms (0.2%)

series2.6s (12.2%)

simplify76.0ms (0.4%)

prune153.0ms (0.7%)

localize17.0ms (0.1%)

rewrite45.0ms (0.2%)

series2.9s (13.5%)

simplify67.0ms (0.3%)

prune157.0ms (0.7%)

localize20.0ms (0.1%)

rewrite56.0ms (0.3%)

series4.3s (20%)

simplify52.0ms (0.2%)

prune226.0ms (1.1%)

regimes1.2s (5.5%)

bsearch5.0ms (0%)

simplify28.0ms (0.1%)

end0.0ms (0%)

sample4.0s (18.4%)

Profiling