Details

analyze2.4s (7.1%)

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)

sample113.0ms (0.3%)

Algorithm

1×

intervals

Results

42.0ms	467×	body	128	nan
23.0ms	256×	body	128	valid
3.0ms	31×	body	128	invalid

Compiler

Compiled 57 to 53 computations (7% saved)

simplify56.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (48.0ms)

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

30.1b

Counts

2 → 2

Compiler

Compiled 80 to 63 computations (21.3% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

1.0b	(.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))))
7.0b	(.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)))))))
12.8b	(.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))
21.4b	(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))))))))

rewrite258.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Error

23.2b

Rules

30×	`pow1_binary64_480` `add-exp-log_binary64_457` `add-cbrt-cube_binary64_455`
29×	`add-sqr-sqrt_binary64_441`
27×	`associate-l_binary64_360`
24×	`add-cube-cbrt_binary64_454` `*-un-lft-identity_binary64_419`
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×	`add-log-exp_binary64_458` `sqrt-pow1_binary64_437` `flip3-+_binary64_422` `flip-+_binary64_393` `frac-times_binary64_429` `sub-neg_binary64_412`
3×	`div-exp_binary64_470` `cbrt-undiv_binary64_453` `*-commutative_binary64_350`
2×	`sqrt-div_binary64_436` `flip3--_binary64_423` `flip--_binary64_394` `associate-*l/_binary64_362` `div-inv_binary64_416` `unswap-sqr_binary64_387`
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)))))
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))))))))

Compiler

Compiled 5195 to 2032 computations (60.9% saved)

series4.7s (13.8%)

Error

18.8b

Counts

4 → 114

Calls

4 calls:

2.0s	(.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)))))))
1.3s	(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))))))))
843.0ms	(.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))))
320.0ms	(.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))

Compiler

Compiled 12479 to 9411 computations (24.6% saved)

simplify129.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

245 → 245

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4983	8274
1	4983	8274

prune365.0ms (1.1%)

Pruning

19 alts after pruning (19 fresh and 0 done)

	Pruned	Kept	Total
New	226	19	245
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	228	19	247

Error

14.5b

Counts

247 → 19

Compiler

Compiled 8986 to 3320 computations (63.1% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

6.2b	(*.f64 n (/.f64 l Om))
7.0b	(.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))))))
8.2b	(.f64 (.f64 n (/.f64 l Om)) (-.f64 U* U))
21.4b	(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)))))))

rewrite193.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Error

14.2b

Rules

30×	`pow1_binary64_480`
27×	`add-exp-log_binary64_457` `add-cbrt-cube_binary64_455`
23×	`add-sqr-sqrt_binary64_441`
21×	`associate-r_binary64_359`
18×	`*-un-lft-identity_binary64_419`
16×	`add-cube-cbrt_binary64_454` `pow-prod-down_binary64_490`
13×	`prod-exp_binary64_468` `cbrt-unprod_binary64_452`
10×	`associate-*r/_binary64_361` `times-frac_binary64_425`
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` `flip-+_binary64_393` `div-exp_binary64_470` `cbrt-undiv_binary64_453` `flip3--_binary64_423` `frac-times_binary64_429` `flip--_binary64_394` `sub-neg_binary64_412` `unswap-sqr_binary64_387`
1×	`pow1/2_binary64_499` `sqrt-prod_binary64_435` `associate-*l/_binary64_362` `difference-of-squares_binary64_388` `distribute-lft-out--_binary64_371` `div-inv_binary64_416`

Counts

4 → 107

Calls

4 calls:

13.0ms	(.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)))))))

Compiler

Compiled 4070 to 1665 computations (59.1% saved)

series3.9s (11.5%)

Error

13.8b

Counts

4 → 96

Calls

4 calls:

2.0s	(.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))))))
1.3s	(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)))))))
341.0ms	(.f64 (.f64 n (/.f64 l Om)) (-.f64 U* U))
111.0ms	(*.f64 n (/.f64 l Om))

Compiler

Compiled 10959 to 8198 computations (25.2% saved)

simplify110.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

203 → 203

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4974	6583
1	4974	6583

prune265.0ms (0.8%)

Pruning

19 alts after pruning (19 fresh and 0 done)

	Pruned	Kept	Total
New	200	3	203
Fresh	2	16	18
Picked	1	0	1
Done	0	0	0
Total	203	19	222

Error

14.4b

Counts

222 → 19

Compiler

Compiled 7595 to 2879 computations (62.1% saved)

localize17.0ms (0%)

Local error

Found 4 expressions with local error:

4.9b	(.f64 n (.f64 (-.f64 U* U) (/.f64 l Om)))
7.0b	(.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (-.f64 U U) (/.f64 l Om)))))))
7.8b	(.f64 (-.f64 U U) (/.f64 l Om))
21.4b	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (-.f64 U U) (/.f64 l Om))))))))

rewrite181.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Error

14.4b

Rules

30×	`pow1_binary64_480`
27×	`add-exp-log_binary64_457` `add-cbrt-cube_binary64_455`
21×	`add-sqr-sqrt_binary64_441`
17×	`associate-r_binary64_359`
16×	`pow-prod-down_binary64_490` `*-un-lft-identity_binary64_419`
14×	`add-cube-cbrt_binary64_454`
13×	`prod-exp_binary64_468` `cbrt-unprod_binary64_452`
11×	`associate-*r/_binary64_361`
10×	`times-frac_binary64_425`
9×	`associate-l_binary64_360`
4×	`add-log-exp_binary64_458` `sqrt-pow1_binary64_437` `flip3--_binary64_423` `frac-times_binary64_429` `flip--_binary64_394` `associate-*l/_binary64_362`
3×	`*-commutative_binary64_350`
2×	`flip3-+_binary64_422` `sqrt-div_binary64_436` `flip-+_binary64_393` `div-exp_binary64_470` `cbrt-undiv_binary64_453` `unswap-sqr_binary64_387`
1×	`pow1/2_binary64_499` `sqrt-prod_binary64_435` `difference-of-squares_binary64_388` `distribute-lft-out--_binary64_371` `div-inv_binary64_416` `distribute-rgt-in_binary64_369` `distribute-lft-in_binary64_368`

Counts

4 → 103

Calls

4 calls:

10.0ms	(.f64 (-.f64 U U) (/.f64 l Om))
10.0ms	(.f64 n (.f64 (-.f64 U* U) (/.f64 l Om)))
9.0ms	(.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (-.f64 U U) (/.f64 l Om)))))))
7.0ms	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (-.f64 U U) (/.f64 l Om))))))))

Compiler

Compiled 3954 to 1618 computations (59.1% saved)

series4.0s (11.8%)

Error

13.6b

Counts

4 → 105

Calls

4 calls:

2.0s	(.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (-.f64 U U) (/.f64 l Om)))))))
1.3s	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (-.f64 U U) (/.f64 l Om))))))))
335.0ms	(.f64 n (.f64 (-.f64 U* U) (/.f64 l Om)))
229.0ms	(.f64 (-.f64 U U) (/.f64 l Om))

Compiler

Compiled 11583 to 8594 computations (25.8% saved)

simplify74.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

208 → 208

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	5271	6639

prune261.0ms (0.8%)

Pruning

19 alts after pruning (18 fresh and 1 done)

	Pruned	Kept	Total
New	208	0	208
Fresh	0	18	18
Picked	0	1	1
Done	0	0	0
Total	208	19	227

Error

14.4b

Counts

227 → 19

Compiler

Compiled 7677 to 2926 computations (61.9% saved)

localize25.0ms (0.1%)

Local error

Found 4 expressions with local error:

7.0b	(.f64 (.f64 U (.f64 2 n)) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (/.f64 (.f64 l (-.f64 U* U)) Om)) (*.f64 l -2)))))
7.0b	(.f64 (.f64 U (.f64 2 n)) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (/.f64 (.f64 l (-.f64 U* U)) Om)) (*.f64 l -2)))))
21.4b	(sqrt.f64 (.f64 (.f64 U (.f64 2 n)) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (/.f64 (.f64 l (-.f64 U* U)) Om)) (*.f64 l -2))))))
21.4b	(sqrt.f64 (.f64 (.f64 U (.f64 2 n)) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (/.f64 (.f64 l (-.f64 U* U)) Om)) (*.f64 l -2))))))

rewrite227.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Error

14.4b

Rules

42×	`pow1_binary64_480`
24×	`pow-prod-down_binary64_490`
22×	`add-exp-log_binary64_457` `add-cbrt-cube_binary64_455`
12×	`prod-exp_binary64_468` `cbrt-unprod_binary64_452`
8×	`sqrt-pow1_binary64_437` `associate-*r/_binary64_361`
6×	`add-cube-cbrt_binary64_454` `add-sqr-sqrt_binary64_441` `-un-lft-identity_binary64_419` `associate-r*_binary64_359`
4×	`add-log-exp_binary64_458` `flip3-+_binary64_422` `sqrt-div_binary64_436` `flip-+_binary64_393`
2×	`pow1/2_binary64_499` `sqrt-prod_binary64_435` `distribute-rgt-in_binary64_369` `distribute-lft-in_binary64_368` `associate-l_binary64_360` `*-commutative_binary64_350`

Counts

4 → 80

Calls

4 calls:

9.0ms	(.f64 (.f64 U (.f64 2 n)) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (/.f64 (.f64 l (-.f64 U* U)) Om)) (*.f64 l -2)))))
9.0ms	(.f64 (.f64 U (.f64 2 n)) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (/.f64 (.f64 l (-.f64 U* U)) Om)) (*.f64 l -2)))))
7.0ms	(sqrt.f64 (.f64 (.f64 U (.f64 2 n)) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (/.f64 (.f64 l (-.f64 U* U)) Om)) (*.f64 l -2))))))
7.0ms	(sqrt.f64 (.f64 (.f64 U (.f64 2 n)) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (/.f64 (.f64 l (-.f64 U* U)) Om)) (*.f64 l -2))))))

Compiler

Compiled 5946 to 2494 computations (58.1% saved)

series7.0s (20.5%)

Error

14.4b

Counts

4 → 126

Calls

4 calls:

2.0s	(.f64 (.f64 U (.f64 2 n)) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (/.f64 (.f64 l (-.f64 U* U)) Om)) (*.f64 l -2)))))
2.0s	(.f64 (.f64 U (.f64 2 n)) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (/.f64 (.f64 l (-.f64 U* U)) Om)) (*.f64 l -2)))))
1.4s	(sqrt.f64 (.f64 (.f64 U (.f64 2 n)) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (/.f64 (.f64 l (-.f64 U* U)) Om)) (*.f64 l -2))))))
1.2s	(sqrt.f64 (.f64 (.f64 U (.f64 2 n)) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (/.f64 (.f64 l (-.f64 U* U)) Om)) (*.f64 l -2))))))

Compiler

Compiled 25586 to 17748 computations (30.6% saved)

simplify128.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

206 → 206

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4976	10118
1	4976	10118

prune472.0ms (1.4%)

Pruning

19 alts after pruning (18 fresh and 1 done)

	Pruned	Kept	Total
New	204	2	206
Fresh	1	16	17
Picked	1	0	1
Done	0	1	1
Total	206	19	225

Error

14.4b

Counts

225 → 19

Compiler

Compiled 13716 to 4971 computations (63.8% saved)

regimes2.8s (8.3%)

Accuracy

Total 14.1b remaining (50.7%)

Threshold costs 0b (0%)

Compiler

Compiled 37106 to 27386 computations (26.2% saved)

bsearch10.0ms (0%)

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

simplify65.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	1338	442
1	1338	442

end0.0ms (0%)

sample6.3s (18.4%)

Algorithm

1×

intervals

Results

1.2s	12873×	body	128	nan
752.0ms	8000×	body	128	valid
112.0ms	1209×	body	128	invalid

Compiler

Compiled 4945 to 3596 computations (27.3% saved)

Details

analyze2.4s (7.1%)

sample113.0ms (0.3%)

simplify56.0ms (0.2%)

prune5.0ms (0%)

localize17.0ms (0.1%)

rewrite258.0ms (0.8%)

series4.7s (13.8%)

simplify129.0ms (0.4%)

prune365.0ms (1.1%)

localize17.0ms (0.1%)

rewrite193.0ms (0.6%)

series3.9s (11.5%)

simplify110.0ms (0.3%)

prune265.0ms (0.8%)

localize17.0ms (0%)

rewrite181.0ms (0.5%)

series4.0s (11.8%)

simplify74.0ms (0.2%)

prune261.0ms (0.8%)

localize25.0ms (0.1%)

rewrite227.0ms (0.7%)

series7.0s (20.5%)

simplify128.0ms (0.4%)

prune472.0ms (1.4%)

regimes2.8s (8.3%)

bsearch10.0ms (0%)

simplify65.0ms (0.2%)

end0.0ms (0%)

sample6.3s (18.4%)

Profiling