Details

analyze2.4s (9.3%)

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)

sample93.0ms (0.4%)

Algorithm

1×

intervals

Results

36.0ms	403×	body	128	nan
23.0ms	256×	body	128	valid
2.0ms	26×	body	128	invalid

Compiler

Compiled 57 to 53 computations (7% saved)

simplify141.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (44.0ms)

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: 31.7b

Counts

2 → 2

Compiler

Compiled 80 to 63 computations (21.3% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.9b	(.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))))
10.2b	(.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))
11.6b	(.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)))))))
18.6b	(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))))))))

rewrite52.0ms (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)))))
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))))))))

series3.8s (14.5%)

Counts

4 → 104

Calls

4 calls:

1.8s	(.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)))))))
1.0s	(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))))))))
732.0ms	(.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))))
252.0ms	(.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))

Compiler

Compiled 7412 to 6098 computations (17.7% saved)

simplify100.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

235 → 235

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	4987	7671
1	4987	7671

prune354.0ms (1.4%)

Pruning

26 alts after pruning (26 fresh and 0 done)

	Pruned	Kept	Total
New	210	25	235
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	211	26	237

Merged error: 18.9b

Counts

237 → 26

Compiler

Compiled 8696 to 3352 computations (61.5% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

5.1b	(*.f64 n (/.f64 l Om))
5.7b	(.f64 (.f64 n (/.f64 l Om)) (-.f64 U* U))
11.6b	(.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))))))
18.6b	(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)))))))

rewrite45.0ms (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:

10.0ms	(.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)))))))

series3.1s (12.1%)

Counts

4 → 88

Calls

4 calls:

1.8s	(.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))))))
999.0ms	(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)))))))
273.0ms	(.f64 (.f64 n (/.f64 l Om)) (-.f64 U* U))
108.0ms	(*.f64 n (/.f64 l Om))

Compiler

Compiled 6578 to 5384 computations (18.2% saved)

simplify70.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

195 → 195

Iterations

Useful iterations: 0 (21.0ms)

Iter	Nodes	Cost
0	5554	5851

prune264.0ms (1%)

Pruning

28 alts after pruning (27 fresh and 1 done)

	Pruned	Kept	Total
New	192	3	195
Fresh	1	24	25
Picked	0	1	1
Done	0	0	0
Total	193	28	221

Merged error: 18.7b

Counts

221 → 28

Compiler

Compiled 7298 to 2957 computations (59.5% saved)

localize21.0ms (0.1%)

Local error

Found 4 expressions with local error:

3.2b	(.f64 (.f64 (cbrt.f64 n) (cbrt.f64 n)) (*.f64 (/.f64 l Om) (cbrt.f64 n)))
5.7b	(.f64 (.f64 (.f64 (cbrt.f64 n) (cbrt.f64 n)) (.f64 (/.f64 l Om) (cbrt.f64 n))) (-.f64 U* U))
11.6b	(.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (.f64 (.f64 (cbrt.f64 n) (cbrt.f64 n)) (.f64 (/.f64 l Om) (cbrt.f64 n))) (-.f64 U U))))))
18.6b	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (.f64 (.f64 (cbrt.f64 n) (cbrt.f64 n)) (.f64 (/.f64 l Om) (cbrt.f64 n))) (-.f64 U U)))))))

rewrite64.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

63×	`add-exp-log_binary64_457`
53×	`pow1_binary64_480`
43×	`add-cbrt-cube_binary64_455`
39×	`prod-exp_binary64_468` `cbrt-unprod_binary64_452`
33×	`pow-prod-down_binary64_490`
10×	`-un-lft-identity_binary64_419` `add-sqr-sqrt_binary64_441` `associate-r/_binary64_361`
9×	`associate-r_binary64_359`
8×	`add-cube-cbrt_binary64_454`
6×	`cancel-sign-sub-inv_binary64_385`
5×	`associate-*l/_binary64_362` `distribute-rgt-in_binary64_369` `distribute-lft-in_binary64_368`
4×	`add-log-exp_binary64_458` `sqrt-pow1_binary64_437` `div-exp_binary64_470` `cbrt-undiv_binary64_453`
3×	`-commutative_binary64_350` `associate-l*_binary64_360`
2×	`flip3-+_binary64_422` `sqrt-div_binary64_436` `sub-neg_binary64_412` `frac-times_binary64_429` `flip3--_binary64_423` `flip-+_binary64_393` `flip--_binary64_394`
1×	`difference-of-squares_binary64_388` `pow1/2_binary64_499` `distribute-lft-out--_binary64_371` `sqrt-prod_binary64_435`

Counts

4 → 113

Calls

4 calls:

18.0ms	(.f64 (.f64 (.f64 (cbrt.f64 n) (cbrt.f64 n)) (.f64 (/.f64 l Om) (cbrt.f64 n))) (-.f64 U* U))
14.0ms	(.f64 (.f64 (cbrt.f64 n) (cbrt.f64 n)) (*.f64 (/.f64 l Om) (cbrt.f64 n)))
9.0ms	(.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (.f64 (.f64 (cbrt.f64 n) (cbrt.f64 n)) (.f64 (/.f64 l Om) (cbrt.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 (.f64 (cbrt.f64 n) (cbrt.f64 n)) (.f64 (/.f64 l Om) (cbrt.f64 n))) (-.f64 U U)))))))

series3.3s (12.9%)

Counts

4 → 88

Calls

4 calls:

1.9s	(.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (.f64 (.f64 (cbrt.f64 n) (cbrt.f64 n)) (.f64 (/.f64 l Om) (cbrt.f64 n))) (-.f64 U U))))))
1.1s	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (.f64 (.f64 (cbrt.f64 n) (cbrt.f64 n)) (.f64 (/.f64 l Om) (cbrt.f64 n))) (-.f64 U U)))))))
281.0ms	(.f64 (.f64 (.f64 (cbrt.f64 n) (cbrt.f64 n)) (.f64 (/.f64 l Om) (cbrt.f64 n))) (-.f64 U* U))
123.0ms	(.f64 (.f64 (cbrt.f64 n) (cbrt.f64 n)) (*.f64 (/.f64 l Om) (cbrt.f64 n)))

Compiler

Compiled 6720 to 5526 computations (17.8% saved)

simplify110.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

201 → 201

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4975	7119
1	4975	7119

prune266.0ms (1%)

Pruning

28 alts after pruning (26 fresh and 2 done)

	Pruned	Kept	Total
New	201	0	201
Fresh	0	26	26
Picked	0	1	1
Done	0	1	1
Total	201	28	229

Merged error: 18.7b

Counts

229 → 28

Compiler

Compiled 8217 to 2978 computations (63.8% saved)

localize16.0ms (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 l Om) (.f64 n (-.f64 U U)))))))
5.4b	(.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U U))))))))
10.2b	(.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))
18.6b	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U U)))))))))

rewrite49.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`pow1_binary64_480`
30×	`add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
21×	`distribute-rgt-in_binary64_369` `distribute-lft-in_binary64_368`
20×	`pow-prod-down_binary64_490`
19×	`add-sqr-sqrt_binary64_441`
17×	`-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454` `associate-l*_binary64_360`
16×	`associate-*r/_binary64_361`
15×	`prod-exp_binary64_468` `cbrt-unprod_binary64_452`
12×	`cancel-sign-sub-inv_binary64_385`
9×	`times-frac_binary64_425`
5×	`associate-r_binary64_359` `sqrt-pow1_binary64_437`
4×	`sub-neg_binary64_412` `add-log-exp_binary64_458`
3×	`flip3-+_binary64_422` `*-commutative_binary64_350` `flip-+_binary64_393`
2×	`sqrt-div_binary64_436` `frac-times_binary64_429` `flip3--_binary64_423` `flip--_binary64_394` `div-exp_binary64_470` `cbrt-undiv_binary64_453`
1×	`associate-*l/_binary64_362` `pow1/2_binary64_499` `div-inv_binary64_416` `unswap-sqr_binary64_387` `sqrt-prod_binary64_435`

Counts

4 → 119

Calls

4 calls:

14.0ms	(.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))
9.0ms	(.f64 (.f64 2 n) (.f64 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 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U U)))))))))
5.0ms	(.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U U)))))))

series4.4s (16.8%)

Counts

4 → 117

Calls

4 calls:

1.7s	(.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U U))))))))
1.4s	(.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U U)))))))
981.0ms	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U U)))))))))
266.0ms	(.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))

Compiler

Compiled 8162 to 6725 computations (17.6% saved)

simplify83.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

236 → 236

Iterations

Useful iterations: 0 (21.0ms)

Iter	Nodes	Cost
0	5107	8200

prune284.0ms (1.1%)

Pruning

31 alts after pruning (29 fresh and 2 done)

	Pruned	Kept	Total
New	226	10	236
Fresh	6	19	25
Picked	1	0	1
Done	0	2	2
Total	233	31	264

Merged error: 15.6b

Counts

264 → 31

Compiler

Compiled 7900 to 2718 computations (65.6% saved)

regimes2.2s (8.5%)

Compiler: Compiled 25458 to 17010 computations (33.2% saved)

bsearch7.0ms (0%)

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

simplify37.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	1045	415
1	1045	415

end0.0ms (0%)

sample4.6s (17.8%)

Algorithm

1×

intervals

Results

1.1s	12495×	body	128	nan
736.0ms	8000×	body	128	valid
115.0ms	1173×	body	128	invalid

Compiler

Compiled 3471 to 2271 computations (34.6% saved)

Details

analyze2.4s (9.3%)

sample93.0ms (0.4%)

simplify141.0ms (0.5%)

prune5.0ms (0%)

localize17.0ms (0.1%)

rewrite52.0ms (0.2%)

series3.8s (14.5%)

simplify100.0ms (0.4%)

prune354.0ms (1.4%)

localize19.0ms (0.1%)

rewrite45.0ms (0.2%)

series3.1s (12.1%)

simplify70.0ms (0.3%)

prune264.0ms (1%)

localize21.0ms (0.1%)

rewrite64.0ms (0.2%)

series3.3s (12.9%)

simplify110.0ms (0.4%)

prune266.0ms (1%)

localize16.0ms (0.1%)

rewrite49.0ms (0.2%)

series4.4s (16.8%)

simplify83.0ms (0.3%)

prune284.0ms (1.1%)

regimes2.2s (8.5%)

bsearch7.0ms (0%)

simplify37.0ms (0.1%)

end0.0ms (0%)

sample4.6s (17.8%)

Profiling