Details

analyze2.6s (8.1%)

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)

sample109.0ms (0.3%)

Algorithm

1×

intervals

Results

39.0ms	420×	body	128	nan
24.0ms	256×	body	128	valid
7.0ms	36×	body	128	invalid

Compiler

Compiled 57 to 53 computations (7% saved)

simplify51.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (45.0ms)

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

30.6b

Counts

2 → 2

Compiler

Compiled 80 to 63 computations (21.3% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

1.8b	(.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)))))))
11.4b	(.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))
19.9b	(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))))))))

rewrite259.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Error

23.0b

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)

series4.4s (13.9%)

Error

21.2b

Counts

4 → 114

Calls

4 calls:

1.9s	(.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)))))))
1.2s	(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))))))))
822.0ms	(.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))))
314.0ms	(.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))

Compiler

Compiled 11997 to 9021 computations (24.8% saved)

simplify126.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

245 → 245

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4959	8056
1	4959	8056

prune323.0ms (1%)

Pruning

17 alts after pruning (16 fresh and 1 done)

	Pruned	Kept	Total
New	229	16	245
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	230	17	247

Error

18.3b

Counts

247 → 17

Compiler

Compiled 8677 to 3190 computations (63.2% saved)

localize22.0ms (0.1%)

Local error

Found 4 expressions with local error:

4.6b	(.f64 n (/.f64 (.f64 l (-.f64 U* U)) Om))
4.6b	(.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (/.f64 (.f64 l (-.f64 U* U)) Om)) (*.f64 l -2))))))
6.0b	(/.f64 (.f64 l (-.f64 U U)) Om)
19.9b	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (/.f64 (.f64 l (-.f64 U* U)) Om)) (*.f64 l -2)))))))

rewrite168.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Error

13.5b

Rules

31×	`pow1_binary64_480`
30×	`add-exp-log_binary64_457` `add-cbrt-cube_binary64_455`
17×	`pow-prod-down_binary64_490`
13×	`prod-exp_binary64_468` `cbrt-unprod_binary64_452`
11×	`add-sqr-sqrt_binary64_441` `associate-*r/_binary64_361`
9×	`add-cube-cbrt_binary64_454` `*-un-lft-identity_binary64_419`
8×	`associate-r_binary64_359`
6×	`times-frac_binary64_425`
5×	`sqrt-pow1_binary64_437`
4×	`add-log-exp_binary64_458` `div-exp_binary64_470` `cbrt-undiv_binary64_453` `distribute-rgt-in_binary64_369` `distribute-lft-in_binary64_368` `associate-l_binary64_360`
3×	`associate-/r*_binary64_363`
2×	`flip3-+_binary64_422` `sqrt-div_binary64_436` `flip-+_binary64_393` `div-inv_binary64_416` `associate-/l/_binary64_366` `*-commutative_binary64_350`
1×	`pow1/2_binary64_499` `sqrt-prod_binary64_435` `frac-2neg_binary64_430` `clear-num_binary64_418` `flip3--_binary64_423` `flip--_binary64_394` `associate-/l*_binary64_364` `unswap-sqr_binary64_387`

Counts

4 → 94

Calls

4 calls:

10.0ms	(.f64 n (/.f64 (.f64 l (-.f64 U* U)) Om))
9.0ms	(.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (/.f64 (.f64 l (-.f64 U* U)) Om)) (*.f64 l -2))))))
8.0ms	(/.f64 (.f64 l (-.f64 U U)) Om)
7.0ms	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (/.f64 (.f64 l (-.f64 U* U)) Om)) (*.f64 l -2)))))))

Compiler

Compiled 3589 to 1455 computations (59.5% saved)

series3.8s (12%)

Error

17.2b

Counts

4 → 105

Calls

4 calls:

2.0s	(.f64 (.f64 2 n) (.f64 U (+.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 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (/.f64 (.f64 l (-.f64 U* U)) Om)) (*.f64 l -2)))))))
312.0ms	(.f64 n (/.f64 (.f64 l (-.f64 U* U)) Om))
206.0ms	(/.f64 (.f64 l (-.f64 U U)) Om)

Compiler

Compiled 11101 to 8204 computations (26.1% saved)

simplify92.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

199 → 199

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	4983	6295
1	4983	6295

prune253.0ms (0.8%)

Pruning

22 alts after pruning (21 fresh and 1 done)

	Pruned	Kept	Total
New	192	7	199
Fresh	1	14	15
Picked	1	0	1
Done	0	1	1
Total	194	22	216

Error

13.5b

Counts

216 → 22

Compiler

Compiled 7222 to 2793 computations (61.3% saved)

localize27.0ms (0.1%)

Local error

Found 4 expressions with local error:

6.0b	(/.f64 (.f64 l (-.f64 U U)) Om)
19.9b	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (/.f64 (.f64 l (-.f64 U* U)) Om)) (*.f64 l -2)))))))
19.9b	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (/.f64 (.f64 l (-.f64 U* U)) Om)) (*.f64 l -2)))))))
19.9b	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (/.f64 (.f64 l (-.f64 U* U)) Om)) (*.f64 l -2)))))))

rewrite264.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Error

13.5b

Rules

43×	`pow1_binary64_480`
24×	`pow-prod-down_binary64_490`
15×	`sqrt-pow1_binary64_437`
14×	`associate-*r/_binary64_361`
9×	`add-exp-log_binary64_457` `add-cbrt-cube_binary64_455`
6×	`add-cube-cbrt_binary64_454` `add-sqr-sqrt_binary64_441` `sqrt-div_binary64_436` `*-un-lft-identity_binary64_419`
4×	`add-log-exp_binary64_458`
3×	`pow1/2_binary64_499` `flip3-+_binary64_422` `flip-+_binary64_393` `sqrt-prod_binary64_435` `times-frac_binary64_425` `associate-/r*_binary64_363`
2×	`div-exp_binary64_470` `cbrt-undiv_binary64_453` `associate-/l/_binary64_366`
1×	`prod-exp_binary64_468` `cbrt-unprod_binary64_452` `frac-2neg_binary64_430` `clear-num_binary64_418` `div-inv_binary64_416` `flip3--_binary64_423` `flip--_binary64_394` `associate-/l*_binary64_364`

Counts

4 → 71

Calls

4 calls:

9.0ms	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (/.f64 (.f64 l (-.f64 U* U)) Om)) (*.f64 l -2)))))))
8.0ms	(/.f64 (.f64 l (-.f64 U U)) Om)
7.0ms	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (+.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 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (/.f64 (.f64 l (-.f64 U* U)) Om)) (*.f64 l -2)))))))

Compiler

Compiled 6860 to 2967 computations (56.7% saved)

series4.9s (15.3%)

Error

13.5b

Counts

4 → 102

Calls

4 calls:

1.5s	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (+.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 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (/.f64 (.f64 l (-.f64 U* U)) Om)) (*.f64 l -2)))))))
1.3s	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (/.f64 (.f64 l (-.f64 U* U)) Om)) (*.f64 l -2)))))))
250.0ms	(/.f64 (.f64 l (-.f64 U U)) Om)

Compiler

Compiled 30231 to 18688 computations (38.2% saved)

simplify86.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

173 → 173

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5327	6279

prune619.0ms (2%)

Pruning

22 alts after pruning (20 fresh and 2 done)

	Pruned	Kept	Total
New	173	0	173
Fresh	0	20	20
Picked	0	1	1
Done	0	1	1
Total	173	22	195

Error

13.5b

Counts

195 → 22

Compiler

Compiled 16158 to 7048 computations (56.4% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

4.6b	(.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (/.f64 (.f64 l (.f64 n U)) Om) (.f64 l -2))))))
6.2b	(.f64 l (.f64 n U*))
6.7b	(/.f64 (.f64 l (.f64 n U*)) Om)
19.9b	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (/.f64 (.f64 l (.f64 n U)) Om) (.f64 l -2)))))))

rewrite148.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Error

13.3b

Rules

34×	`pow1_binary64_480`
30×	`add-exp-log_binary64_457` `add-cbrt-cube_binary64_455`
19×	`pow-prod-down_binary64_490`
14×	`prod-exp_binary64_468` `cbrt-unprod_binary64_452`
8×	`associate-*r/_binary64_361`
7×	`add-cube-cbrt_binary64_454` `add-sqr-sqrt_binary64_441` `*-un-lft-identity_binary64_419`
5×	`sqrt-pow1_binary64_437`
4×	`add-log-exp_binary64_458` `associate-l_binary64_360` `distribute-rgt-in_binary64_369` `distribute-lft-in_binary64_368`
3×	`div-exp_binary64_470` `cbrt-undiv_binary64_453` `times-frac_binary64_425` `associate-/r*_binary64_363`
2×	`flip3-+_binary64_422` `sqrt-div_binary64_436` `flip-+_binary64_393` `associate-r_binary64_359` `*-commutative_binary64_350`
1×	`pow1/2_binary64_499` `sqrt-prod_binary64_435` `frac-2neg_binary64_430` `clear-num_binary64_418` `div-inv_binary64_416` `associate-/l*_binary64_364`

Counts

4 → 85

Calls

4 calls:

9.0ms	(.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (/.f64 (.f64 l (.f64 n U)) Om) (.f64 l -2))))))
7.0ms	(.f64 l (.f64 n U*))
7.0ms	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (/.f64 (.f64 l (.f64 n U)) Om) (.f64 l -2)))))))
6.0ms	(/.f64 (.f64 l (.f64 n U*)) Om)

Compiler

Compiled 3007 to 1324 computations (56% saved)

series2.6s (8%)

Error

11.0b

Counts

4 → 85

Calls

4 calls:

1.3s	(.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (/.f64 (.f64 l (.f64 n U)) Om) (.f64 l -2))))))
883.0ms	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (/.f64 (.f64 l (.f64 n U)) Om) (.f64 l -2)))))))
186.0ms	(/.f64 (.f64 l (.f64 n U*)) Om)
91.0ms	(.f64 l (.f64 n U*))

Compiler

Compiled 7508 to 5722 computations (23.8% saved)

simplify103.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

170 → 170

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	4967	4708
1	4967	4708

prune184.0ms (0.6%)

Pruning

23 alts after pruning (20 fresh and 3 done)

	Pruned	Kept	Total
New	164	6	170
Fresh	5	14	19
Picked	0	1	1
Done	0	2	2
Total	169	23	192

Error

10.8b

Counts

192 → 23

Compiler

Compiled 4804 to 1956 computations (59.3% saved)

regimes3.8s (11.9%)

Accuracy

Total 18.7b remaining (68.5%)

Threshold costs 0b (0%)

Compiler

Compiled 45706 to 33106 computations (27.6% saved)

bsearch13.0ms (0%)

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

simplify35.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	1029	211
1	1029	211

end0.0ms (0%)

sample6.8s (21.5%)

Algorithm

1×

intervals

Results

1.2s	12855×	body	128	nan
787.0ms	8000×	body	128	valid
115.0ms	1224×	body	128	invalid

Compiler

Compiled 5867 to 4228 computations (27.9% saved)

Details

analyze2.6s (8.1%)

sample109.0ms (0.3%)

simplify51.0ms (0.2%)

prune5.0ms (0%)

localize17.0ms (0.1%)

rewrite259.0ms (0.8%)

series4.4s (13.9%)

simplify126.0ms (0.4%)

prune323.0ms (1%)

localize22.0ms (0.1%)

rewrite168.0ms (0.5%)

series3.8s (12%)

simplify92.0ms (0.3%)

prune253.0ms (0.8%)

localize27.0ms (0.1%)

rewrite264.0ms (0.8%)

series4.9s (15.3%)

simplify86.0ms (0.3%)

prune619.0ms (2%)

localize18.0ms (0.1%)

rewrite148.0ms (0.5%)

series2.6s (8%)

simplify103.0ms (0.3%)

prune184.0ms (0.6%)

regimes3.8s (11.9%)

bsearch13.0ms (0%)

simplify35.0ms (0.1%)

end0.0ms (0%)

sample6.8s (21.5%)

Profiling