Details

analyze2.4s (7.3%)

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)

sample100.0ms (0.3%)

Algorithm

1×

intervals

Results

37.0ms	357×	body	128	nan
24.0ms	256×	body	128	valid
4.0ms	36×	body	128	invalid

Compiler

Compiled 57 to 53 computations (7% saved)

simplify148.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5178	39

prune6.0ms (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

28.1b

Counts

2 → 2

Compiler

Compiled 80 to 63 computations (21.3% saved)

localize18.0ms (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)))))
8.4b	(.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)))))))
11.3b	(.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))
18.2b	(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))))))))

rewrite260.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Error

21.0b

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)

series5.0s (15.5%)

Error

16.7b

Counts

4 → 119

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)))))))
1.7s	(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))))))))
818.0ms	(.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))))
309.0ms	(.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))

Compiler

Compiled 14085 to 10577 computations (24.9% saved)

simplify131.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

250 → 250

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	5045	9428

prune363.0ms (1.1%)

Pruning

24 alts after pruning (23 fresh and 1 done)

	Pruned	Kept	Total
New	228	22	250
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	228	24	252

Error

12.2b

Counts

252 → 24

Compiler

Compiled 9854 to 3665 computations (62.8% saved)

localize22.0ms (0.1%)

Local error

Found 4 expressions with local error:

12.8b	(cbrt.f64 (/.f64 l Om))
12.8b	(cbrt.f64 (/.f64 l Om))
12.8b	(cbrt.f64 (/.f64 l Om))
18.2b	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (.f64 (cbrt.f64 (/.f64 l Om)) (cbrt.f64 (/.f64 l Om))) (.f64 (+.f64 (.f64 (.f64 n (-.f64 U* U)) (/.f64 l Om)) (*.f64 l -2)) (cbrt.f64 (/.f64 l Om)))))))

rewrite130.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Error

12.2b

Rules

39×	`cbrt-prod_binary64_450`
27×	`times-frac_binary64_425`
25×	`add-cube-cbrt_binary64_454` `add-sqr-sqrt_binary64_441` `*-un-lft-identity_binary64_419`
14×	`pow1_binary64_480`
6×	`pow-prod-down_binary64_490`
4×	`add-log-exp_binary64_458` `add-exp-log_binary64_457` `add-cbrt-cube_binary64_455` `sqrt-pow1_binary64_437`
3×	`pow1/3_binary64_501` `cbrt-div_binary64_451` `div-inv_binary64_416`
2×	`associate-*r/_binary64_361` `sqrt-div_binary64_436`
1×	`pow1/2_binary64_499` `flip3-+_binary64_422` `flip-+_binary64_393` `sqrt-prod_binary64_435`

Counts

4 → 81

Calls

4 calls:

7.0ms	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (.f64 (cbrt.f64 (/.f64 l Om)) (cbrt.f64 (/.f64 l Om))) (.f64 (+.f64 (.f64 (.f64 n (-.f64 U* U)) (/.f64 l Om)) (*.f64 l -2)) (cbrt.f64 (/.f64 l Om)))))))
5.0ms	(cbrt.f64 (/.f64 l Om))
2.0ms	(cbrt.f64 (/.f64 l Om))
2.0ms	(cbrt.f64 (/.f64 l Om))

Compiler

Compiled 3835 to 1225 computations (68.1% saved)

series2.8s (8.6%)

Error

12.2b

Counts

4 → 50

Calls

4 calls:

2.1s	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (.f64 (cbrt.f64 (/.f64 l Om)) (cbrt.f64 (/.f64 l Om))) (.f64 (+.f64 (.f64 (.f64 n (-.f64 U* U)) (/.f64 l Om)) (*.f64 l -2)) (cbrt.f64 (/.f64 l Om)))))))
214.0ms	(cbrt.f64 (/.f64 l Om))
193.0ms	(cbrt.f64 (/.f64 l Om))
189.0ms	(cbrt.f64 (/.f64 l Om))

Compiler

Compiled 8978 to 6597 computations (26.5% saved)

simplify74.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5106	4365

prune215.0ms (0.7%)

Pruning

24 alts after pruning (22 fresh and 2 done)

	Pruned	Kept	Total
New	131	0	131
Fresh	0	22	22
Picked	0	1	1
Done	0	1	1
Total	131	24	155

Error

12.2b

Counts

155 → 24

Compiler

Compiled 6712 to 2555 computations (61.9% saved)

localize24.0ms (0.1%)

Local error

Found 4 expressions with local error:

11.3b	(.f64 (.f64 n (-.f64 U* U)) (/.f64 l Om))
11.3b	(.f64 (.f64 n (-.f64 U* U)) (/.f64 l Om))
18.2b	(sqrt.f64 (.f64 (.f64 U (.f64 2 n)) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 (.f64 n (-.f64 U* U)) (/.f64 l Om)) (*.f64 l -2))))))
18.2b	(sqrt.f64 (.f64 (.f64 U (.f64 2 n)) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 (.f64 n (-.f64 U* U)) (/.f64 l Om)) (*.f64 l -2))))))

rewrite280.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Error

12.2b

Rules

34×	`pow1_binary64_480`
28×	`add-exp-log_binary64_457` `add-cbrt-cube_binary64_455`
26×	`associate-r_binary64_359`
18×	`add-cube-cbrt_binary64_454` `add-sqr-sqrt_binary64_441` `pow-prod-down_binary64_490` `*-un-lft-identity_binary64_419` `times-frac_binary64_425`
14×	`associate-*r/_binary64_361`
12×	`prod-exp_binary64_468` `cbrt-unprod_binary64_452`
8×	`sqrt-pow1_binary64_437`
4×	`add-log-exp_binary64_458` `sqrt-div_binary64_436` `div-exp_binary64_470` `cbrt-undiv_binary64_453` `flip3--_binary64_423` `frac-times_binary64_429` `flip--_binary64_394` `associate-*l/_binary64_362`
2×	`pow1/2_binary64_499` `flip3-+_binary64_422` `flip-+_binary64_393` `sqrt-prod_binary64_435` `associate-l_binary64_360` `div-inv_binary64_416` `*-commutative_binary64_350`

Counts

4 → 104

Calls

4 calls:

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

Compiler

Compiled 6888 to 2840 computations (58.8% saved)

series4.2s (12.9%)

Error

12.2b

Counts

4 → 104

Calls

4 calls:

1.6s	(sqrt.f64 (.f64 (.f64 U (.f64 2 n)) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 (.f64 n (-.f64 U* U)) (/.f64 l Om)) (*.f64 l -2))))))
1.6s	(sqrt.f64 (.f64 (.f64 U (.f64 2 n)) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 (.f64 n (-.f64 U* U)) (/.f64 l Om)) (*.f64 l -2))))))
341.0ms	(.f64 (.f64 n (-.f64 U* U)) (/.f64 l Om))
339.0ms	(.f64 (.f64 n (-.f64 U* U)) (/.f64 l Om))

Compiler

Compiled 22366 to 14684 computations (34.3% saved)

simplify93.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

208 → 208

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5048	7408

prune523.0ms (1.6%)

Pruning

24 alts after pruning (21 fresh and 3 done)

	Pruned	Kept	Total
New	208	0	208
Fresh	0	21	21
Picked	0	1	1
Done	0	2	2
Total	208	24	232

Error

12.2b

Counts

232 → 24

Compiler

Compiled 14242 to 6092 computations (57.2% saved)

localize28.0ms (0.1%)

Local error

Found 4 expressions with local error:

11.3b	(.f64 (.f64 n (-.f64 U* U)) (/.f64 l Om))
18.2b	(sqrt.f64 (.f64 (.f64 U (.f64 2 n)) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 (.f64 n (-.f64 U* U)) (/.f64 l Om)) (*.f64 l -2))))))
18.2b	(sqrt.f64 (.f64 (.f64 U (.f64 2 n)) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 (.f64 n (-.f64 U* U)) (/.f64 l Om)) (*.f64 l -2))))))
18.2b	(sqrt.f64 (.f64 (.f64 U (.f64 2 n)) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 (.f64 n (-.f64 U* U)) (/.f64 l Om)) (*.f64 l -2))))))

rewrite297.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Error

12.2b

Rules

39×	`pow1_binary64_480`
21×	`pow-prod-down_binary64_490`
16×	`add-exp-log_binary64_457` `add-cbrt-cube_binary64_455`
13×	`associate-r_binary64_359`
12×	`sqrt-pow1_binary64_437`
11×	`add-cube-cbrt_binary64_454` `add-sqr-sqrt_binary64_441` `associate-r/_binary64_361` `-un-lft-identity_binary64_419`
9×	`times-frac_binary64_425`
6×	`sqrt-div_binary64_436` `prod-exp_binary64_468` `cbrt-unprod_binary64_452`
4×	`add-log-exp_binary64_458`
3×	`pow1/2_binary64_499` `flip3-+_binary64_422` `flip-+_binary64_393` `sqrt-prod_binary64_435`
2×	`div-exp_binary64_470` `cbrt-undiv_binary64_453` `flip3--_binary64_423` `frac-times_binary64_429` `flip--_binary64_394` `associate-*l/_binary64_362`
1×	`associate-l_binary64_360` `div-inv_binary64_416` `*-commutative_binary64_350`

Counts

4 → 82

Calls

4 calls:

11.0ms	(.f64 (.f64 n (-.f64 U* U)) (/.f64 l Om))
7.0ms	(sqrt.f64 (.f64 (.f64 U (.f64 2 n)) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 (.f64 n (-.f64 U* U)) (/.f64 l Om)) (*.f64 l -2))))))
7.0ms	(sqrt.f64 (.f64 (.f64 U (.f64 2 n)) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 (.f64 n (-.f64 U* U)) (/.f64 l Om)) (*.f64 l -2))))))
7.0ms	(sqrt.f64 (.f64 (.f64 U (.f64 2 n)) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 (.f64 n (-.f64 U* U)) (/.f64 l Om)) (*.f64 l -2))))))

Compiler

Compiled 7928 to 3384 computations (57.3% saved)

series6.0s (18.4%)

Error

12.2b

Counts

4 → 114

Calls

4 calls:

1.6s	(sqrt.f64 (.f64 (.f64 U (.f64 2 n)) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 (.f64 n (-.f64 U* U)) (/.f64 l Om)) (*.f64 l -2))))))
1.6s	(sqrt.f64 (.f64 (.f64 U (.f64 2 n)) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 (.f64 n (-.f64 U* U)) (/.f64 l Om)) (*.f64 l -2))))))
1.6s	(sqrt.f64 (.f64 (.f64 U (.f64 2 n)) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 (.f64 n (-.f64 U* U)) (/.f64 l Om)) (*.f64 l -2))))))
380.0ms	(.f64 (.f64 n (-.f64 U* U)) (/.f64 l Om))

Compiler

Compiled 35319 to 21841 computations (38.2% saved)

simplify105.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

196 → 196

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5048	9392

prune773.0ms (2.4%)

Pruning

24 alts after pruning (21 fresh and 3 done)

	Pruned	Kept	Total
New	195	1	196
Fresh	0	20	20
Picked	1	0	1
Done	0	3	3
Total	196	24	220

Error

12.2b

Counts

220 → 24

Compiler

Compiled 19040 to 7959 computations (58.2% saved)

regimes2.5s (7.6%)

Accuracy

Total 13.6b remaining (49.5%)

Threshold costs 0b (0%)

Compiler

Compiled 33754 to 23338 computations (30.9% saved)

bsearch313.0ms (1%)

Steps

Iters	Range		Point
7	4.712528720384536e+155	1.0443306763622066e+157	3.2263965288855882e+156
6	2.7178116704040336e-73	3.2765922934867646e-72	2.7567949355391264e-73
8	4.4346495556236637e-100	1.2471870448438338e-96	1.1846863934485895e-96
9	-1.6921938273643864e+158	-3.115636498472264e+149	-3.1970951713919756e+152

Compiler

Compiled 1 to 6 computations (-500% saved)

simplify6.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	192	239
1	192	239

end0.0ms (0%)

sample5.7s (17.6%)

Algorithm

1×

intervals

Results

1.2s	12640×	body	128	nan
768.0ms	8000×	body	128	valid
107.0ms	1146×	body	128	invalid

Compiler

Compiled 4391 to 3022 computations (31.2% saved)

Details

analyze2.4s (7.3%)

sample100.0ms (0.3%)

simplify148.0ms (0.5%)

prune6.0ms (0%)

localize18.0ms (0.1%)

rewrite260.0ms (0.8%)

series5.0s (15.5%)

simplify131.0ms (0.4%)

prune363.0ms (1.1%)

localize22.0ms (0.1%)

rewrite130.0ms (0.4%)

series2.8s (8.6%)

simplify74.0ms (0.2%)

prune215.0ms (0.7%)

localize24.0ms (0.1%)

rewrite280.0ms (0.9%)

series4.2s (12.9%)

simplify93.0ms (0.3%)

prune523.0ms (1.6%)

localize28.0ms (0.1%)

rewrite297.0ms (0.9%)

series6.0s (18.4%)

simplify105.0ms (0.3%)

prune773.0ms (2.4%)

regimes2.5s (7.6%)

bsearch313.0ms (1%)

simplify6.0ms (0%)

end0.0ms (0%)

sample5.7s (17.6%)

Profiling