Details

analyze2.4s (7.6%)

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)

sample118.0ms (0.4%)

Algorithm

1×

intervals

Results

45.0ms	489×	body	128	nan
24.0ms	256×	body	128	valid
4.0ms	38×	body	128	invalid

Compiler

Compiled 57 to 53 computations (7% saved)

simplify53.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5178	39

prune8.0ms (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

33.2b

Counts

2 → 2

Compiler

Compiled 80 to 63 computations (21.3% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

1.2b	(.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))))
10.0b	(.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)))))))
12.3b	(.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))
21.9b	(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))))))))

rewrite268.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Error

26.6b

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)

series4.3s (13.5%)

Error

21.1b

Counts

4 → 111

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)))))))
1.1s	(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))))))))
831.0ms	(.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))))
330.0ms	(.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))

Compiler

Compiled 11603 to 8738 computations (24.7% saved)

simplify127.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

242 → 242

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4973	7841
1	4973	7841

prune351.0ms (1.1%)

Pruning

17 alts after pruning (16 fresh and 1 done)

	Pruned	Kept	Total
New	226	16	242
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	227	17	244

Error

16.6b

Counts

244 → 17

Compiler

Compiled 8518 to 3165 computations (62.8% saved)

localize24.0ms (0.1%)

Local error

Found 4 expressions with local error:

14.6b	(cbrt.f64 (/.f64 l Om))
14.6b	(cbrt.f64 (/.f64 l Om))
14.6b	(cbrt.f64 (/.f64 l Om))
21.9b	(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 n (/.f64 (.f64 l (-.f64 U* U)) Om)) (*.f64 l -2)) (cbrt.f64 (/.f64 l Om)))))))

rewrite134.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Error

16.6b

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 n (/.f64 (.f64 l (-.f64 U* U)) Om)) (*.f64 l -2)) (cbrt.f64 (/.f64 l Om)))))))
2.0ms	(cbrt.f64 (/.f64 l Om))
2.0ms	(cbrt.f64 (/.f64 l Om))
2.0ms	(cbrt.f64 (/.f64 l Om))

Compiler

Compiled 3835 to 1226 computations (68% saved)

series2.0s (6.4%)

Error

16.6b

Counts

4 → 44

Calls

4 calls:

1.4s	(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 n (/.f64 (.f64 l (-.f64 U* U)) Om)) (*.f64 l -2)) (cbrt.f64 (/.f64 l Om)))))))
209.0ms	(cbrt.f64 (/.f64 l Om))
199.0ms	(cbrt.f64 (/.f64 l Om))
195.0ms	(cbrt.f64 (/.f64 l Om))

Compiler

Compiled 6574 to 4808 computations (26.9% saved)

simplify75.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4967	2929
1	4967	2929

prune183.0ms (0.6%)

Pruning

19 alts after pruning (17 fresh and 2 done)

	Pruned	Kept	Total
New	121	4	125
Fresh	2	13	15
Picked	0	1	1
Done	0	1	1
Total	123	19	142

Error

14.9b

Counts

142 → 19

Compiler

Compiled 5562 to 2143 computations (61.5% saved)

localize30.0ms (0.1%)

Local error

Found 4 expressions with local error:

10.0b	(.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)))))
21.9b	(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))))))
21.9b	(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))))))
21.9b	(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))))))

rewrite260.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Error

14.9b

Rules

43×	`pow1_binary64_480`
24×	`pow-prod-down_binary64_490`
13×	`add-exp-log_binary64_457` `add-cbrt-cube_binary64_455`
12×	`sqrt-pow1_binary64_437`
8×	`associate-*r/_binary64_361`
6×	`sqrt-div_binary64_436` `prod-exp_binary64_468` `cbrt-unprod_binary64_452`
5×	`add-cube-cbrt_binary64_454` `add-sqr-sqrt_binary64_441` `*-un-lft-identity_binary64_419`
4×	`add-log-exp_binary64_458` `flip3-+_binary64_422` `flip-+_binary64_393`
3×	`pow1/2_binary64_499` `sqrt-prod_binary64_435` `associate-r_binary64_359`
1×	`distribute-rgt-in_binary64_369` `distribute-lft-in_binary64_368` `associate-l_binary64_360` `*-commutative_binary64_350`

Counts

4 → 70

Calls

4 calls:

10.0ms	(.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))))))
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 7121 to 3020 computations (57.6% saved)

series6.2s (19.6%)

Error

14.9b

Counts

4 → 118

Calls

4 calls:

1.9s	(.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)))))
1.3s	(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))))))
1.3s	(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))))))
1.3s	(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 34289 to 21493 computations (37.3% saved)

simplify140.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

188 → 188

Iterations

Useful iterations: 0 (70.0ms)

Iter	Nodes	Cost
0	4991	9086
1	4991	9086

prune748.0ms (2.4%)

Pruning

19 alts after pruning (16 fresh and 3 done)

	Pruned	Kept	Total
New	188	0	188
Fresh	0	16	16
Picked	0	1	1
Done	0	2	2
Total	188	19	207

Error

14.9b

Counts

207 → 19

Compiler

Compiled 18050 to 7372 computations (59.2% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

6.6b	(.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))))))
6.8b	(.f64 n (/.f64 (.f64 l (-.f64 U* U)) Om))
7.2b	(.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (/.f64 (.f64 l (-.f64 U* U)) Om)) (*.f64 l -2)))))
21.9b	(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)))))))

rewrite167.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Error

12.0b

Rules

33×	`pow1_binary64_480`
27×	`add-exp-log_binary64_457` `add-cbrt-cube_binary64_455`
18×	`pow-prod-down_binary64_490`
13×	`add-sqr-sqrt_binary64_441` `prod-exp_binary64_468` `cbrt-unprod_binary64_452`
11×	`associate-r/_binary64_361` `associate-r*_binary64_359`
9×	`add-cube-cbrt_binary64_454` `*-un-lft-identity_binary64_419`
7×	`associate-l_binary64_360`
5×	`sqrt-pow1_binary64_437` `distribute-rgt-in_binary64_369` `distribute-lft-in_binary64_368`
4×	`add-log-exp_binary64_458`
3×	`flip3-+_binary64_422` `flip-+_binary64_393` `*-commutative_binary64_350` `times-frac_binary64_425`
2×	`sqrt-div_binary64_436` `unswap-sqr_binary64_387` `div-exp_binary64_470` `cbrt-undiv_binary64_453`
1×	`pow1/2_binary64_499` `sqrt-prod_binary64_435` `div-inv_binary64_416`

Counts

4 → 93

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

Compiler

Compiled 3800 to 1507 computations (60.3% saved)

series4.9s (15.4%)

Error

14.4b

Counts

4 → 119

Calls

4 calls:

1.8s	(.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	(.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (/.f64 (.f64 l (-.f64 U* U)) Om)) (*.f64 l -2)))))
1.1s	(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 n (/.f64 (.f64 l (-.f64 U* U)) Om))

Compiler

Compiled 12485 to 9489 computations (24% saved)

simplify82.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

212 → 212

Iterations

Useful iterations: 0 (21.0ms)

Iter	Nodes	Cost
0	5083	7909

prune232.0ms (0.7%)

Pruning

22 alts after pruning (19 fresh and 3 done)

	Pruned	Kept	Total
New	207	5	212
Fresh	1	14	15
Picked	1	0	1
Done	0	3	3
Total	209	22	231

Error

12.0b

Counts

231 → 22

Compiler

Compiled 7187 to 2345 computations (67.4% saved)

regimes2.7s (8.5%)

Accuracy

Total 16.8b remaining (62.5%)

Threshold costs 0b (0%)

Compiler

Compiled 34898 to 25674 computations (26.4% saved)

bsearch10.0ms (0%)

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

simplify46.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	1291	340
1	1291	340

end0.0ms (0%)

sample6.1s (19.2%)

Algorithm

1×

intervals

Results

1.2s	12769×	body	128	nan
764.0ms	8000×	body	128	valid
117.0ms	1200×	body	128	invalid

Compiler

Compiled 4601 to 3341 computations (27.4% saved)

Details

analyze2.4s (7.6%)

sample118.0ms (0.4%)

simplify53.0ms (0.2%)

prune8.0ms (0%)

localize18.0ms (0.1%)

rewrite268.0ms (0.8%)

series4.3s (13.5%)

simplify127.0ms (0.4%)

prune351.0ms (1.1%)

localize24.0ms (0.1%)

rewrite134.0ms (0.4%)

series2.0s (6.4%)

simplify75.0ms (0.2%)

prune183.0ms (0.6%)

localize30.0ms (0.1%)

rewrite260.0ms (0.8%)

series6.2s (19.6%)

simplify140.0ms (0.4%)

prune748.0ms (2.4%)

localize19.0ms (0.1%)

rewrite167.0ms (0.5%)

series4.9s (15.4%)

simplify82.0ms (0.3%)

prune232.0ms (0.7%)

regimes2.7s (8.5%)

bsearch10.0ms (0%)

simplify46.0ms (0.1%)

end0.0ms (0%)

sample6.1s (19.2%)

Profiling