Details

analyze2.5s (7.4%)

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)

sample99.0ms (0.3%)

Algorithm

1×

intervals

Results

37.0ms	391×	body	128	nan
23.0ms	256×	body	128	valid
4.0ms	41×	body	128	invalid

Compiler

Compiled 57 to 53 computations (7% saved)

simplify52.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (47.0ms)

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

32.1b

Counts

2 → 2

Compiler

Compiled 80 to 63 computations (21.3% saved)

localize17.0ms (0%)

Local error

Found 4 expressions with local error:

1.3b	(.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))))
11.7b	(.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))
12.3b	(.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)))))))
18.0b	(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))))))))

rewrite255.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Error

25.5b

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×	`*-commutative_binary64_350` `div-exp_binary64_470` `cbrt-undiv_binary64_453`
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:

15.0ms	(.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 (12.8%)

Error

18.3b

Counts

4 → 112

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)))))))
1.0s	(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))))))))
880.0ms	(.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 11564 to 8738 computations (24.4% saved)

simplify122.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

243 → 243

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4974	7813
1	4974	7813

prune330.0ms (1%)

Pruning

20 alts after pruning (20 fresh and 0 done)

	Pruned	Kept	Total
New	224	19	243
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	225	20	245

Error

16.1b

Counts

245 → 20

Compiler

Compiled 8668 to 3266 computations (62.3% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

6.4b	(.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (/.f64 (.f64 l (-.f64 U* U)) Om)) (*.f64 l -2)))))
7.9b	(.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))))))
8.2b	(.f64 n (/.f64 (.f64 l (-.f64 U* U)) Om))
18.0b	(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)))))))

rewrite173.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Error

14.1b

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` `times-frac_binary64_425` `*-commutative_binary64_350`
2×	`sqrt-div_binary64_436` `div-exp_binary64_470` `cbrt-undiv_binary64_453` `unswap-sqr_binary64_387`
1×	`pow1/2_binary64_499` `sqrt-prod_binary64_435` `div-inv_binary64_416`

Counts

4 → 93

Calls

4 calls:

10.0ms	(.f64 n (/.f64 (.f64 l (-.f64 U* U)) Om))
10.0ms	(.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))))))
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)))))))
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)

series5.2s (15.2%)

Error

15.7b

Counts

4 → 124

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))))))
1.5s	(.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)))))))
334.0ms	(.f64 n (/.f64 (.f64 l (-.f64 U* U)) Om))

Compiler

Compiled 12730 to 9658 computations (24.1% saved)

simplify81.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

217 → 217

Iterations

Useful iterations: 0 (20.0ms)

Iter	Nodes	Cost
0	5044	7981

prune298.0ms (0.9%)

Pruning

25 alts after pruning (25 fresh and 0 done)

	Pruned	Kept	Total
New	208	9	217
Fresh	3	16	19
Picked	1	0	1
Done	0	0	0
Total	212	25	237

Error

14.0b

Counts

237 → 25

Compiler

Compiled 8180 to 2975 computations (63.6% saved)

localize23.0ms (0.1%)

Local error

Found 4 expressions with local error:

8.2b	(.f64 n (.f64 (/.f64 l Om) (-.f64 U* U)))
8.2b	(.f64 n (.f64 (/.f64 l Om) (-.f64 U* U)))
18.0b	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (.f64 (/.f64 l Om) (-.f64 U* U))) (*.f64 l -2)))))))
18.0b	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (.f64 (/.f64 l Om) (-.f64 U* U))) (*.f64 l -2)))))))

rewrite294.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Error

14.0b

Rules

40×	`pow1_binary64_480`
32×	`distribute-rgt-in_binary64_369` `distribute-lft-in_binary64_368`
24×	`cancel-sign-sub-inv_binary64_385`
22×	`add-exp-log_binary64_457` `add-cbrt-cube_binary64_455` `pow-prod-down_binary64_490` `associate-*r/_binary64_361`
14×	`add-cube-cbrt_binary64_454` `add-sqr-sqrt_binary64_441` `*-un-lft-identity_binary64_419`
10×	`sqrt-pow1_binary64_437` `prod-exp_binary64_468` `cbrt-unprod_binary64_452`
8×	`sub-neg_binary64_412`
6×	`associate-l_binary64_360`
4×	`add-log-exp_binary64_458` `sqrt-div_binary64_436` `flip3--_binary64_423` `frac-times_binary64_429` `flip--_binary64_394`
2×	`pow1/2_binary64_499` `flip3-+_binary64_422` `flip-+_binary64_393` `sqrt-prod_binary64_435` `div-exp_binary64_470` `cbrt-undiv_binary64_453` `associate-l/_binary64_362` `associate-r_binary64_359` `-commutative_binary64_350`

Counts

4 → 114

Calls

4 calls:

12.0ms	(.f64 n (.f64 (/.f64 l Om) (-.f64 U* U)))
12.0ms	(.f64 n (.f64 (/.f64 l Om) (-.f64 U* U)))
7.0ms	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (.f64 (/.f64 l Om) (-.f64 U* U))) (*.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 Om) (-.f64 U* U))) (*.f64 l -2)))))))

Compiler

Compiled 7550 to 3093 computations (59% saved)

series3.8s (11.1%)

Error

14.0b

Counts

4 → 96

Calls

4 calls:

1.4s	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (.f64 (/.f64 l Om) (-.f64 U* U))) (*.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 Om) (-.f64 U* U))) (*.f64 l -2)))))))
371.0ms	(.f64 n (.f64 (/.f64 l Om) (-.f64 U* U)))
368.0ms	(.f64 n (.f64 (/.f64 l Om) (-.f64 U* U)))

Compiler

Compiled 19938 to 13020 computations (34.7% saved)

simplify90.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

210 → 210

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	4980	6558
1	4980	6558

prune524.0ms (1.5%)

Pruning

25 alts after pruning (24 fresh and 1 done)

	Pruned	Kept	Total
New	210	0	210
Fresh	0	24	24
Picked	0	1	1
Done	0	0	0
Total	210	25	235

Error

14.0b

Counts

235 → 25

Compiler

Compiled 14048 to 5947 computations (57.7% saved)

localize24.0ms (0.1%)

Local error

Found 4 expressions with local error:

8.2b	(.f64 n (.f64 (/.f64 l Om) (-.f64 U* U)))
18.0b	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (.f64 (/.f64 l Om) (-.f64 U* U))) (*.f64 l -2)))))))
18.0b	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (.f64 (/.f64 l Om) (-.f64 U* U))) (*.f64 l -2)))))))
18.0b	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (.f64 (/.f64 l Om) (-.f64 U* U))) (*.f64 l -2)))))))

rewrite341.0ms (1%)

Algorithm

1×	rewrite-expression-head

Error

14.0b

Rules

48×	`pow1_binary64_480`
27×	`pow-prod-down_binary64_490`
19×	`associate-*r/_binary64_361`
16×	`distribute-rgt-in_binary64_369` `distribute-lft-in_binary64_368`
15×	`sqrt-pow1_binary64_437`
13×	`add-exp-log_binary64_457` `add-cbrt-cube_binary64_455`
12×	`cancel-sign-sub-inv_binary64_385`
9×	`add-cube-cbrt_binary64_454` `add-sqr-sqrt_binary64_441` `*-un-lft-identity_binary64_419`
6×	`sqrt-div_binary64_436`
5×	`prod-exp_binary64_468` `cbrt-unprod_binary64_452`
4×	`add-log-exp_binary64_458` `sub-neg_binary64_412`
3×	`pow1/2_binary64_499` `flip3-+_binary64_422` `flip-+_binary64_393` `sqrt-prod_binary64_435` `associate-l_binary64_360`
2×	`flip3--_binary64_423` `frac-times_binary64_429` `flip--_binary64_394`
1×	`div-exp_binary64_470` `cbrt-undiv_binary64_453` `associate-l/_binary64_362` `associate-r_binary64_359` `-commutative_binary64_350`

Counts

4 → 89

Calls

4 calls:

12.0ms	(.f64 n (.f64 (/.f64 l Om) (-.f64 U* U)))
7.0ms	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (.f64 (/.f64 l Om) (-.f64 U* U))) (*.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 Om) (-.f64 U* U))) (*.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 Om) (-.f64 U* U))) (*.f64 l -2)))))))

Compiler

Compiled 8571 to 3656 computations (57.3% saved)

series5.0s (14.7%)

Error

14.0b

Counts

4 → 102

Calls

4 calls:

1.4s	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (.f64 (/.f64 l Om) (-.f64 U* U))) (*.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 Om) (-.f64 U* U))) (*.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 Om) (-.f64 U* U))) (*.f64 l -2)))))))
388.0ms	(.f64 n (.f64 (/.f64 l Om) (-.f64 U* U)))

Compiler

Compiled 31005 to 19057 computations (38.5% saved)

simplify96.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

191 → 191

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	4980	7857
1	4980	7857

prune727.0ms (2.1%)

Pruning

25 alts after pruning (23 fresh and 2 done)

	Pruned	Kept	Total
New	191	0	191
Fresh	0	23	23
Picked	0	1	1
Done	0	1	1
Total	191	25	216

Error

14.0b

Counts

216 → 25

Compiler

Compiled 17891 to 7377 computations (58.8% saved)

regimes3.2s (9.4%)

Accuracy

Total 18.3b remaining (63%)

Threshold costs 0b (0%)

Compiler

Compiled 37826 to 27258 computations (27.9% saved)

bsearch305.0ms (0.9%)

Steps

Iters	Range		Point
9	6.14112552232578e+91	2.1166210360140988e+99	2.0898665093457604e+99
9	-5.15267670333867e-270	-7.474554969385408e-275	-1.9399217652603554e-272
6	-7.342318407237246e-229	-5.291125005492369e-230	-5.414462230876741e-230
8	-9.413826579080718e+73	-9.809636732934086e+70	-9.30463153096067e+73

Compiler

Compiled 1 to 6 computations (-500% saved)

simplify7.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	275	240
1	275	240

end0.0ms (0%)

sample6.2s (18.1%)

Algorithm

1×

intervals

Results

1.2s	12999×	body	128	nan
734.0ms	8000×	body	128	valid
109.0ms	1212×	body	128	invalid

Compiler

Compiled 4901 to 3521 computations (28.2% saved)

Details

analyze2.5s (7.4%)

sample99.0ms (0.3%)

simplify52.0ms (0.2%)

prune5.0ms (0%)

localize17.0ms (0%)

rewrite255.0ms (0.7%)

series4.4s (12.8%)

simplify122.0ms (0.4%)

prune330.0ms (1%)

localize18.0ms (0.1%)

rewrite173.0ms (0.5%)

series5.2s (15.2%)

simplify81.0ms (0.2%)

prune298.0ms (0.9%)

localize23.0ms (0.1%)

rewrite294.0ms (0.9%)

series3.8s (11.1%)

simplify90.0ms (0.3%)

prune524.0ms (1.5%)

localize24.0ms (0.1%)

rewrite341.0ms (1%)

series5.0s (14.7%)

simplify96.0ms (0.3%)

prune727.0ms (2.1%)

regimes3.2s (9.4%)

bsearch305.0ms (0.9%)

simplify7.0ms (0%)

end0.0ms (0%)

sample6.2s (18.1%)

Profiling