Details

analyze2.7s (9.3%)

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)

sample103.0ms (0.4%)

Algorithm

1×

intervals

Results

34.0ms	391×	body	128	nan
23.0ms	256×	body	128	valid
8.0ms	48×	body	128	invalid

Compiler

Compiled 57 to 53 computations (7% saved)

simplify54.0ms (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

28.5b

Counts

2 → 2

Compiler

Compiled 80 to 63 computations (21.3% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.6b	(.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))))
9.9b	(.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)))))))
10.4b	(.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))
17.5b	(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))))))))

rewrite296.0ms (1%)

Algorithm

1×	rewrite-expression-head

Error

20.1b

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:

13.0ms	(.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))
12.0ms	(.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)))))))
10.0ms	(.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)

series4.8s (16.6%)

Error

17.4b

Counts

4 → 116

Calls

4 calls:

2.0s	(.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)))))))
1.4s	(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))))))))
846.0ms	(.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))))
323.0ms	(.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))

Compiler

Compiled 13123 to 9915 computations (24.4% saved)

simplify122.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

247 → 247

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4989	8853
1	4989	8853

prune382.0ms (1.3%)

Pruning

19 alts after pruning (19 fresh and 0 done)

	Pruned	Kept	Total
New	228	19	247
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	230	19	249

Error

13.7b

Counts

249 → 19

Compiler

Compiled 9400 to 3553 computations (62.2% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

5.1b	(*.f64 n (/.f64 l Om))
7.4b	(.f64 (.f64 n (/.f64 l Om)) (-.f64 U* U))
9.9b	(.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))))))
17.5b	(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)))))))

rewrite180.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Error

13.7b

Rules

30×	`pow1_binary64_480`
27×	`add-exp-log_binary64_457` `add-cbrt-cube_binary64_455`
23×	`add-sqr-sqrt_binary64_441`
21×	`associate-r_binary64_359`
18×	`*-un-lft-identity_binary64_419`
16×	`add-cube-cbrt_binary64_454` `pow-prod-down_binary64_490`
13×	`prod-exp_binary64_468` `cbrt-unprod_binary64_452`
10×	`associate-*r/_binary64_361` `times-frac_binary64_425`
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` `flip-+_binary64_393` `div-exp_binary64_470` `cbrt-undiv_binary64_453` `flip3--_binary64_423` `frac-times_binary64_429` `flip--_binary64_394` `sub-neg_binary64_412` `unswap-sqr_binary64_387`
1×	`pow1/2_binary64_499` `sqrt-prod_binary64_435` `associate-*l/_binary64_362` `difference-of-squares_binary64_388` `distribute-lft-out--_binary64_371` `div-inv_binary64_416`

Counts

4 → 107

Calls

4 calls:

11.0ms	(.f64 (.f64 n (/.f64 l Om)) (-.f64 U* U))
10.0ms	(.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)))))))

Compiler

Compiled 4070 to 1665 computations (59.1% saved)

series3.9s (13.7%)

Error

12.5b

Counts

4 → 98

Calls

4 calls:

2.0s	(.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))))))
1.4s	(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)))))))
323.0ms	(.f64 (.f64 n (/.f64 l Om)) (-.f64 U* U))
105.0ms	(*.f64 n (/.f64 l Om))

Compiler

Compiled 11603 to 8702 computations (25% saved)

simplify80.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

205 → 205

Iterations

Useful iterations: 0 (20.0ms)

Iter	Nodes	Cost
0	5099	6893

prune278.0ms (1%)

Pruning

19 alts after pruning (18 fresh and 1 done)

	Pruned	Kept	Total
New	204	1	205
Fresh	1	17	18
Picked	0	1	1
Done	0	0	0
Total	205	19	224

Error

13.7b

Counts

224 → 19

Compiler

Compiled 7804 to 3066 computations (60.7% saved)

localize21.0ms (0.1%)

Local error

Found 4 expressions with local error:

14.4b	(cbrt.f64 (/.f64 l Om))
14.4b	(cbrt.f64 (/.f64 l Om))
14.4b	(cbrt.f64 (/.f64 l Om))
17.5b	(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)))))))

rewrite139.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Error

13.7b

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)))))))
3.0ms	(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)

series2.3s (8.1%)

Error

13.2b

Counts

4 → 47

Calls

4 calls:

1.6s	(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)))))))
209.0ms	(cbrt.f64 (/.f64 l Om))
195.0ms	(cbrt.f64 (/.f64 l Om))
193.0ms	(cbrt.f64 (/.f64 l Om))

Compiler

Compiled 7925 to 5839 computations (26.3% saved)

simplify89.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4960	3713
1	4960	3713

prune197.0ms (0.7%)

Pruning

19 alts after pruning (17 fresh and 2 done)

	Pruned	Kept	Total
New	128	0	128
Fresh	0	17	17
Picked	0	1	1
Done	0	1	1
Total	128	19	147

Error

13.7b

Counts

147 → 19

Compiler

Compiled 6194 to 2429 computations (60.8% saved)

localize23.0ms (0.1%)

Local error

Found 4 expressions with local error:

10.4b	(.f64 (.f64 n (-.f64 U* U)) (/.f64 l Om))
10.4b	(.f64 (.f64 n (-.f64 U* U)) (/.f64 l Om))
17.5b	(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))))))
17.5b	(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))))))

rewrite263.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Error

13.7b

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:

11.0ms	(.f64 (.f64 n (-.f64 U* U)) (/.f64 l Om))
11.0ms	(.f64 (.f64 n (-.f64 U* U)) (/.f64 l Om))
9.0ms	(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)

series3.5s (12.1%)

Error

13.7b

Counts

4 → 96

Calls

4 calls:

1.3s	(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))))))
1.2s	(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))))))
361.0ms	(.f64 (.f64 n (-.f64 U* U)) (/.f64 l Om))
353.0ms	(.f64 (.f64 n (-.f64 U* U)) (/.f64 l Om))

Compiler

Compiled 20342 to 13409 computations (34.1% saved)

simplify113.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

200 → 200

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4975	6374
1	4975	6374

prune477.0ms (1.7%)

Pruning

19 alts after pruning (16 fresh and 3 done)

	Pruned	Kept	Total
New	200	0	200
Fresh	0	16	16
Picked	0	1	1
Done	0	2	2
Total	200	19	219

Error

13.7b

Counts

219 → 19

Compiler

Compiled 12632 to 5439 computations (56.9% saved)

regimes2.9s (10.2%)

Accuracy

Total 12.6b remaining (48%)

Threshold costs 0b (0%)

Compiler

Compiled 31586 to 22786 computations (27.9% saved)

bsearch9.0ms (0%)

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

simplify59.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	1338	358
1	1338	358

end0.0ms (0%)

sample5.7s (19.8%)

Algorithm

1×

intervals

Results

1.2s	13076×	body	128	nan
736.0ms	8000×	body	128	valid
111.0ms	1214×	body	128	invalid

Compiler

Compiled 4199 to 2995 computations (28.7% saved)

Details

analyze2.7s (9.3%)

sample103.0ms (0.4%)

simplify54.0ms (0.2%)

prune5.0ms (0%)

localize17.0ms (0.1%)

rewrite296.0ms (1%)

series4.8s (16.6%)

simplify122.0ms (0.4%)

prune382.0ms (1.3%)

localize17.0ms (0.1%)

rewrite180.0ms (0.6%)

series3.9s (13.7%)

simplify80.0ms (0.3%)

prune278.0ms (1%)

localize21.0ms (0.1%)

rewrite139.0ms (0.5%)

series2.3s (8.1%)

simplify89.0ms (0.3%)

prune197.0ms (0.7%)

localize23.0ms (0.1%)

rewrite263.0ms (0.9%)

series3.5s (12.1%)

simplify113.0ms (0.4%)

prune477.0ms (1.7%)

regimes2.9s (10.2%)

bsearch9.0ms (0%)

simplify59.0ms (0.2%)

end0.0ms (0%)

sample5.7s (19.8%)

Profiling