Details

analyze2.4s (7.7%)

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)

sample98.0ms (0.3%)

Algorithm

1×

intervals

Results

34.0ms	370×	body	128	nan
27.0ms	256×	body	128	valid
3.0ms	31×	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 (46.0ms)

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

31.5b

Counts

2 → 2

Compiler

Compiled 80 to 63 computations (21.3% saved)

localize22.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.4b	(.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)))
10.5b	(.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)))))))
20.4b	(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))))))))

rewrite257.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Error

24.6b

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×	`*-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:

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 (13.8%)

Error

19.6b

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)))))))
1.2s	(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))))))))
836.0ms	(.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))))
252.0ms	(.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))

Compiler

Compiled 12094 to 9174 computations (24.1% saved)

simplify124.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

243 → 243

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	5049	8173

prune335.0ms (1.1%)

Pruning

19 alts after pruning (19 fresh and 0 done)

	Pruned	Kept	Total
New	224	19	243
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	226	19	245

Error

17.2b

Counts

245 → 19

Compiler

Compiled 8717 to 3290 computations (62.3% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

5.2b	(*.f64 n (/.f64 l Om))
6.1b	(.f64 (.f64 n (/.f64 l Om)) (-.f64 U* U))
10.5b	(.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))))))
20.4b	(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)))))))

rewrite184.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Error

17.0b

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))
9.0ms	(.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)

series3.7s (11.6%)

Error

16.3b

Counts

4 → 94

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))))))
1.2s	(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)))))))
263.0ms	(.f64 (.f64 n (/.f64 l Om)) (-.f64 U* U))
110.0ms	(*.f64 n (/.f64 l Om))

Compiler

Compiled 10574 to 7961 computations (24.7% saved)

simplify72.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

201 → 201

Iterations

Useful iterations: 0 (20.0ms)

Iter	Nodes	Cost
0	5226	6452

prune251.0ms (0.8%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	199	2	201
Fresh	2	16	18
Picked	1	0	1
Done	0	0	0
Total	202	18	220

Error

17.2b

Counts

220 → 18

Compiler

Compiled 7272 to 2804 computations (61.4% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

4.8b	(.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))))))
5.4b	(.f64 n (/.f64 (.f64 l (-.f64 U* U)) Om))
5.5b	(.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (/.f64 (.f64 l (-.f64 U* U)) Om)) (*.f64 l -2)))))
20.4b	(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)))))))

rewrite174.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Error

13.2b

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	(.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))))))
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)))))))
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)

series5.3s (16.8%)

Error

16.0b

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)))))))
301.0ms	(.f64 n (/.f64 (.f64 l (-.f64 U* U)) Om))

Compiler

Compiled 13260 to 10094 computations (23.9% saved)

simplify85.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

217 → 217

Iterations

Useful iterations: 0 (21.0ms)

Iter	Nodes	Cost
0	5242	8341

prune286.0ms (0.9%)

Pruning

22 alts after pruning (22 fresh and 0 done)

	Pruned	Kept	Total
New	210	7	217
Fresh	2	15	17
Picked	1	0	1
Done	0	0	0
Total	213	22	235

Error

13.0b

Counts

235 → 22

Compiler

Compiled 8102 to 2930 computations (63.8% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

6.1b	(/.f64 (*.f64 l n) Om)
6.1b	(.f64 (/.f64 (.f64 l n) Om) (-.f64 U* U))
10.5b	(.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (/.f64 (.f64 l n) Om) (-.f64 U U))))))
20.4b	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (/.f64 (.f64 l n) Om) (-.f64 U U)))))))

rewrite169.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Error

13.0b

Rules

27×	`add-exp-log_binary64_457` `add-cbrt-cube_binary64_455`
25×	`pow1_binary64_480`
16×	`add-sqr-sqrt_binary64_441`
14×	`*-un-lft-identity_binary64_419`
13×	`pow-prod-down_binary64_490`
12×	`add-cube-cbrt_binary64_454`
11×	`prod-exp_binary64_468` `cbrt-unprod_binary64_452`
8×	`associate-l_binary64_360` `associate-r_binary64_359`
6×	`associate-*r/_binary64_361` `cancel-sign-sub-inv_binary64_385` `times-frac_binary64_425`
5×	`distribute-rgt-in_binary64_369` `distribute-lft-in_binary64_368`
4×	`add-log-exp_binary64_458` `sqrt-pow1_binary64_437` `div-exp_binary64_470` `cbrt-undiv_binary64_453`
3×	`associate-/r*_binary64_363`
2×	`flip3-+_binary64_422` `sqrt-div_binary64_436` `flip-+_binary64_393` `*-commutative_binary64_350` `flip3--_binary64_423` `frac-times_binary64_429` `flip--_binary64_394` `sub-neg_binary64_412` `div-inv_binary64_416`
1×	`pow1/2_binary64_499` `sqrt-prod_binary64_435` `unswap-sqr_binary64_387` `associate-l/_binary64_362` `difference-of-squares_binary64_388` `distribute-lft-out--_binary64_371` `frac-2neg_binary64_430` `clear-num_binary64_418` `associate-/l_binary64_364`

Counts

4 → 102

Calls

4 calls:

13.0ms	(.f64 (/.f64 (.f64 l n) Om) (-.f64 U* U))
10.0ms	(.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (/.f64 (.f64 l n) Om) (-.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 (.f64 l n) Om) (-.f64 U U)))))))
5.0ms	(/.f64 (*.f64 l n) Om)

Compiler

Compiled 3888 to 1575 computations (59.5% saved)

series3.6s (11.4%)

Error

12.2b

Counts

4 → 94

Calls

4 calls:

1.9s	(.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (/.f64 (.f64 l n) Om) (-.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 (.f64 l n) Om) (-.f64 U U)))))))
259.0ms	(.f64 (/.f64 (.f64 l n) Om) (-.f64 U* U))
96.0ms	(/.f64 (*.f64 l n) Om)

Compiler

Compiled 10574 to 7961 computations (24.7% saved)

simplify70.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

196 → 196

Iterations

Useful iterations: 0 (20.0ms)

Iter	Nodes	Cost
0	5037	6418

prune216.0ms (0.7%)

Pruning

22 alts after pruning (21 fresh and 1 done)

	Pruned	Kept	Total
New	196	0	196
Fresh	0	21	21
Picked	0	1	1
Done	0	0	0
Total	196	22	218

Error

13.0b

Counts

218 → 22

Compiler

Compiled 6603 to 2349 computations (64.4% saved)

regimes3.2s (10.1%)

Accuracy

Total 17.0b remaining (60.4%)

Threshold costs 0b (0%)

Compiler

Compiled 38786 to 28698 computations (26% saved)

bsearch237.0ms (0.8%)

Steps

Iters	Range		Point
9	1.4985768977921183e+138	2.28811816246111e+144	7.521405414691739e+143
10	-2.0748948113763207e+189	-1.4143229607512836e+171	-6.704024741456845e+171

Compiler

Compiled 1 to 6 computations (-500% saved)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	205	144
1	205	144

end0.0ms (0%)

sample6.3s (20%)

Algorithm

1×

intervals

Results

1.2s	12930×	body	128	nan
768.0ms	8000×	body	128	valid
114.0ms	1165×	body	128	invalid

Compiler

Compiled 4957 to 3658 computations (26.2% saved)

Details

analyze2.4s (7.7%)

sample98.0ms (0.3%)

simplify51.0ms (0.2%)

prune5.0ms (0%)

localize22.0ms (0.1%)

rewrite257.0ms (0.8%)

series4.4s (13.8%)

simplify124.0ms (0.4%)

prune335.0ms (1.1%)

localize17.0ms (0.1%)

rewrite184.0ms (0.6%)

series3.7s (11.6%)

simplify72.0ms (0.2%)

prune251.0ms (0.8%)

localize19.0ms (0.1%)

rewrite174.0ms (0.6%)

series5.3s (16.8%)

simplify85.0ms (0.3%)

prune286.0ms (0.9%)

localize19.0ms (0.1%)

rewrite169.0ms (0.5%)

series3.6s (11.4%)

simplify70.0ms (0.2%)

prune216.0ms (0.7%)

regimes3.2s (10.1%)

bsearch237.0ms (0.8%)

simplify5.0ms (0%)

end0.0ms (0%)

sample6.3s (20%)

Profiling