Details

analyze4.2s (2.8%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
0%	99.8%	0.2%	9
0%	99.8%	0.2%	10
0.8%	99%	0.2%	11
4.7%	95.1%	0.2%	12
5.9%	93.2%	0.8%	13
8.5%	90.2%	1.3%	14

Compiler

Compiled 33 to 22 computations (33.3% saved)

sample154.0ms (0.1%)

Algorithm

1×

intervals

Results

38.0ms	192×	body	128	valid
19.0ms	30×	body	512	valid
16.0ms	18×	body	1024	valid
13.0ms	69×	body	128	invalid
11.0ms	12×	body	1024	invalid
8.0ms	12×	body	512	invalid
7.0ms	16×	body	256	valid
2.0ms	5×	body	256	invalid

Compiler

Compiled 65 to 48 computations (26.2% saved)

simplify412.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (247.0ms)

Iter	Nodes	Cost
0	4960	49
1	4960	49

prune7.0ms (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

42.2b

Counts

2 → 1

Compiler

Compiled 64 to 42 computations (34.4% saved)

localize34.0ms (0%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))
3.7b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
3.7b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
38.5b	(sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))

rewrite755.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Error

42.2b

Rules

142×	`associate-*l/_binary64_362`
102×	`flip3--_binary64_423` `flip--_binary64_394`
68×	`frac-times_binary64_429`
66×	`sqrt-div_binary64_436`
64×	`frac-add_binary64_427`
44×	`pow1_binary64_480`
34×	`associate-*r/_binary64_361`
17×	`pow-prod-down_binary64_490`
16×	`add-exp-log_binary64_457` `add-cbrt-cube_binary64_455`
8×	`prod-exp_binary64_468` `cbrt-unprod_binary64_452`
6×	`add-sqr-sqrt_binary64_441`
5×	`add-cube-cbrt_binary64_454` `*-un-lft-identity_binary64_419`
4×	`add-log-exp_binary64_458` `pow-prod-up_binary64_489` `pow-sqr_binary64_392`
3×	`sqrt-prod_binary64_435`
2×	`pow-plus_binary64_482`
1×	`pow1/2_binary64_499` `sqrt-pow1_binary64_437` `flip3-+_binary64_422` `flip-+_binary64_393` `rem-sqrt-square_binary64_432` `pow2_binary64_500` `swap-sqr_binary64_386` `associate-l_binary64_360` `associate-r_binary64_359` `*-commutative_binary64_350`

Counts

4 → 135

Calls

4 calls:

47.0ms	(sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))
30.0ms	(.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))
18.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
12.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

Compiler

Compiled 9145 to 2868 computations (68.6% saved)

series24.3s (16.2%)

Error

4.8b

Counts

4 → 85

Calls

4 calls:

21.9s	(sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))
1.4s	(.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))
100.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
100.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

Compiler

Compiled 25365 to 19167 computations (24.4% saved)

simplify356.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

220 → 220

Iterations

Useful iterations: 0 (73.0ms)

Iter	Nodes	Cost
0	5434	18323

prune1.3s (0.9%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	211	9	220
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	212	9	221

Error

4.8b

Counts

221 → 9

Compiler

Compiled 14893 to 6368 computations (57.2% saved)

localize46.0ms (0%)

Local error

Found 4 expressions with local error:

3.7b	(cos.f64 (/.f64 (+.f64 phi2 phi1) 2))
3.7b	(cos.f64 (/.f64 (+.f64 phi2 phi1) 2))
38.5b	(sqrt.f64 (+.f64 (.f64 (pow.f64 (-.f64 lambda1 lambda2) 2) (.f64 (cos.f64 (/.f64 (+.f64 phi2 phi1) 2)) (cos.f64 (/.f64 (+.f64 phi2 phi1) 2)))) (*.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))
38.5b	(sqrt.f64 (+.f64 (.f64 (pow.f64 (-.f64 lambda1 lambda2) 2) (.f64 (cos.f64 (/.f64 (+.f64 phi2 phi1) 2)) (cos.f64 (/.f64 (+.f64 phi2 phi1) 2)))) (*.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))

rewrite495.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Error

4.8b

Rules

20×	`associate-*r/_binary64_361` `sqrt-div_binary64_436`
16×	`cos-mult_binary64_573` `frac-add_binary64_427`
12×	`flip3--_binary64_423` `flip--_binary64_394`
8×	`add-sqr-sqrt_binary64_441` `frac-times_binary64_429`
6×	`pow1_binary64_480` `add-cube-cbrt_binary64_454` `sqrt-prod_binary64_435` `*-un-lft-identity_binary64_419`
4×	`add-log-exp_binary64_458` `add-exp-log_binary64_457` `add-cbrt-cube_binary64_455` `associate-*l/_binary64_362`
2×	`pow1/2_binary64_499` `sqrt-pow1_binary64_437` `flip3-+_binary64_422` `flip-+_binary64_393` `rem-sqrt-square_binary64_432`

Counts

4 → 60

Calls

4 calls:

32.0ms	(sqrt.f64 (+.f64 (.f64 (pow.f64 (-.f64 lambda1 lambda2) 2) (.f64 (cos.f64 (/.f64 (+.f64 phi2 phi1) 2)) (cos.f64 (/.f64 (+.f64 phi2 phi1) 2)))) (*.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))
28.0ms	(sqrt.f64 (+.f64 (.f64 (pow.f64 (-.f64 lambda1 lambda2) 2) (.f64 (cos.f64 (/.f64 (+.f64 phi2 phi1) 2)) (cos.f64 (/.f64 (+.f64 phi2 phi1) 2)))) (*.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))
11.0ms	(cos.f64 (/.f64 (+.f64 phi2 phi1) 2))
11.0ms	(cos.f64 (/.f64 (+.f64 phi2 phi1) 2))

Compiler

Compiled 5318 to 2438 computations (54.2% saved)

series44.9s (29.9%)

Error

4.8b

Counts

4 → 100

Calls

4 calls:

21.5s	(sqrt.f64 (+.f64 (.f64 (pow.f64 (-.f64 lambda1 lambda2) 2) (.f64 (cos.f64 (/.f64 (+.f64 phi2 phi1) 2)) (cos.f64 (/.f64 (+.f64 phi2 phi1) 2)))) (*.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))
21.3s	(sqrt.f64 (+.f64 (.f64 (pow.f64 (-.f64 lambda1 lambda2) 2) (.f64 (cos.f64 (/.f64 (+.f64 phi2 phi1) 2)) (cos.f64 (/.f64 (+.f64 phi2 phi1) 2)))) (*.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))
124.0ms	(cos.f64 (/.f64 (+.f64 phi2 phi1) 2))
119.0ms	(cos.f64 (/.f64 (+.f64 phi2 phi1) 2))

Compiler

Compiled 47960 to 35339 computations (26.3% saved)

simplify288.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

160 → 160

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	5353	15920

prune1.7s (1.1%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	157	3	160
Fresh	1	7	8
Picked	1	0	1
Done	0	0	0
Total	159	10	169

Error

4.8b

Counts

169 → 10

Compiler

Compiled 17375 to 9025 computations (48.1% saved)

localize42.0ms (0%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))
2.2b	(+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (.f64 (-.f64 lambda1 lambda2) (cos.f64 (.f64 1/2 phi1)))) (*.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2)))
3.7b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
35.8b	(sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (.f64 (-.f64 lambda1 lambda2) (cos.f64 (.f64 1/2 phi1)))) (*.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))

rewrite1.0s (0.7%)

Algorithm

1×	rewrite-expression-head

Error

4.8b

Rules

258×	`associate-*l/_binary64_362`
193×	`flip3--_binary64_423` `flip--_binary64_394`
128×	`frac-times_binary64_429` `frac-add_binary64_427`
66×	`sqrt-div_binary64_436`
64×	`associate-*r/_binary64_361`
14×	`add-sqr-sqrt_binary64_441`
11×	`*-un-lft-identity_binary64_419`
9×	`add-cube-cbrt_binary64_454`
8×	`associate-+r+_binary64_351`
7×	`pow1_binary64_480`
6×	`add-log-exp_binary64_458` `add-exp-log_binary64_457` `add-cbrt-cube_binary64_455` `cancel-sign-sub-inv_binary64_385`
5×	`associate-l_binary64_360`
4×	`distribute-rgt-in_binary64_369` `distribute-lft-in_binary64_368`
3×	`sqrt-prod_binary64_435` `associate-r_binary64_359`
2×	`flip3-+_binary64_422` `flip-+_binary64_393` `sub-neg_binary64_412`
1×	`pow1/2_binary64_499` `sqrt-pow1_binary64_437` `rem-sqrt-square_binary64_432` `sum-log_binary64_510` `+-commutative_binary64_349` `pow-prod-down_binary64_490` `prod-exp_binary64_468` `cbrt-unprod_binary64_452` `unswap-sqr_binary64_387` `difference-of-squares_binary64_388` `distribute-lft-out--_binary64_371` `*-commutative_binary64_350`

Counts

4 → 191

Calls

4 calls:

36.0ms	(sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (.f64 (-.f64 lambda1 lambda2) (cos.f64 (.f64 1/2 phi1)))) (*.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))
34.0ms	(+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (.f64 (-.f64 lambda1 lambda2) (cos.f64 (.f64 1/2 phi1)))) (*.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2)))
14.0ms	(*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))
8.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

Compiler

Compiled 14487 to 4270 computations (70.5% saved)

series17.3s (11.6%)

Error

4.8b

Counts

4 → 106

Calls

4 calls:

12.5s	(sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (.f64 (-.f64 lambda1 lambda2) (cos.f64 (.f64 1/2 phi1)))) (*.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))
3.4s	(+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (.f64 (-.f64 lambda1 lambda2) (cos.f64 (.f64 1/2 phi1)))) (*.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2)))
558.0ms	(*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))
97.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

Compiler

Compiled 23842 to 17888 computations (25% saved)

simplify476.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

297 → 297

Iterations

Useful iterations: 0 (75.0ms)

Iter	Nodes	Cost
0	5533	26707

prune1.6s (1.1%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	294	3	297
Fresh	1	8	9
Picked	0	1	1
Done	0	0	0
Total	295	12	307

Error

4.8b

Counts

307 → 12

Compiler

Compiled 20607 to 8155 computations (60.4% saved)

localize67.0ms (0%)

Local error

Found 4 expressions with local error:

3.7b	(cos.f64 (/.f64 (+.f64 phi2 phi1) 2))
3.7b	(cos.f64 (/.f64 (+.f64 phi2 phi1) 2))
35.8b	(sqrt.f64 (+.f64 (.f64 (pow.f64 (-.f64 lambda1 lambda2) 2) (.f64 (cos.f64 (/.f64 (+.f64 phi2 phi1) 2)) (cos.f64 (.f64 1/2 phi1)))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))
38.5b	(sqrt.f64 (+.f64 (.f64 (pow.f64 (-.f64 lambda1 lambda2) 2) (.f64 (cos.f64 (/.f64 (+.f64 phi2 phi1) 2)) (cos.f64 (/.f64 (+.f64 phi2 phi1) 2)))) (*.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))

rewrite442.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Error

4.8b

Rules

20×	`associate-*r/_binary64_361` `sqrt-div_binary64_436`
16×	`cos-mult_binary64_573` `frac-add_binary64_427`
12×	`flip3--_binary64_423` `flip--_binary64_394`
8×	`add-sqr-sqrt_binary64_441` `frac-times_binary64_429`
6×	`pow1_binary64_480` `add-cube-cbrt_binary64_454` `sqrt-prod_binary64_435` `*-un-lft-identity_binary64_419`
4×	`add-log-exp_binary64_458` `add-exp-log_binary64_457` `add-cbrt-cube_binary64_455` `associate-*l/_binary64_362`
2×	`pow1/2_binary64_499` `sqrt-pow1_binary64_437` `flip3-+_binary64_422` `flip-+_binary64_393` `rem-sqrt-square_binary64_432`

Counts

4 → 60

Calls

4 calls:

28.0ms	(sqrt.f64 (+.f64 (.f64 (pow.f64 (-.f64 lambda1 lambda2) 2) (.f64 (cos.f64 (/.f64 (+.f64 phi2 phi1) 2)) (cos.f64 (/.f64 (+.f64 phi2 phi1) 2)))) (*.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))
27.0ms	(sqrt.f64 (+.f64 (.f64 (pow.f64 (-.f64 lambda1 lambda2) 2) (.f64 (cos.f64 (/.f64 (+.f64 phi2 phi1) 2)) (cos.f64 (.f64 1/2 phi1)))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))
11.0ms	(cos.f64 (/.f64 (+.f64 phi2 phi1) 2))
10.0ms	(cos.f64 (/.f64 (+.f64 phi2 phi1) 2))

Compiler

Compiled 5156 to 2438 computations (52.7% saved)

series35.7s (23.8%)

Error

4.8b

Counts

4 → 98

Calls

4 calls:

21.4s	(sqrt.f64 (+.f64 (.f64 (pow.f64 (-.f64 lambda1 lambda2) 2) (.f64 (cos.f64 (/.f64 (+.f64 phi2 phi1) 2)) (cos.f64 (/.f64 (+.f64 phi2 phi1) 2)))) (*.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))
12.3s	(sqrt.f64 (+.f64 (.f64 (pow.f64 (-.f64 lambda1 lambda2) 2) (.f64 (cos.f64 (/.f64 (+.f64 phi2 phi1) 2)) (cos.f64 (.f64 1/2 phi1)))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))
135.0ms	(cos.f64 (/.f64 (+.f64 phi2 phi1) 2))
124.0ms	(cos.f64 (/.f64 (+.f64 phi2 phi1) 2))

Compiler

Compiled 43944 to 32332 computations (26.4% saved)

simplify308.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

158 → 158

Iterations

Useful iterations: 0 (74.0ms)

Iter	Nodes	Cost
0	5001	15599

prune1.8s (1.2%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	158	0	158
Fresh	0	10	10
Picked	0	1	1
Done	0	1	1
Total	158	12	170

Error

4.8b

Counts

170 → 12

Compiler

Compiled 16186 to 8468 computations (47.7% saved)

regimes11.7s (7.8%)

Compiler: Compiled 68360 to 48664 computations (28.8% saved)

bsearch520.0ms (0.3%)

Steps

Iters	Range		Point
9	-2.886449120691266e-288	-5.7847199541408265e-297	-4.201655072743132e-289
7	-3.4366394543580216e-230	-1.9209969059428654e-231	-4.0815347611052884e-231
8	-2.4828310117539257e-164	-3.4927223679281035e-167	-1.5836358402941557e-164
6	-2.5417761378089177e-96	-4.457764058539201e-97	-7.194555376606329e-97
6	-420819176.08343655	-29983668.60360263	-412890876.8457351

Compiler

Compiled 1 to 5 computations (-400% saved)

Details

analyze4.2s (2.8%)

sample154.0ms (0.1%)

simplify412.0ms (0.3%)

prune7.0ms (0%)

localize34.0ms (0%)

rewrite755.0ms (0.5%)

series24.3s (16.2%)

simplify356.0ms (0.2%)

prune1.3s (0.9%)

localize46.0ms (0%)

rewrite495.0ms (0.3%)

series44.9s (29.9%)

simplify288.0ms (0.2%)

prune1.7s (1.1%)

localize42.0ms (0%)

rewrite1.0s (0.7%)

series17.3s (11.6%)

simplify476.0ms (0.3%)

prune1.6s (1.1%)

localize67.0ms (0%)

rewrite442.0ms (0.3%)

series35.7s (23.8%)

simplify308.0ms (0.2%)

prune1.8s (1.2%)

regimes11.7s (7.8%)

bsearch520.0ms (0.3%)

Profiling