Details

analyze2.1s (9.6%)

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)

sample91.0ms (0.4%)

Algorithm

1×

intervals

Results

22.0ms	181×	body	128	valid
19.0ms	36×	body	1024	valid
9.0ms	25×	body	512	valid
7.0ms	13×	body	1024	invalid
6.0ms	65×	body	128	invalid
4.0ms	12×	body	512	invalid
3.0ms	14×	body	256	valid
2.0ms	7×	body	256	invalid

Compiler

Compiled 65 to 48 computations (26.2% saved)

simplify311.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (143.0ms)

Iter	Nodes	Cost
0	4986	49
1	4986	49

prune4.0ms (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

Merged error: 39.1b

Counts

2 → 1

Compiler

Compiled 64 to 42 computations (34.4% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))
2.7b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
2.7b	(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 (+.f64 phi1 phi2) 2)))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))

rewrite76.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

130×	`associate-*l/_binary64_710`
97×	`flip--_binary64_742` `flip3--_binary64_771`
66×	`sqrt-div_binary64_784`
64×	`frac-times_binary64_777` `frac-add_binary64_775`
32×	`associate-*r/_binary64_709`
12×	`add-sqr-sqrt_binary64_789`
9×	`*-un-lft-identity_binary64_767`
7×	`pow1_binary64_828` `add-cube-cbrt_binary64_802`
6×	`add-exp-log_binary64_805` `add-cbrt-cube_binary64_803`
5×	`associate-l_binary64_708`
4×	`add-log-exp_binary64_806`
3×	`associate-r_binary64_707` `sqrt-prod_binary64_783`
1×	`unswap-sqr_binary64_735` `rem-sqrt-square_binary64_780` `cbrt-unprod_binary64_800` `prod-exp_binary64_816` `*-commutative_binary64_698` `flip-+_binary64_741` `distribute-lft-out--_binary64_719` `pow1/2_binary64_847` `flip3-+_binary64_770` `sqrt-pow1_binary64_785` `pow-prod-down_binary64_838` `difference-of-squares_binary64_736`

Counts

4 → 115

Calls

4 calls:

22.0ms	(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))))
8.0ms	(*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))
6.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
5.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

series1.5s (7.1%)

Counts

4 → 12

Calls

4 calls:

1.3s	(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))))
183.0ms	(*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))
27.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
26.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

simplify90.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 0 (20.0ms)

Iter	Nodes	Cost
0	5141	9677

prune302.0ms (1.4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	122	5	127
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	122	6	128

Merged error: 27.1b

Counts

128 → 6

Compiler

Compiled 9087 to 3282 computations (63.9% saved)

localize22.0ms (0.1%)

Local error

Found 4 expressions with local error:

2.7b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
2.7b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
36.9b	(cbrt.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))))
36.9b	(cbrt.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))))

rewrite125.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

256×	`associate-*l/_binary64_710`
192×	`flip--_binary64_742` `flip3--_binary64_771`
132×	`cbrt-div_binary64_799`
128×	`frac-times_binary64_777` `frac-add_binary64_775`
64×	`associate-*r/_binary64_709`
6×	`add-sqr-sqrt_binary64_789` `*-un-lft-identity_binary64_767` `cbrt-prod_binary64_798` `add-cube-cbrt_binary64_802`
4×	`add-exp-log_binary64_805` `pow1_binary64_828` `add-log-exp_binary64_806` `add-cbrt-cube_binary64_803`
2×	`pow1/3_binary64_849` `flip-+_binary64_741` `flip3-+_binary64_770`

Counts

4 → 168

Calls

4 calls:

22.0ms	(cbrt.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))))
22.0ms	(cbrt.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))))
6.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
6.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

series3.6s (16.9%)

Counts

4 → 12

Calls

4 calls:

1.8s	(cbrt.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))))
1.8s	(cbrt.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))))
28.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
26.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

simplify151.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

180 → 180

Iterations

Useful iterations: 0 (22.0ms)

Iter	Nodes	Cost
0	4993	18474
1	4993	18474

prune775.0ms (3.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	178	2	180
Fresh	0	4	4
Picked	1	0	1
Done	0	1	1
Total	179	7	186

Merged error: 27.1b

Counts

186 → 7

Compiler

Compiled 20655 to 7379 computations (64.3% saved)

localize20.0ms (0.1%)

Local error

Found 4 expressions with local error:

2.7b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
2.7b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
6.2b	(exp.f64 (log.f64 (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))))))
35.8b	(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))))

rewrite126.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

256×	`associate-*l/_binary64_710`
192×	`flip--_binary64_742` `flip3--_binary64_771`
132×	`sqrt-div_binary64_784`
128×	`frac-times_binary64_777` `frac-add_binary64_775`
66×	`log-div_binary64_854` `exp-diff_binary64_815`
64×	`associate-*r/_binary64_709`
9×	`add-sqr-sqrt_binary64_789`
8×	`*-un-lft-identity_binary64_767` `add-cube-cbrt_binary64_802`
7×	`pow1_binary64_828`
6×	`exp-prod_binary64_819` `exp-sum_binary64_813` `sqrt-prod_binary64_783` `log-prod_binary64_853`
4×	`add-exp-log_binary64_805` `add-log-exp_binary64_806` `add-cbrt-cube_binary64_803`
3×	`log-pow_binary64_856`
2×	`flip-+_binary64_741` `pow1/2_binary64_847` `flip3-+_binary64_770` `sqrt-pow1_binary64_785`
1×	`rem-sqrt-square_binary64_780` `rem-exp-log_binary64_807`

Counts

4 → 179

Calls

4 calls:

34.0ms	(exp.f64 (log.f64 (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))))))
22.0ms	(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))))
6.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
6.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

series3.3s (15.3%)

Counts

4 → 12

Calls

4 calls:

1.9s	(exp.f64 (log.f64 (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	(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))))
27.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
27.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

simplify150.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

191 → 191

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	5220	18510

prune670.0ms (3.1%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	182	9	191
Fresh	2	3	5
Picked	1	0	1
Done	0	1	1
Total	185	13	198

Merged error: 17.6b

Counts

198 → 13

Compiler

Compiled 18231 to 7204 computations (60.5% saved)

localize27.0ms (0.1%)

Local error

Found 4 expressions with local error:

2.7b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
2.7b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
6.4b	(pow.f64 (exp.f64 1/2) (log.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)))))
37.3b	(log.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))))

rewrite135.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

256×	`associate-*l/_binary64_710`
192×	`flip--_binary64_742` `flip3--_binary64_771`
132×	`log-div_binary64_854`
128×	`frac-times_binary64_777` `frac-add_binary64_775`
66×	`pow-sub_binary64_843`
64×	`associate-*r/_binary64_709`
9×	`add-sqr-sqrt_binary64_789` `*-un-lft-identity_binary64_767` `add-cube-cbrt_binary64_802`
7×	`pow1_binary64_828`
6×	`log-prod_binary64_853`
5×	`add-exp-log_binary64_805`
4×	`add-log-exp_binary64_806` `pow-unpow_binary64_844` `add-cbrt-cube_binary64_803` `pow-pow_binary64_839`
3×	`exp-prod_binary64_819` `unpow-prod-down_binary64_846` `unpow-prod-up_binary64_845`
2×	`flip-+_binary64_741` `log-pow_binary64_856` `flip3-+_binary64_770`
1×	`pow-to-exp_binary64_836` `sqr-pow_binary64_739` `pow-exp_binary64_835` `rem-log-exp_binary64_808`

Counts

4 → 182

Calls

4 calls:

30.0ms	(pow.f64 (exp.f64 1/2) (log.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)))))
26.0ms	(log.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))))
6.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
6.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

series3.3s (15.5%)

Counts

4 → 12

Calls

4 calls:

2.1s	(pow.f64 (exp.f64 1/2) (log.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)))))
1.1s	(log.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))))
28.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
27.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

simplify156.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

194 → 194

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	5021	20063

prune751.0ms (3.5%)

Pruning

17 alts after pruning (16 fresh and 1 done)

	Pruned	Kept	Total
New	187	7	194
Fresh	2	9	11
Picked	1	0	1
Done	0	1	1
Total	190	17	207

Merged error: 17.6b

Counts

207 → 17

Compiler

Compiled 19024 to 7999 computations (58% saved)

regimes595.0ms (2.8%)

Compiler: Compiled 4732 to 3653 computations (22.8% saved)

bsearch3.0ms (0%)

Compiler: Compiled 32 to 21 computations (34.4% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	61	166
1	61	166

end0.0ms (0%)

sample3.1s (14.3%)

Algorithm

1×

intervals

Results

627.0ms	5974×	body	128	valid
471.0ms	880×	body	1024	valid
260.0ms	489×	body	1024	invalid
257.0ms	747×	body	512	valid
248.0ms	2433×	body	128	invalid
130.0ms	371×	body	512	invalid
97.0ms	391×	body	256	valid
49.0ms	201×	body	256	invalid
12.0ms	8×	body	2048	valid

Compiler

Compiled 595 to 432 computations (27.4% saved)

Details

analyze2.1s (9.6%)

sample91.0ms (0.4%)

simplify311.0ms (1.4%)

prune4.0ms (0%)

localize17.0ms (0.1%)

rewrite76.0ms (0.4%)

series1.5s (7.1%)

simplify90.0ms (0.4%)

prune302.0ms (1.4%)

localize22.0ms (0.1%)

rewrite125.0ms (0.6%)

series3.6s (16.9%)

simplify151.0ms (0.7%)

prune775.0ms (3.6%)

localize20.0ms (0.1%)

rewrite126.0ms (0.6%)

series3.3s (15.3%)

simplify150.0ms (0.7%)

prune670.0ms (3.1%)

localize27.0ms (0.1%)

rewrite135.0ms (0.6%)

series3.3s (15.5%)

simplify156.0ms (0.7%)

prune751.0ms (3.5%)

regimes595.0ms (2.8%)

bsearch3.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample3.1s (14.3%)

Profiling