Details

analyze2.2s (15.5%)

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)

sample81.0ms (0.6%)

Algorithm

1×

intervals

Results

22.0ms	203×	body	128	valid
9.0ms	19×	body	1024	invalid
9.0ms	25×	body	512	valid
8.0ms	75×	body	128	invalid
8.0ms	17×	body	1024	valid
3.0ms	8×	body	512	invalid
3.0ms	11×	body	256	valid
1.0ms	5×	body	256	invalid

Compiler

Compiled 65 to 48 computations (26.2% saved)

simplify220.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (123.0ms)

Iter	Nodes	Cost
0	4960	49
1	4960	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: 38.5b

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 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))
3.4b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
3.4b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
35.5b	(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))))

rewrite76.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

142×	`associate-*l/_binary64_4113`
102×	`flip3--_binary64_4174` `flip--_binary64_4145`
68×	`frac-times_binary64_4180`
66×	`sqrt-div_binary64_4187`
64×	`frac-add_binary64_4178`
44×	`pow1_binary64_4231`
34×	`associate-*r/_binary64_4112`
17×	`pow-prod-down_binary64_4241`
16×	`add-exp-log_binary64_4208` `add-cbrt-cube_binary64_4206`
8×	`prod-exp_binary64_4219` `cbrt-unprod_binary64_4203`
6×	`add-sqr-sqrt_binary64_4192`
5×	`*-un-lft-identity_binary64_4170` `add-cube-cbrt_binary64_4205`
4×	`pow-prod-up_binary64_4240` `add-log-exp_binary64_4209` `pow-sqr_binary64_4143`
3×	`sqrt-prod_binary64_4186`
2×	`pow-plus_binary64_4233`
1×	`swap-sqr_binary64_4137` `associate-l_binary64_4111` `flip-+_binary64_4144` `associate-r_binary64_4110` `pow2_binary64_4251` `pow1/2_binary64_4250` `sqrt-pow1_binary64_4188` `flip3-+_binary64_4173` `*-commutative_binary64_4101` `rem-sqrt-square_binary64_4183`

Counts

4 → 135

Calls

4 calls:

19.0ms	(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))))
13.0ms	(.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))
5.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
5.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

series853.0ms (6.1%)

Counts

4 → 12

Calls

4 calls:

674.0ms	(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))))
146.0ms	(.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))
17.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
17.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

simplify98.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

147 → 147

Iterations

Useful iterations: 0 (20.0ms)

Iter	Nodes	Cost
0	5228	10334

prune308.0ms (2.2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	139	8	147
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	140	8	148

Merged error: 23.5b

Counts

148 → 8

Compiler

Compiled 8757 to 2934 computations (66.5% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.4b	(*.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))
3.4b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
3.4b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
35.5b	(sqrt.f64 (+.f64 (.f64 (-.f64 lambda1 lambda2) (.f64 (-.f64 lambda1 lambda2) (.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))

rewrite96.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

198×	`flip3--_binary64_4174` `flip--_binary64_4145`
196×	`frac-times_binary64_4180`
138×	`sqrt-div_binary64_4187`
136×	`frac-add_binary64_4178`
98×	`associate-r/_binary64_4112` `associate-l/_binary64_4113`
73×	`cos-mult_binary64_4324`
12×	`pow1_binary64_4231` `add-sqr-sqrt_binary64_4192`
9×	`*-un-lft-identity_binary64_4170` `add-cube-cbrt_binary64_4205`
6×	`add-exp-log_binary64_4208` `add-cbrt-cube_binary64_4206`
4×	`add-log-exp_binary64_4209`
3×	`swap-sqr_binary64_4137` `associate-l_binary64_4111` `associate-r_binary64_4110` `sqrt-prod_binary64_4186`
1×	`pow-plus_binary64_4233` `prod-exp_binary64_4219` `cbrt-unprod_binary64_4203` `flip-+_binary64_4144` `pow2_binary64_4251` `pow1/2_binary64_4250` `sqrt-pow1_binary64_4188` `flip3-+_binary64_4173` `pow-prod-up_binary64_4240` `*-commutative_binary64_4101` `sqr-cos-a_binary64_4319` `rem-sqrt-square_binary64_4183` `pow-prod-down_binary64_4241` `unswap-sqr_binary64_4138` `pow-sqr_binary64_4143`

Counts

4 → 192

Calls

4 calls:

25.0ms	(sqrt.f64 (+.f64 (.f64 (-.f64 lambda1 lambda2) (.f64 (-.f64 lambda1 lambda2) (.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))
5.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
5.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
5.0ms	(*.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))

series760.0ms (5.4%)

Counts

4 → 12

Calls

4 calls:

694.0ms	(sqrt.f64 (+.f64 (.f64 (-.f64 lambda1 lambda2) (.f64 (-.f64 lambda1 lambda2) (.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))
35.0ms	(*.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))
16.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
15.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

simplify181.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

204 → 204

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5003	17592

prune434.0ms (3.1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	201	3	204
Fresh	4	3	7
Picked	0	1	1
Done	0	0	0
Total	205	7	212

Merged error: 22.9b

Counts

212 → 7

Compiler

Compiled 13667 to 4379 computations (68% saved)

localize21.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.5b	(log.f64 (exp.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))
3.4b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
3.4b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
35.5b	(sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (.f64 (-.f64 lambda1 lambda2) (log.f64 (exp.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))

rewrite68.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

128×	`associate-*l/_binary64_4113`
96×	`flip3--_binary64_4174` `flip--_binary64_4145`
66×	`sqrt-div_binary64_4187`
64×	`frac-times_binary64_4180` `frac-add_binary64_4178`
32×	`associate-*r/_binary64_4112`
8×	`add-sqr-sqrt_binary64_4192`
7×	`*-un-lft-identity_binary64_4170` `add-cube-cbrt_binary64_4205`
6×	`pow1_binary64_4231`
4×	`add-exp-log_binary64_4208` `add-cbrt-cube_binary64_4206` `log-pow_binary64_4259` `add-log-exp_binary64_4209`
3×	`exp-prod_binary64_4222` `sqrt-prod_binary64_4186` `log-prod_binary64_4256`
1×	`rem-log-exp_binary64_4211` `flip-+_binary64_4144` `pow1/2_binary64_4250` `sqrt-pow1_binary64_4188` `flip3-+_binary64_4173` `rem-sqrt-square_binary64_4183`

Counts

4 → 108

Calls

4 calls:

20.0ms	(sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (.f64 (-.f64 lambda1 lambda2) (log.f64 (exp.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))
6.0ms	(log.f64 (exp.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))
5.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
5.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

series1.3s (9%)

Counts

4 → 12

Calls

4 calls:

1.2s	(sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (.f64 (-.f64 lambda1 lambda2) (log.f64 (exp.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))
47.0ms	(log.f64 (exp.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))
16.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
15.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

simplify93.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 0 (18.0ms)

Iter	Nodes	Cost
0	5363	9530

prune245.0ms (1.8%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	119	1	120
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	119	8	127

Merged error: 22.4b

Counts

127 → 8

Compiler

Compiled 7976 to 2678 computations (66.4% saved)

localize22.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.8b	(pow.f64 (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) 6)
3.4b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
6.2b	(exp.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 (-.f64 lambda1 lambda2) (.f64 (-.f64 lambda1 lambda2) (pow.f64 (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) 6))) (*.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))))
35.5b	(sqrt.f64 (+.f64 (.f64 (-.f64 lambda1 lambda2) (.f64 (-.f64 lambda1 lambda2) (pow.f64 (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) 6))) (*.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))

rewrite108.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

192×	`flip3--_binary64_4174` `flip--_binary64_4145`
160×	`associate-*l/_binary64_4113`
132×	`sqrt-div_binary64_4187`
128×	`frac-times_binary64_4180` `frac-add_binary64_4178`
66×	`log-div_binary64_4257` `exp-diff_binary64_4218`
64×	`associate-*r/_binary64_4112`
12×	`add-sqr-sqrt_binary64_4192`
11×	`*-un-lft-identity_binary64_4170` `add-cube-cbrt_binary64_4205`
8×	`pow1_binary64_4231`
6×	`exp-prod_binary64_4222` `sqrt-prod_binary64_4186` `unpow-prod-down_binary64_4249` `log-prod_binary64_4256` `exp-sum_binary64_4216`
5×	`add-exp-log_binary64_4208`
4×	`add-cbrt-cube_binary64_4206` `add-log-exp_binary64_4209`
3×	`pow-unpow_binary64_4247` `log-pow_binary64_4259` `cbrt-prod_binary64_4201`
2×	`flip-+_binary64_4144` `pow1/2_binary64_4250` `pow-pow_binary64_4242` `sqrt-pow1_binary64_4188` `flip3-+_binary64_4173`
1×	`pow-to-exp_binary64_4239` `pow1/3_binary64_4252` `sqr-pow_binary64_4142` `pow-exp_binary64_4238` `rem-sqrt-square_binary64_4183` `rem-exp-log_binary64_4210`

Counts

4 → 193

Calls

4 calls:

30.0ms	(exp.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 (-.f64 lambda1 lambda2) (.f64 (-.f64 lambda1 lambda2) (pow.f64 (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) 6))) (*.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))))
19.0ms	(sqrt.f64 (+.f64 (.f64 (-.f64 lambda1 lambda2) (.f64 (-.f64 lambda1 lambda2) (pow.f64 (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) 6))) (*.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))
5.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
3.0ms	(pow.f64 (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) 6)

series1.8s (13%)

Counts

4 → 12

Calls

4 calls:

979.0ms	(exp.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 (-.f64 lambda1 lambda2) (.f64 (-.f64 lambda1 lambda2) (pow.f64 (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) 6))) (*.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))))
694.0ms	(sqrt.f64 (+.f64 (.f64 (-.f64 lambda1 lambda2) (.f64 (-.f64 lambda1 lambda2) (pow.f64 (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) 6))) (*.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))
127.0ms	(pow.f64 (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) 6)
18.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

simplify153.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

205 → 205

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	5073	17943

prune491.0ms (3.5%)

Pruning

14 alts after pruning (12 fresh and 2 done)

	Pruned	Kept	Total
New	198	7	205
Fresh	0	5	5
Picked	1	0	1
Done	0	2	2
Total	199	14	213

Merged error: 14.4b

Counts

213 → 14

Compiler

Compiled 13693 to 4405 computations (67.8% saved)

regimes1.0s (7.4%)

Compiler: Compiled 10759 to 6972 computations (35.2% saved)

bsearch3.0ms (0%)

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

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	71	158
1	71	158

end0.0ms (0%)

sample3.3s (23.9%)

Algorithm

1×

intervals

Results

678.0ms	6071×	body	128	valid
370.0ms	765×	body	1024	valid
275.0ms	758×	body	512	valid
262.0ms	2324×	body	128	invalid
221.0ms	464×	body	1024	invalid
124.0ms	359×	body	512	invalid
98.0ms	402×	body	256	valid
52.0ms	191×	body	256	invalid
3.0ms	4×	body	2048	valid

Compiler

Compiled 1196 to 762 computations (36.3% saved)

Details

analyze2.2s (15.5%)

sample81.0ms (0.6%)

simplify220.0ms (1.6%)

prune4.0ms (0%)

localize17.0ms (0.1%)

rewrite76.0ms (0.5%)

series853.0ms (6.1%)

simplify98.0ms (0.7%)

prune308.0ms (2.2%)

localize17.0ms (0.1%)

rewrite96.0ms (0.7%)

series760.0ms (5.4%)

simplify181.0ms (1.3%)

prune434.0ms (3.1%)

localize21.0ms (0.2%)

rewrite68.0ms (0.5%)

series1.3s (9%)

simplify93.0ms (0.7%)

prune245.0ms (1.8%)

localize22.0ms (0.2%)

rewrite108.0ms (0.8%)

series1.8s (13%)

simplify153.0ms (1.1%)

prune491.0ms (3.5%)

regimes1.0s (7.4%)

bsearch3.0ms (0%)

simplify4.0ms (0%)

end0.0ms (0%)

sample3.3s (23.9%)

Profiling