Details

analyze2.2s (15.3%)

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)

sample88.0ms (0.6%)

Algorithm

1×

intervals

Results

20.0ms	191×	body	128	valid
14.0ms	25×	body	1024	valid
10.0ms	27×	body	512	valid
9.0ms	85×	body	128	invalid
7.0ms	14×	body	1024	invalid
5.0ms	14×	body	512	invalid
3.0ms	12×	body	256	valid
2.0ms	7×	body	256	invalid
1.0ms	1×	body	2048	valid

Compiler

Compiled 65 to 48 computations (26.2% saved)

simplify303.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (136.0ms)

Iter	Nodes	Cost
0	4986	49
1	4986	49

prune3.0ms (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: 38.4b

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))))
2.4b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
2.4b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
35.7b	(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))))

rewrite87.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

142×	`associate-*l/_binary64_696`
102×	`flip--_binary64_726` `flip3--_binary64_755`
68×	`frac-times_binary64_761`
66×	`sqrt-div_binary64_767`
64×	`frac-add_binary64_759`
44×	`pow1_binary64_809`
34×	`associate-*r/_binary64_695`
17×	`pow-prod-down_binary64_819`
16×	`add-cbrt-cube_binary64_784` `add-exp-log_binary64_786`
8×	`prod-exp_binary64_797` `cbrt-unprod_binary64_781`
6×	`add-sqr-sqrt_binary64_772`
5×	`add-cube-cbrt_binary64_783` `*-un-lft-identity_binary64_751`
4×	`pow-sqr_binary64_724` `add-log-exp_binary64_787` `pow-prod-up_binary64_818`
3×	`sqrt-prod_binary64_766`
2×	`pow-plus_binary64_811`
1×	`flip3-+_binary64_754` `rem-sqrt-square_binary64_764` `pow1/2_binary64_828` `-commutative_binary64_684` `swap-sqr_binary64_718` `associate-l_binary64_694` `associate-r*_binary64_693` `pow2_binary64_829` `sqrt-pow1_binary64_768` `flip-+_binary64_725`

Counts

4 → 135

Calls

4 calls:

26.0ms	(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))))
14.0ms	(.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (*.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))

series1.8s (12.9%)

Counts

4 → 12

Calls

4 calls:

1.5s	(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))))
286.0ms	(.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))
26.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
25.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

simplify96.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

147 → 147

Iterations

Useful iterations: 0 (19.0ms)

Iter	Nodes	Cost
0	5181	10334

prune300.0ms (2.1%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	140	7	147
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	141	7	148

Merged error: 25.3b

Counts

148 → 7

Compiler

Compiled 8779 to 2936 computations (66.6% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b	(*.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))
2.4b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
2.4b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
35.7b	(sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (-.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))))

rewrite115.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

198×	`flip--_binary64_726` `flip3--_binary64_755`
196×	`frac-times_binary64_761`
138×	`sqrt-div_binary64_767`
136×	`frac-add_binary64_759`
130×	`associate-*l/_binary64_696`
74×	`associate-*r/_binary64_695`
73×	`cos-mult_binary64_902`
12×	`pow1_binary64_809` `add-sqr-sqrt_binary64_772`
9×	`add-cube-cbrt_binary64_783` `*-un-lft-identity_binary64_751`
6×	`add-cbrt-cube_binary64_784` `add-exp-log_binary64_786`
4×	`add-log-exp_binary64_787`
3×	`swap-sqr_binary64_718` `associate-l_binary64_694` `sqrt-prod_binary64_766` `associate-r_binary64_693`
1×	`prod-exp_binary64_797` `unswap-sqr_binary64_719` `flip3-+_binary64_754` `rem-sqrt-square_binary64_764` `pow1/2_binary64_828` `pow-plus_binary64_811` `pow-sqr_binary64_724` `pow-prod-up_binary64_818` `pow-prod-down_binary64_819` `*-commutative_binary64_684` `cbrt-unprod_binary64_781` `pow2_binary64_829` `sqr-cos-a_binary64_897` `sqrt-pow1_binary64_768` `flip-+_binary64_725`

Counts

4 → 192

Calls

4 calls:

31.0ms	(sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (-.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)))

series1.4s (10%)

Counts

4 → 12

Calls

4 calls:

1.3s	(sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (-.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))))
61.0ms	(*.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))
30.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
27.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

simplify205.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

204 → 204

Iterations

Useful iterations: 0 (74.0ms)

Iter	Nodes	Cost
0	4942	17322
1	4942	17322

prune424.0ms (3%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	201	3	204
Fresh	1	5	6
Picked	1	0	1
Done	0	0	0
Total	203	8	211

Merged error: 24.2b

Counts

211 → 8

Compiler

Compiled 13626 to 4252 computations (68.8% saved)

localize21.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.5b	(pow.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) 3)
2.4b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
2.4b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
35.7b	(sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (.f64 (-.f64 lambda1 lambda2) (cbrt.f64 (pow.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) 3)))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))

rewrite70.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

128×	`associate-*l/_binary64_696`
96×	`flip--_binary64_726` `flip3--_binary64_755`
66×	`sqrt-div_binary64_767`
64×	`frac-times_binary64_761` `frac-add_binary64_759`
32×	`associate-*r/_binary64_695`
9×	`add-sqr-sqrt_binary64_772`
8×	`add-cube-cbrt_binary64_783` `*-un-lft-identity_binary64_751`
6×	`pow1_binary64_809`
5×	`add-cbrt-cube_binary64_784` `add-exp-log_binary64_786`
4×	`add-log-exp_binary64_787`
3×	`unpow-prod-down_binary64_827` `sqrt-prod_binary64_766` `pow-unpow_binary64_825` `cube-prod_binary64_776`
1×	`cube-mult_binary64_778` `pow-to-exp_binary64_817` `flip3-+_binary64_754` `pow-exp_binary64_816` `sqr-pow_binary64_723` `rem-sqrt-square_binary64_764` `pow1/2_binary64_828` `rem-cube-cbrt_binary64_773` `pow-pow_binary64_820` `unpow3_binary64_814` `sqrt-pow1_binary64_768` `flip-+_binary64_725`

Counts

4 → 116

Calls

4 calls:

24.0ms	(sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (.f64 (-.f64 lambda1 lambda2) (cbrt.f64 (pow.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) 3)))) (.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))
3.0ms	(pow.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) 3)

series1.5s (10.3%)

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) (cbrt.f64 (pow.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) 3)))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))
94.0ms	(pow.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) 3)
27.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
25.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

simplify89.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 0 (19.0ms)

Iter	Nodes	Cost
0	5106	9242

prune262.0ms (1.9%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	128	0	128
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	128	8	136

Merged error: 24.2b

Counts

136 → 8

Compiler

Compiled 8154 to 2791 computations (65.8% saved)

localize26.0ms (0.2%)

Local error

Found 4 expressions with local error:

2.4b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
2.4b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
2.4b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
35.7b	(sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (.f64 (-.f64 lambda1 lambda2) (.f64 (.f64 (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))) (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))

rewrite83.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

128×	`associate-*l/_binary64_696`
96×	`flip--_binary64_726` `flip3--_binary64_755`
66×	`sqrt-div_binary64_767`
64×	`frac-times_binary64_761` `frac-add_binary64_759`
32×	`associate-*r/_binary64_695`
6×	`add-sqr-sqrt_binary64_772`
5×	`add-cube-cbrt_binary64_783` `pow1_binary64_809` `*-un-lft-identity_binary64_751`
4×	`add-log-exp_binary64_787` `add-cbrt-cube_binary64_784` `add-exp-log_binary64_786`
3×	`sqrt-prod_binary64_766`
1×	`flip3-+_binary64_754` `rem-sqrt-square_binary64_764` `pow1/2_binary64_828` `sqrt-pow1_binary64_768` `flip-+_binary64_725`

Counts

4 → 100

Calls

4 calls:

32.0ms	(sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (.f64 (-.f64 lambda1 lambda2) (.f64 (.f64 (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))) (cbrt.f64 (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))
6.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

series1.4s (10.2%)

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) (.f64 (.f64 (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))) (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))
32.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
32.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
26.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

simplify97.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 0 (19.0ms)

Iter	Nodes	Cost
0	5554	9867

prune275.0ms (1.9%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	112	0	112
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	112	8	120

Merged error: 24.2b

Counts

120 → 8

Compiler

Compiled 8315 to 3003 computations (63.9% saved)

regimes264.0ms (1.9%)

Compiler: Compiled 1734 to 1274 computations (26.5% saved)

bsearch68.0ms (0.5%)

Steps

Iters	Range		Point
7	-3.387717681765664e+96	-1.9564235207466203e+94	-9.716029243139434e+95

Compiler

Compiled 1 to 5 computations (-400% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	61	67
1	61	67

end0.0ms (0%)

sample2.9s (20.6%)

Algorithm

1×

intervals

Results

651.0ms	6037×	body	128	valid
430.0ms	787×	body	1024	valid
273.0ms	745×	body	512	valid
267.0ms	483×	body	1024	invalid
243.0ms	2385×	body	128	invalid
134.0ms	362×	body	512	invalid
116.0ms	425×	body	256	valid
39.0ms	169×	body	256	invalid
6.0ms	6×	body	2048	valid

Compiler

Compiled 339 to 240 computations (29.2% saved)

Details

analyze2.2s (15.3%)

sample88.0ms (0.6%)

simplify303.0ms (2.1%)

prune3.0ms (0%)

localize17.0ms (0.1%)

rewrite87.0ms (0.6%)

series1.8s (12.9%)

simplify96.0ms (0.7%)

prune300.0ms (2.1%)

localize19.0ms (0.1%)

rewrite115.0ms (0.8%)

series1.4s (10%)

simplify205.0ms (1.5%)

prune424.0ms (3%)

localize21.0ms (0.1%)

rewrite70.0ms (0.5%)

series1.5s (10.3%)

simplify89.0ms (0.6%)

prune262.0ms (1.9%)

localize26.0ms (0.2%)

rewrite83.0ms (0.6%)

series1.4s (10.2%)

simplify97.0ms (0.7%)

prune275.0ms (1.9%)

regimes264.0ms (1.9%)

bsearch68.0ms (0.5%)

simplify3.0ms (0%)

end0.0ms (0%)

sample2.9s (20.6%)

Profiling