Details

analyze2.1s (13.9%)

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)

sample86.0ms (0.6%)

Algorithm

1×

intervals

Results

19.0ms	197×	body	128	valid
13.0ms	26×	body	1024	valid
13.0ms	14×	body	1024	invalid
7.0ms	19×	body	512	valid
6.0ms	67×	body	128	invalid
4.0ms	13×	body	512	invalid
3.0ms	14×	body	256	valid
0.0ms	2×	body	256	invalid

Compiler

Compiled 65 to 48 computations (26.2% saved)

simplify309.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (144.0ms)

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: 41.0b

Counts

2 → 1

Compiler

Compiled 64 to 42 computations (34.4% saved)

localize18.0ms (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))))
3.0b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
3.0b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
37.6b	(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))))

rewrite88.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

142×	`associate-*l/_binary64_1398`
102×	`flip--_binary64_1430` `flip3--_binary64_1459`
68×	`frac-times_binary64_1465`
66×	`sqrt-div_binary64_1472`
64×	`frac-add_binary64_1463`
44×	`pow1_binary64_1516`
34×	`associate-*r/_binary64_1397`
17×	`pow-prod-down_binary64_1526`
16×	`add-cbrt-cube_binary64_1491` `add-exp-log_binary64_1493`
8×	`prod-exp_binary64_1504` `cbrt-unprod_binary64_1488`
6×	`add-sqr-sqrt_binary64_1477`
5×	`add-cube-cbrt_binary64_1490` `*-un-lft-identity_binary64_1455`
4×	`add-log-exp_binary64_1494` `pow-prod-up_binary64_1525` `pow-sqr_binary64_1428`
3×	`sqrt-prod_binary64_1471`
2×	`pow-plus_binary64_1518`
1×	`sqrt-pow1_binary64_1473` `associate-r_binary64_1395` `rem-sqrt-square_binary64_1468` `swap-sqr_binary64_1422` `flip-+_binary64_1429` `-commutative_binary64_1386` `pow2_binary64_1536` `pow1/2_binary64_1535` `flip3-+_binary64_1458` `associate-l*_binary64_1396`

Counts

4 → 135

Calls

4 calls:

23.0ms	(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))))
16.0ms	(.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))
6.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

series1.6s (11%)

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))))
288.0ms	(.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (*.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))

simplify93.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

147 → 147

Iterations

Useful iterations: 0 (20.0ms)

Iter	Nodes	Cost
0	5222	10334

prune519.0ms (3.5%)

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: 24.8b

Counts

148 → 8

Compiler

Compiled 14068 to 6084 computations (56.8% saved)

localize20.0ms (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)))
3.0b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
3.0b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
37.6b	(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))))

rewrite112.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

198×	`flip--_binary64_1430` `flip3--_binary64_1459`
196×	`frac-times_binary64_1465`
138×	`sqrt-div_binary64_1472`
136×	`frac-add_binary64_1463`
130×	`associate-*l/_binary64_1398`
74×	`associate-*r/_binary64_1397`
73×	`cos-mult_binary64_1609`
12×	`add-sqr-sqrt_binary64_1477` `pow1_binary64_1516`
9×	`add-cube-cbrt_binary64_1490` `*-un-lft-identity_binary64_1455`
6×	`add-cbrt-cube_binary64_1491` `add-exp-log_binary64_1493`
4×	`add-log-exp_binary64_1494`
3×	`associate-r_binary64_1395` `sqrt-prod_binary64_1471` `swap-sqr_binary64_1422` `associate-l_binary64_1396`
1×	`prod-exp_binary64_1504` `sqrt-pow1_binary64_1473` `rem-sqrt-square_binary64_1468` `flip-+_binary64_1429` `pow-plus_binary64_1518` `*-commutative_binary64_1386` `pow2_binary64_1536` `cbrt-unprod_binary64_1488` `pow1/2_binary64_1535` `flip3-+_binary64_1458` `pow-prod-up_binary64_1525` `pow-prod-down_binary64_1526` `sqr-cos-a_binary64_1604` `unswap-sqr_binary64_1423` `pow-sqr_binary64_1428`

Counts

4 → 192

Calls

4 calls:

30.0ms	(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))))
6.0ms	(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 (9.5%)

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))))
65.0ms	(*.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))
29.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
25.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

simplify189.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

204 → 204

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	5086	17276

prune566.0ms (3.8%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	199	5	204
Fresh	2	5	7
Picked	1	0	1
Done	0	0	0
Total	202	10	212

Merged error: 24.4b

Counts

212 → 10

Compiler

Compiled 16304 to 6094 computations (62.6% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(.f64 (.f64 (-.f64 lambda1 lambda2) (-.f64 lambda1 lambda2)) (pow.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) 2))
0.4b	(pow.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) 2)
3.0b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
37.6b	(sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (-.f64 lambda1 lambda2)) (pow.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) 2)) (pow.f64 (-.f64 phi1 phi2) 2)))

rewrite56.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-exp-log_binary64_1493`
12×	`add-sqr-sqrt_binary64_1477`
10×	`associate-*l/_binary64_1398`
9×	`prod-exp_binary64_1504` `add-cbrt-cube_binary64_1491` `add-cube-cbrt_binary64_1490` `*-un-lft-identity_binary64_1455`
8×	`associate-r_binary64_1395`
7×	`unpow-prod-down_binary64_1534`
6×	`pow1_binary64_1516` `flip--_binary64_1430` `flip3--_binary64_1459`
4×	`add-log-exp_binary64_1494` `frac-times_binary64_1465` `unswap-sqr_binary64_1423`
3×	`sqrt-prod_binary64_1471` `unpow2_binary64_1520` `pow-to-exp_binary64_1524` `sqr-pow_binary64_1427` `cbrt-unprod_binary64_1488` `pow-exp_binary64_1523` `pow-unpow_binary64_1532`
2×	`associate-*r/_binary64_1397` `sqrt-div_binary64_1472`
1×	`sqrt-pow1_binary64_1473` `rem-sqrt-square_binary64_1468` `flip-+_binary64_1429` `-commutative_binary64_1386` `pow-pow_binary64_1527` `pow2_binary64_1536` `pow1/2_binary64_1535` `flip3-+_binary64_1458` `associate-l*_binary64_1396` `pow-prod-down_binary64_1526`

Counts

4 → 78

Calls

4 calls:

20.0ms	(sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (-.f64 lambda1 lambda2)) (pow.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) 2)) (pow.f64 (-.f64 phi1 phi2) 2)))
19.0ms	(.f64 (.f64 (-.f64 lambda1 lambda2) (-.f64 lambda1 lambda2)) (pow.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) 2))
5.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
3.0ms	(pow.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) 2)

series1.7s (11.4%)

Counts

4 → 12

Calls

4 calls:

1.3s	(sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (-.f64 lambda1 lambda2)) (pow.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) 2)) (pow.f64 (-.f64 phi1 phi2) 2)))
307.0ms	(.f64 (.f64 (-.f64 lambda1 lambda2) (-.f64 lambda1 lambda2)) (pow.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) 2))
58.0ms	(pow.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) 2)
27.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

simplify79.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4986	2059
1	4986	2059

prune177.0ms (1.2%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	89	1	90
Fresh	1	8	9
Picked	0	1	1
Done	0	0	0
Total	90	10	100

Merged error: 24.4b

Counts

100 → 10

Compiler

Compiled 3799 to 2261 computations (40.5% saved)

localize22.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.6b	(pow.f64 (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) 4)
3.0b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
3.0b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
37.6b	(sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (-.f64 lambda1 lambda2)) (.f64 (pow.f64 (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) 4) (pow.f64 (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) 2))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))

rewrite75.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

96×	`flip--_binary64_1430` `flip3--_binary64_1459` `associate-*l/_binary64_1398`
66×	`sqrt-div_binary64_1472`
64×	`frac-times_binary64_1465` `frac-add_binary64_1463`
32×	`associate-*r/_binary64_1397`
9×	`add-sqr-sqrt_binary64_1477`
8×	`add-cube-cbrt_binary64_1490` `*-un-lft-identity_binary64_1455`
6×	`pow1_binary64_1516` `unpow-prod-down_binary64_1534`
5×	`add-exp-log_binary64_1493`
4×	`add-log-exp_binary64_1494` `add-cbrt-cube_binary64_1491`
3×	`sqrt-prod_binary64_1471` `cbrt-prod_binary64_1486` `pow-unpow_binary64_1532`
2×	`pow-pow_binary64_1527`
1×	`sqrt-pow1_binary64_1473` `pow1/3_binary64_1537` `rem-sqrt-square_binary64_1468` `flip-+_binary64_1429` `pow-to-exp_binary64_1524` `sqr-pow_binary64_1427` `pow1/2_binary64_1535` `flip3-+_binary64_1458` `pow-exp_binary64_1523`

Counts

4 → 114

Calls

4 calls:

30.0ms	(sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (-.f64 lambda1 lambda2)) (.f64 (pow.f64 (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) 4) (pow.f64 (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) 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))
3.0ms	(pow.f64 (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) 4)

series1.9s (12.6%)

Counts

4 → 12

Calls

4 calls:

1.5s	(sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (-.f64 lambda1 lambda2)) (.f64 (pow.f64 (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) 4) (pow.f64 (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) 2))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))
331.0ms	(pow.f64 (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) 4)
29.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
26.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

simplify92.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 0 (21.0ms)

Iter	Nodes	Cost
0	5342	9460

prune295.0ms (2%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	126	0	126
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	126	10	136

Merged error: 24.4b

Counts

136 → 10

Compiler

Compiled 8402 to 3095 computations (63.2% saved)

regimes385.0ms (2.6%)

Compiler: Compiled 2498 to 1933 computations (22.6% saved)

bsearch2.0ms (0%)

Compiler: Compiled 29 to 19 computations (34.5% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	65	94
1	65	94

end0.0ms (0%)

sample2.9s (19.8%)

Algorithm

1×

intervals

Results

623.0ms	5999×	body	128	valid
459.0ms	824×	body	1024	valid
261.0ms	494×	body	1024	invalid
259.0ms	734×	body	512	valid
242.0ms	2415×	body	128	invalid
133.0ms	379×	body	512	invalid
111.0ms	440×	body	256	valid
39.0ms	173×	body	256	invalid
3.0ms	3×	body	2048	valid

Compiler

Compiled 373 to 273 computations (26.8% saved)

Details

analyze2.1s (13.9%)

sample86.0ms (0.6%)

simplify309.0ms (2.1%)

prune4.0ms (0%)

localize18.0ms (0.1%)

rewrite88.0ms (0.6%)

series1.6s (11%)

simplify93.0ms (0.6%)

prune519.0ms (3.5%)

localize20.0ms (0.1%)

rewrite112.0ms (0.8%)

series1.4s (9.5%)

simplify189.0ms (1.3%)

prune566.0ms (3.8%)

localize19.0ms (0.1%)

rewrite56.0ms (0.4%)

series1.7s (11.4%)

simplify79.0ms (0.5%)

prune177.0ms (1.2%)

localize22.0ms (0.1%)

rewrite75.0ms (0.5%)

series1.9s (12.6%)

simplify92.0ms (0.6%)

prune295.0ms (2%)

regimes385.0ms (2.6%)

bsearch2.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample2.9s (19.8%)

Profiling