Details

analyze2.2s (9.8%)

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)

sample89.0ms (0.4%)

Algorithm

1×

intervals

Results

20.0ms	36×	body	1024	valid
19.0ms	181×	body	128	valid
9.0ms	25×	body	512	valid
7.0ms	13×	body	1024	invalid
7.0ms	65×	body	128	invalid
4.0ms	12×	body	512	invalid
4.0ms	14×	body	256	valid
2.0ms	7×	body	256	invalid

Compiler

Compiled 65 to 48 computations (26.2% saved)

simplify305.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (134.0ms)

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: 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))))

rewrite75.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

130×	`associate-*l/_binary64_1370`
97×	`flip--_binary64_1400` `flip3--_binary64_1429`
66×	`sqrt-div_binary64_1441`
64×	`frac-add_binary64_1433` `frac-times_binary64_1435`
32×	`associate-*r/_binary64_1369`
12×	`add-sqr-sqrt_binary64_1446`
9×	`*-un-lft-identity_binary64_1425`
7×	`add-cube-cbrt_binary64_1457` `pow1_binary64_1483`
6×	`add-cbrt-cube_binary64_1458` `add-exp-log_binary64_1460`
5×	`associate-l_binary64_1368`
4×	`add-log-exp_binary64_1461`
3×	`associate-r_binary64_1367` `sqrt-prod_binary64_1440`
1×	`distribute-lft-out--_binary64_1379` `unswap-sqr_binary64_1393` `prod-exp_binary64_1471` `flip3-+_binary64_1428` `pow1/2_binary64_1502` `cbrt-unprod_binary64_1455` `sqrt-pow1_binary64_1442` `difference-of-squares_binary64_1394` `flip-+_binary64_1399` `rem-sqrt-square_binary64_1438` `*-commutative_binary64_1358` `pow-prod-down_binary64_1493`

Counts

4 → 115

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

series1.5s (6.9%)

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))))
155.0ms	(*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))
29.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
29.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

simplify92.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 0 (19.0ms)

Iter	Nodes	Cost
0	5098	9677

prune268.0ms (1.2%)

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 8163 to 2685 computations (67.1% saved)

localize21.0ms (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))))

rewrite133.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

256×	`associate-*l/_binary64_1370`
192×	`flip--_binary64_1400` `flip3--_binary64_1429`
132×	`cbrt-div_binary64_1454`
128×	`frac-add_binary64_1433` `frac-times_binary64_1435`
64×	`associate-*r/_binary64_1369`
6×	`add-cube-cbrt_binary64_1457` `cbrt-prod_binary64_1453` `add-sqr-sqrt_binary64_1446` `*-un-lft-identity_binary64_1425`
4×	`add-cbrt-cube_binary64_1458` `pow1_binary64_1483` `add-exp-log_binary64_1460` `add-log-exp_binary64_1461`
2×	`flip3-+_binary64_1428` `pow1/3_binary64_1504` `flip-+_binary64_1399`

Counts

4 → 168

Calls

4 calls:

26.0ms	(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 (16.1%)

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))))
26.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
25.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

simplify149.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

180 → 180

Iterations

Useful iterations: 0 (22.0ms)

Iter	Nodes	Cost
0	5487	18484

prune683.0ms (3.1%)

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 19574 to 6675 computations (65.9% saved)

localize24.0ms (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))))

rewrite131.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

256×	`associate-*l/_binary64_1370`
192×	`flip--_binary64_1400` `flip3--_binary64_1429`
132×	`sqrt-div_binary64_1441`
128×	`frac-add_binary64_1433` `frac-times_binary64_1435`
66×	`exp-diff_binary64_1470` `log-div_binary64_1509`
64×	`associate-*r/_binary64_1369`
9×	`add-sqr-sqrt_binary64_1446`
8×	`add-cube-cbrt_binary64_1457` `*-un-lft-identity_binary64_1425`
7×	`pow1_binary64_1483`
6×	`sqrt-prod_binary64_1440` `exp-prod_binary64_1474` `log-prod_binary64_1508` `exp-sum_binary64_1468`
4×	`add-cbrt-cube_binary64_1458` `add-exp-log_binary64_1460` `add-log-exp_binary64_1461`
3×	`log-pow_binary64_1511`
2×	`flip3-+_binary64_1428` `pow1/2_binary64_1502` `sqrt-pow1_binary64_1442` `flip-+_binary64_1399`
1×	`rem-exp-log_binary64_1462` `rem-sqrt-square_binary64_1438`

Counts

4 → 179

Calls

4 calls:

31.0ms	(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))))))
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))))
6.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
6.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

series3.1s (14.1%)

Counts

4 → 12

Calls

4 calls:

1.8s	(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))))))
1.3s	(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))))
26.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
26.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

simplify148.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

191 → 191

Iterations

Useful iterations: 0 (22.0ms)

Iter	Nodes	Cost
0	5180	18510

prune618.0ms (2.8%)

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 14304 to 4621 computations (67.7% saved)

localize31.0ms (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))))

rewrite133.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

256×	`associate-*l/_binary64_1370`
192×	`flip--_binary64_1400` `flip3--_binary64_1429`
132×	`log-div_binary64_1509`
128×	`frac-add_binary64_1433` `frac-times_binary64_1435`
66×	`pow-sub_binary64_1498`
64×	`associate-*r/_binary64_1369`
9×	`add-cube-cbrt_binary64_1457` `add-sqr-sqrt_binary64_1446` `*-un-lft-identity_binary64_1425`
7×	`pow1_binary64_1483`
6×	`log-prod_binary64_1508`
5×	`add-exp-log_binary64_1460`
4×	`pow-pow_binary64_1494` `pow-unpow_binary64_1499` `add-cbrt-cube_binary64_1458` `add-log-exp_binary64_1461`
3×	`unpow-prod-up_binary64_1500` `unpow-prod-down_binary64_1501` `exp-prod_binary64_1474`
2×	`flip3-+_binary64_1428` `flip-+_binary64_1399` `log-pow_binary64_1511`
1×	`pow-to-exp_binary64_1491` `pow-exp_binary64_1490` `rem-log-exp_binary64_1463` `sqr-pow_binary64_1397`

Counts

4 → 182

Calls

4 calls:

31.0ms	(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)))))
25.0ms	(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 (14.9%)

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))))
29.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
26.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

simplify158.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

194 → 194

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	4978	20063
1	4978	20063

prune560.0ms (2.5%)

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 14857 to 5051 computations (66% saved)

regimes1.2s (5.2%)

Compiler: Compiled 13640 to 8779 computations (35.6% saved)

bsearch4.0ms (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	61	166
1	61	166

end0.0ms (0%)

sample3.7s (16.5%)

Algorithm

1×

intervals

Results

683.0ms	5974×	body	128	valid
489.0ms	880×	body	1024	valid
279.0ms	747×	body	512	valid
266.0ms	489×	body	1024	invalid
256.0ms	2433×	body	128	invalid
131.0ms	371×	body	512	invalid
97.0ms	391×	body	256	valid
48.0ms	201×	body	256	invalid
8.0ms	8×	body	2048	valid

Compiler

Compiled 1396 to 895 computations (35.9% saved)

Details

analyze2.2s (9.8%)

sample89.0ms (0.4%)

simplify305.0ms (1.4%)

prune3.0ms (0%)

localize17.0ms (0.1%)

rewrite75.0ms (0.3%)

series1.5s (6.9%)

simplify92.0ms (0.4%)

prune268.0ms (1.2%)

localize21.0ms (0.1%)

rewrite133.0ms (0.6%)

series3.6s (16.1%)

simplify149.0ms (0.7%)

prune683.0ms (3.1%)

localize24.0ms (0.1%)

rewrite131.0ms (0.6%)

series3.1s (14.1%)

simplify148.0ms (0.7%)

prune618.0ms (2.8%)

localize31.0ms (0.1%)

rewrite133.0ms (0.6%)

series3.3s (14.9%)

simplify158.0ms (0.7%)

prune560.0ms (2.5%)

regimes1.2s (5.2%)

bsearch4.0ms (0%)

simplify4.0ms (0%)

end0.0ms (0%)

sample3.7s (16.5%)

Profiling