Details

analyze2.5s (18.7%)

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
7.8%	92%	0.2%	9
7.8%	92%	0.2%	10
10.1%	89.7%	0.2%	11
10.1%	89.7%	0.2%	12
13.9%	85.9%	0.2%	13
13.9%	85.9%	0.2%	14

Compiler

Compiled 25 to 18 computations (28% saved)

sample215.0ms (1.6%)

Algorithm

1×

intervals

Results

157.0ms	177×	body	1024	valid
20.0ms	39×	body	512	valid
17.0ms	9×	body	2048	valid
4.0ms	23×	body	128	valid
3.0ms	8×	body	256	valid

Compiler

Compiled 49 to 39 computations (20.4% saved)

simplify118.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (16.0ms)

Iter	Nodes	Cost
0	385	39
1	385	39

prune3.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 12.8b

Counts

2 → 1

Compiler

Compiled 48 to 34 computations (29.2% saved)

localize20.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (cos.f64 phi1) (sin.f64 phi2))
0.2b	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
3.3b	(sin.f64 (-.f64 lambda1 lambda2))
3.3b	(cos.f64 (-.f64 lambda1 lambda2))

rewrite31.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`add-cbrt-cube_binary64_1478` `add-exp-log_binary64_1480` `add-sqr-sqrt_binary64_1464` `pow1_binary64_1503`
9×	`add-cube-cbrt_binary64_1477` `*-un-lft-identity_binary64_1442`
6×	`associate-r_binary64_1382` `cancel-sign-sub-inv_binary64_1408`
4×	`sin-sum_binary64_1575` `cbrt-unprod_binary64_1475` `associate-l_binary64_1383` `pow-prod-down_binary64_1513` `add-log-exp_binary64_1481` `prod-exp_binary64_1491` `cos-sum_binary64_1576`
3×	`cos-diff_binary64_1579`
2×	`sub-neg_binary64_1435` `*-commutative_binary64_1373`
1×	`sin-diff_binary64_1578` `distribute-lft-in_binary64_1391` `sin-cos-mult_binary64_1598` `distribute-rgt-in_binary64_1392` `associate-*l/_binary64_1385` `unswap-sqr_binary64_1410`

Counts

4 → 63

Calls

4 calls:

8.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
5.0ms	(cos.f64 (-.f64 lambda1 lambda2))
5.0ms	(*.f64 (cos.f64 phi1) (sin.f64 phi2))
5.0ms	(sin.f64 (-.f64 lambda1 lambda2))

series187.0ms (1.4%)

Counts

4 → 12

Calls

4 calls:

111.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
41.0ms	(*.f64 (cos.f64 phi1) (sin.f64 phi2))
19.0ms	(sin.f64 (-.f64 lambda1 lambda2))
16.0ms	(cos.f64 (-.f64 lambda1 lambda2))

simplify102.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 0 (86.0ms)

Iter	Nodes	Cost
0	4860	1037
1	4860	1037

prune111.0ms (0.8%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	63	12	75
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	64	12	76

Merged error: 6.0b

Counts

76 → 12

Compiler

Compiled 2491 to 531 computations (78.7% saved)

localize31.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (cos.f64 lambda2) (sin.f64 lambda1))
0.2b	(*.f64 (cos.f64 phi1) (sin.f64 phi2))
0.2b	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
3.3b	(cos.f64 (-.f64 lambda1 lambda2))

rewrite31.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64_1464`
13×	`add-cbrt-cube_binary64_1478` `add-exp-log_binary64_1480` `pow1_binary64_1503`
10×	`add-cube-cbrt_binary64_1477` `*-un-lft-identity_binary64_1442`
9×	`associate-r_binary64_1382`
7×	`associate-l_binary64_1383`
5×	`cbrt-unprod_binary64_1475` `pow-prod-down_binary64_1513` `prod-exp_binary64_1491`
4×	`add-log-exp_binary64_1481` `cos-sum_binary64_1576`
3×	`cancel-sign-sub-inv_binary64_1408` `*-commutative_binary64_1373` `cos-diff_binary64_1579`
2×	`unswap-sqr_binary64_1410`
1×	`sub-neg_binary64_1435` `distribute-lft-in_binary64_1391` `sin-cos-mult_binary64_1598` `distribute-rgt-in_binary64_1392` `associate-*l/_binary64_1385`

Counts

4 → 69

Calls

4 calls:

8.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
5.0ms	(*.f64 (cos.f64 lambda2) (sin.f64 lambda1))
5.0ms	(cos.f64 (-.f64 lambda1 lambda2))
5.0ms	(*.f64 (cos.f64 phi1) (sin.f64 phi2))

series210.0ms (1.6%)

Counts

4 → 12

Calls

4 calls:

112.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
43.0ms	(*.f64 (cos.f64 phi1) (sin.f64 phi2))
38.0ms	(*.f64 (cos.f64 lambda2) (sin.f64 lambda1))
16.0ms	(cos.f64 (-.f64 lambda1 lambda2))

simplify85.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	4870	1089
1	4870	1089

prune118.0ms (0.9%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	77	4	81
Fresh	5	6	11
Picked	1	0	1
Done	0	0	0
Total	83	10	93

Merged error: 0.1b

Counts

93 → 10

Compiler

Compiled 3202 to 565 computations (82.4% saved)

localize31.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (cos.f64 phi1) (sin.f64 phi2))
0.2b	(.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (sin.f64 phi1) (cos.f64 phi2)))
0.2b	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
0.3b	(.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 phi1) (cos.f64 phi2)))

rewrite44.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`add-cbrt-cube_binary64_1478` `add-exp-log_binary64_1480` `pow1_binary64_1503`
18×	`cbrt-unprod_binary64_1475` `pow-prod-down_binary64_1513` `prod-exp_binary64_1491`
12×	`add-sqr-sqrt_binary64_1464`
8×	`associate-r_binary64_1382` `associate-l_binary64_1383` `add-cube-cbrt_binary64_1477` `*-un-lft-identity_binary64_1442`
4×	`*-commutative_binary64_1373` `add-log-exp_binary64_1481` `sin-cos-mult_binary64_1598`
3×	`sin-mult_binary64_1597`
2×	`associate-r/_binary64_1384` `frac-times_binary64_1452` `cos-mult_binary64_1596` `associate-l/_binary64_1385` `unswap-sqr_binary64_1410`

Counts

4 → 87

Calls

4 calls:

11.0ms	(.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 phi1) (cos.f64 phi2)))
10.0ms	(.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (sin.f64 phi1) (cos.f64 phi2)))
5.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
5.0ms	(*.f64 (cos.f64 phi1) (sin.f64 phi2))

series347.0ms (2.6%)

Counts

4 → 12

Calls

4 calls:

139.0ms	(.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 phi1) (cos.f64 phi2)))
126.0ms	(.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (sin.f64 phi1) (cos.f64 phi2)))
42.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
40.0ms	(*.f64 (cos.f64 phi1) (sin.f64 phi2))

simplify73.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4933	1542
1	4933	1542

prune164.0ms (1.2%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	92	7	99
Fresh	4	5	9
Picked	1	0	1
Done	0	0	0
Total	97	12	109

Merged error: 0.0b

Counts

109 → 12

Compiler

Compiled 5238 to 769 computations (85.3% saved)

localize34.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (cos.f64 phi1) (sin.f64 phi2))
0.2b	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (sin.f64 lambda2))
0.3b	(.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 phi1) (cos.f64 phi2)))
0.3b	(.f64 (sin.f64 lambda1) (.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (sin.f64 lambda2)))

rewrite45.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`add-cbrt-cube_binary64_1478` `add-exp-log_binary64_1480` `pow1_binary64_1503`
18×	`cbrt-unprod_binary64_1475` `pow-prod-down_binary64_1513` `prod-exp_binary64_1491`
10×	`add-sqr-sqrt_binary64_1464`
8×	`associate-r_binary64_1382` `associate-l_binary64_1383` `add-cube-cbrt_binary64_1477` `*-un-lft-identity_binary64_1442`
4×	`*-commutative_binary64_1373` `add-log-exp_binary64_1481` `sin-cos-mult_binary64_1598`
3×	`associate-*l/_binary64_1385`
2×	`associate-*r/_binary64_1384` `cos-mult_binary64_1596`
1×	`frac-times_binary64_1452` `unswap-sqr_binary64_1410`

Counts

4 → 84

Calls

4 calls:

11.0ms	(.f64 (sin.f64 lambda1) (.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (sin.f64 lambda2)))
9.0ms	(.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 phi1) (cos.f64 phi2)))
7.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (sin.f64 lambda2))
5.0ms	(*.f64 (cos.f64 phi1) (sin.f64 phi2))

series365.0ms (2.7%)

Counts

4 → 12

Calls

4 calls:

128.0ms	(.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 phi1) (cos.f64 phi2)))
121.0ms	(.f64 (sin.f64 lambda1) (.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (sin.f64 lambda2)))
71.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (sin.f64 lambda2))
45.0ms	(*.f64 (cos.f64 phi1) (sin.f64 phi2))

simplify75.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4949	1555
1	4949	1555

prune130.0ms (1%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	95	1	96
Fresh	1	10	11
Picked	1	0	1
Done	0	0	0
Total	97	11	108

Merged error: 0.0b

Counts

108 → 11

Compiler

Compiled 4562 to 450 computations (90.1% saved)

regimes719.0ms (5.4%)

Compiler: Compiled 10041 to 6311 computations (37.1% saved)

bsearch0.0ms (0%)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	148	73
1	148	73

end0.0ms (0%)

sample7.6s (56.7%)

Algorithm

1×

intervals

Results

4.6s	5321×	body	1024	valid
738.0ms	1315×	body	512	valid
376.0ms	195×	body	2048	valid
143.0ms	406×	body	256	valid
132.0ms	763×	body	128	valid

Compiler

Compiled 1644 to 1027 computations (37.5% saved)

Details

analyze2.5s (18.7%)

sample215.0ms (1.6%)

simplify118.0ms (0.9%)

prune3.0ms (0%)

localize20.0ms (0.1%)

rewrite31.0ms (0.2%)

series187.0ms (1.4%)

simplify102.0ms (0.8%)

prune111.0ms (0.8%)

localize31.0ms (0.2%)

rewrite31.0ms (0.2%)

series210.0ms (1.6%)

simplify85.0ms (0.6%)

prune118.0ms (0.9%)

localize31.0ms (0.2%)

rewrite44.0ms (0.3%)

series347.0ms (2.6%)

simplify73.0ms (0.5%)

prune164.0ms (1.2%)

localize34.0ms (0.3%)

rewrite45.0ms (0.3%)

series365.0ms (2.7%)

simplify75.0ms (0.6%)

prune130.0ms (1%)

regimes719.0ms (5.4%)

bsearch0.0ms (0%)

simplify4.0ms (0%)

end0.0ms (0%)

sample7.6s (56.7%)

Profiling