Details

analyze2.5s (15.1%)

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)

sample256.0ms (1.5%)

Algorithm

1×

intervals

Results

189.0ms	176×	body	1024	valid
28.0ms	47×	body	512	valid
15.0ms	6×	body	2048	valid
7.0ms	18×	body	128	valid
3.0ms	9×	body	256	valid

Compiler

Compiled 49 to 39 computations (20.4% saved)

simplify175.0ms (1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (16.0ms)

Iter	Nodes	Cost
0	367	39
1	367	39

prune4.0ms (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: 14.8b

Counts

2 → 1

Compiler

Compiled 48 to 34 computations (29.2% saved)

localize25.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (sin.f64 phi1) (cos.f64 phi2))
0.2b	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
4.2b	(sin.f64 (-.f64 lambda1 lambda2))
4.4b	(cos.f64 (-.f64 lambda1 lambda2))

rewrite30.0ms (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` `sin-cos-mult_binary64_1598`
1×	`sin-diff_binary64_1578` `distribute-lft-in_binary64_1391` `distribute-rgt-in_binary64_1392` `associate-*l/_binary64_1385` `unswap-sqr_binary64_1410`

Counts

4 → 64

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

series337.0ms (2%)

Counts

4 → 12

Calls

4 calls:

210.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
65.0ms	(*.f64 (sin.f64 phi1) (cos.f64 phi2))
32.0ms	(sin.f64 (-.f64 lambda1 lambda2))
29.0ms	(cos.f64 (-.f64 lambda1 lambda2))

simplify93.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (76.0ms)

Iter	Nodes	Cost
0	4876	1051
1	4876	1051

prune103.0ms (0.6%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	67	9	76
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	68	9	77

Merged error: 8.2b

Counts

77 → 9

Compiler

Compiled 2443 to 496 computations (79.7% saved)

localize38.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (cos.f64 lambda2) (sin.f64 lambda1))
0.2b	(.f64 (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2))
0.2b	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
4.4b	(cos.f64 (-.f64 lambda1 lambda2))

rewrite36.0ms (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` `associate-l/_binary64_1385`
2×	`unswap-sqr_binary64_1410`
1×	`sub-neg_binary64_1435` `flip3--_binary64_1446` `flip--_binary64_1417` `distribute-lft-in_binary64_1391` `sin-cos-mult_binary64_1598` `distribute-rgt-in_binary64_1392`

Counts

4 → 71

Calls

4 calls:

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

series549.0ms (3.3%)

Counts

4 → 12

Calls

4 calls:

245.0ms	(.f64 (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2))
210.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
63.0ms	(*.f64 (cos.f64 lambda2) (sin.f64 lambda1))
30.0ms	(cos.f64 (-.f64 lambda1 lambda2))

simplify50.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	5119	1458

prune120.0ms (0.7%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	77	6	83
Fresh	5	3	8
Picked	1	0	1
Done	0	0	0
Total	83	9	92

Merged error: 0.1b

Counts

92 → 9

Compiler

Compiled 3375 to 549 computations (83.7% saved)

localize38.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite48.0ms (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` `associate-l/_binary64_1385`
3×	`sin-mult_binary64_1597`
2×	`associate-*r/_binary64_1384` `frac-times_binary64_1452` `cos-mult_binary64_1596` `unswap-sqr_binary64_1410`
1×	`flip3--_binary64_1446` `flip--_binary64_1417`

Counts

4 → 89

Calls

4 calls:

11.0ms	(.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (sin.f64 phi1) (cos.f64 phi2)))
10.0ms	(.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 phi1) (cos.f64 phi2)))
8.0ms	(.f64 (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2))
6.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))

series754.0ms (4.5%)

Counts

4 → 12

Calls

4 calls:

262.0ms	(.f64 (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2))
221.0ms	(.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 phi1) (cos.f64 phi2)))
208.0ms	(.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (sin.f64 phi1) (cos.f64 phi2)))
63.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))

simplify70.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5153	1911

prune173.0ms (1%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	94	7	101
Fresh	4	4	8
Picked	1	0	1
Done	0	0	0
Total	99	11	110

Merged error: 0.0b

Counts

110 → 11

Compiler

Compiled 5455 to 768 computations (85.9% saved)

localize39.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(pow.f64 (.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (sin.f64 phi1) (cos.f64 phi2))) 3)
0.2b	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
0.2b	(.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (sin.f64 phi1) (cos.f64 phi2)))
24.7b	(cbrt.f64 (pow.f64 (.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (sin.f64 phi1) (cos.f64 phi2))) 3))

rewrite51.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

31×	`add-cbrt-cube_binary64_1478` `add-exp-log_binary64_1480` `pow1_binary64_1503`
17×	`cbrt-unprod_binary64_1475` `pow-prod-down_binary64_1513` `prod-exp_binary64_1491`
10×	`add-sqr-sqrt_binary64_1464`
8×	`cbrt-prod_binary64_1473` `add-cube-cbrt_binary64_1477` `*-un-lft-identity_binary64_1442`
7×	`sin-mult_binary64_1597`
6×	`sin-cos-mult_binary64_1598` `cube-div_binary64_1471`
5×	`pow-exp_binary64_1510` `rem-cube-cbrt_binary64_1465` `pow-pow_binary64_1514`
4×	`associate-r_binary64_1382` `associate-l_binary64_1383` `add-log-exp_binary64_1481`
3×	`associate-r/_binary64_1384` `cbrt-div_binary64_1474` `pow-unpow_binary64_1519` `frac-times_binary64_1452` `associate-l/_binary64_1385`
2×	`cube-mult_binary64_1472` `cube-prod_binary64_1470` `*-commutative_binary64_1373` `sqr-pow_binary64_1414` `unpow3_binary64_1508` `unpow-prod-down_binary64_1521`
1×	`pow1/3_binary64_1524` `pow-to-exp_binary64_1511` `unswap-sqr_binary64_1410` `rem-cbrt-cube_binary64_1466`

Counts

4 → 98

Calls

4 calls:

11.0ms	(pow.f64 (.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (sin.f64 phi1) (cos.f64 phi2))) 3)
10.0ms	(.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (sin.f64 phi1) (cos.f64 phi2)))
6.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
5.0ms	(cbrt.f64 (pow.f64 (.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (sin.f64 phi1) (cos.f64 phi2))) 3))

series1.0s (6%)

Counts

4 → 12

Calls

4 calls:

509.0ms	(pow.f64 (.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (sin.f64 phi1) (cos.f64 phi2))) 3)
219.0ms	(cbrt.f64 (pow.f64 (.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (sin.f64 phi1) (cos.f64 phi2))) 3))
198.0ms	(.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (sin.f64 phi1) (cos.f64 phi2)))
81.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))

simplify71.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5753	2007

prune158.0ms (0.9%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	109	1	110
Fresh	1	9	10
Picked	1	0	1
Done	0	0	0
Total	111	10	121

Merged error: 0.0b

Counts

121 → 10

Compiler

Compiled 5698 to 863 computations (84.9% saved)

regimes801.0ms (4.8%)

Compiler: Compiled 11082 to 6503 computations (41.3% saved)

bsearch0.0ms (0%)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	160	73
1	160	73

end0.0ms (0%)

sample9.2s (54.9%)

Algorithm

1×

intervals

Results

6.0s	5316×	body	1024	valid
793.0ms	1301×	body	512	valid
473.0ms	181×	body	2048	valid
159.0ms	405×	body	256	valid
139.0ms	797×	body	128	valid

Compiler

Compiled 1836 to 1074 computations (41.5% saved)

Details

analyze2.5s (15.1%)

sample256.0ms (1.5%)

simplify175.0ms (1%)

prune4.0ms (0%)

localize25.0ms (0.2%)

rewrite30.0ms (0.2%)

series337.0ms (2%)

simplify93.0ms (0.6%)

prune103.0ms (0.6%)

localize38.0ms (0.2%)

rewrite36.0ms (0.2%)

series549.0ms (3.3%)

simplify50.0ms (0.3%)

prune120.0ms (0.7%)

localize38.0ms (0.2%)

rewrite48.0ms (0.3%)

series754.0ms (4.5%)

simplify70.0ms (0.4%)

prune173.0ms (1%)

localize39.0ms (0.2%)

rewrite51.0ms (0.3%)

series1.0s (6%)

simplify71.0ms (0.4%)

prune158.0ms (0.9%)

regimes801.0ms (4.8%)

bsearch0.0ms (0%)

simplify5.0ms (0%)

end0.0ms (0%)

sample9.2s (54.9%)

Profiling