Details

analyze2.8s (19.5%)

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)

sample222.0ms (1.6%)

Algorithm

1×

intervals

Results

171.0ms	181×	body	1024	valid
23.0ms	38×	body	512	valid
6.0ms	3×	body	2048	valid
4.0ms	24×	body	128	valid
4.0ms	10×	body	256	valid

Compiler

Compiled 49 to 39 computations (20.4% saved)

simplify111.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (17.0ms)

Iter	Nodes	Cost
0	385	39
1	385	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

Error

12.7b

Counts

2 → 1

Compiler

Compiled 48 to 34 computations (29.2% saved)

localize21.0ms (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)))
2.2b	(cos.f64 (-.f64 lambda1 lambda2))
2.4b	(sin.f64 (-.f64 lambda1 lambda2))

rewrite33.0ms (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 (cos.f64 phi1) (sin.f64 phi2))
8.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
6.0ms	(sin.f64 (-.f64 lambda1 lambda2))
5.0ms	(cos.f64 (-.f64 lambda1 lambda2))

series182.0ms (1.3%)

Counts

4 → 12

Calls

4 calls:

108.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
40.0ms	(*.f64 (cos.f64 phi1) (sin.f64 phi2))
19.0ms	(sin.f64 (-.f64 lambda1 lambda2))
15.0ms	(cos.f64 (-.f64 lambda1 lambda2))

simplify101.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 0 (83.0ms)

Iter	Nodes	Cost
0	4860	1037
1	4860	1037

prune102.0ms (0.7%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	64	11	75
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	65	11	76

Error

7.3b

Counts

76 → 11

Compiler

Compiled 2475 to 517 computations (79.1% saved)

localize30.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(.f64 (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2))
0.2b	(*.f64 (cos.f64 phi1) (sin.f64 phi2))
0.2b	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
2.2b	(cos.f64 (-.f64 lambda1 lambda2))

rewrite33.0ms (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:

9.0ms	(.f64 (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2))
7.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
4.0ms	(*.f64 (cos.f64 phi1) (sin.f64 phi2))
4.0ms	(cos.f64 (-.f64 lambda1 lambda2))

series318.0ms (2.2%)

Counts

4 → 12

Calls

4 calls:

150.0ms	(.f64 (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2))
112.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
41.0ms	(*.f64 (cos.f64 phi1) (sin.f64 phi2))
16.0ms	(cos.f64 (-.f64 lambda1 lambda2))

simplify54.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5316	1458

prune112.0ms (0.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	79	4	83
Fresh	6	4	10
Picked	1	0	1
Done	0	0	0
Total	86	8	94

Error

0.1b

Counts

94 → 8

Compiler

Compiled 3333 to 507 computations (84.8% saved)

localize35.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite40.0ms (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:

10.0ms	(.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (sin.f64 phi1) (cos.f64 phi2)))
9.0ms	(.f64 (.f64 (cos.f64 lambda1) (cos.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))

series357.0ms (2.5%)

Counts

4 → 12

Calls

4 calls:

137.0ms	(.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 phi1) (cos.f64 phi2)))
131.0ms	(.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (sin.f64 phi1) (cos.f64 phi2)))
45.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
44.0ms	(*.f64 (cos.f64 phi1) (sin.f64 phi2))

simplify78.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4933	1542
1	4933	1542

prune160.0ms (1.1%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	93	6	99
Fresh	1	6	7
Picked	1	0	1
Done	0	0	0
Total	95	12	107

Error

0.0b

Counts

107 → 12

Compiler

Compiled 5229 to 763 computations (85.4% saved)

localize37.0ms (0.3%)

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)
0.3b	(.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 phi1) (cos.f64 phi2)))
0.3b	(.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (sin.f64 phi1) (cos.f64 phi2)))
26.4b	(cbrt.f64 (pow.f64 (.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (sin.f64 phi1) (cos.f64 phi2))) 3))

rewrite49.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

41×	`add-cbrt-cube_binary64_1478` `add-exp-log_binary64_1480` `pow1_binary64_1503`
24×	`cbrt-unprod_binary64_1475` `pow-prod-down_binary64_1513` `prod-exp_binary64_1491`
8×	`cbrt-prod_binary64_1473` `sin-cos-mult_binary64_1598`
6×	`add-sqr-sqrt_binary64_1464` `cube-div_binary64_1471` `sin-mult_binary64_1597` `add-cube-cbrt_binary64_1477` `*-un-lft-identity_binary64_1442`
5×	`pow-exp_binary64_1510` `rem-cube-cbrt_binary64_1465` `pow-pow_binary64_1514`
4×	`associate-r/_binary64_1384` `add-log-exp_binary64_1481` `frac-times_binary64_1452` `associate-l/_binary64_1385`
3×	`cbrt-div_binary64_1474` `pow-unpow_binary64_1519`
2×	`associate-r_binary64_1382` `cube-mult_binary64_1472` `cube-prod_binary64_1470` `associate-l_binary64_1383` `*-commutative_binary64_1373` `sqr-pow_binary64_1414` `unpow3_binary64_1508` `cos-mult_binary64_1596` `unpow-prod-down_binary64_1521`
1×	`pow1/3_binary64_1524` `pow-to-exp_binary64_1511` `rem-cbrt-cube_binary64_1466`

Counts

4 → 104

Calls

4 calls:

10.0ms	(pow.f64 (.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (sin.f64 phi1) (cos.f64 phi2))) 3)
9.0ms	(.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 phi1) (cos.f64 phi2)))
9.0ms	(.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (sin.f64 phi1) (cos.f64 phi2)))
4.0ms	(cbrt.f64 (pow.f64 (.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (sin.f64 phi1) (cos.f64 phi2))) 3))

series686.0ms (4.8%)

Counts

4 → 12

Calls

4 calls:

312.0ms	(pow.f64 (.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (sin.f64 phi1) (cos.f64 phi2))) 3)
139.0ms	(.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 phi1) (cos.f64 phi2)))
130.0ms	(cbrt.f64 (pow.f64 (.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (sin.f64 phi1) (cos.f64 phi2))) 3))
104.0ms	(.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (sin.f64 phi1) (cos.f64 phi2)))

simplify80.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5749	2323

prune160.0ms (1.1%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	115	1	116
Fresh	1	10	11
Picked	1	0	1
Done	0	0	0
Total	117	11	128

Error

0.0b

Counts

128 → 11

Compiler

Compiled 5989 to 890 computations (85.1% saved)

regimes687.0ms (4.8%)

Accuracy

Total 0.1b remaining (72.1%)

Threshold costs 0.1b (72.1%)

Compiler

Compiled 9448 to 5858 computations (38% saved)

bsearch0.0ms (0%)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	131	78
1	131	78

end0.0ms (0%)

sample7.8s (54.6%)

Algorithm

1×

intervals

Results

4.8s	5360×	body	1024	valid
727.0ms	1317×	body	512	valid
391.0ms	199×	body	2048	valid
139.0ms	374×	body	256	valid
123.0ms	750×	body	128	valid

Compiler

Compiled 1558 to 959 computations (38.4% saved)

Details

analyze2.8s (19.5%)

sample222.0ms (1.6%)

simplify111.0ms (0.8%)

prune4.0ms (0%)

localize21.0ms (0.1%)

rewrite33.0ms (0.2%)

series182.0ms (1.3%)

simplify101.0ms (0.7%)

prune102.0ms (0.7%)

localize30.0ms (0.2%)

rewrite33.0ms (0.2%)

series318.0ms (2.2%)

simplify54.0ms (0.4%)

prune112.0ms (0.8%)

localize35.0ms (0.2%)

rewrite40.0ms (0.3%)

series357.0ms (2.5%)

simplify78.0ms (0.5%)

prune160.0ms (1.1%)

localize37.0ms (0.3%)

rewrite49.0ms (0.3%)

series686.0ms (4.8%)

simplify80.0ms (0.6%)

prune160.0ms (1.1%)

regimes687.0ms (4.8%)

bsearch0.0ms (0%)

simplify4.0ms (0%)

end0.0ms (0%)

sample7.8s (54.6%)

Profiling