Details

analyze2.7s (16.5%)

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)

sample266.0ms (1.7%)

Algorithm

1×

intervals

Results

207.0ms	182×	body	1024	valid
22.0ms	34×	body	512	valid
17.0ms	6×	body	2048	valid
5.0ms	27×	body	128	valid
3.0ms	7×	body	256	valid

Compiler

Compiled 49 to 39 computations (20.4% saved)

simplify189.0ms (1.2%)

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: 13.2b

Counts

2 → 1

Compiler

Compiled 48 to 34 computations (29.2% saved)

localize24.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2))
0.2b	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
3.5b	(cos.f64 (-.f64 lambda1 lambda2))
3.6b	(sin.f64 (-.f64 lambda1 lambda2))

rewrite35.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`pow1_binary64_2204` `add-sqr-sqrt_binary64_2165` `add-exp-log_binary64_2181` `add-cbrt-cube_binary64_2179`
9×	`add-cube-cbrt_binary64_2178` `*-un-lft-identity_binary64_2143`
6×	`associate-r_binary64_2083` `cancel-sign-sub-inv_binary64_2109`
4×	`add-log-exp_binary64_2182` `sin-sum_binary64_2276` `cbrt-unprod_binary64_2176` `associate-l_binary64_2084` `pow-prod-down_binary64_2214` `prod-exp_binary64_2192` `cos-sum_binary64_2277`
3×	`cos-diff_binary64_2280`
2×	`sin-cos-mult_binary64_2299` `sub-neg_binary64_2136` `*-commutative_binary64_2074`
1×	`sin-diff_binary64_2279` `distribute-rgt-in_binary64_2093` `associate-*l/_binary64_2086` `unswap-sqr_binary64_2111` `distribute-lft-in_binary64_2092`

Counts

4 → 64

Calls

4 calls:

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

series410.0ms (2.5%)

Counts

4 → 12

Calls

4 calls:

217.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
122.0ms	(*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2))
38.0ms	(sin.f64 (-.f64 lambda1 lambda2))
33.0ms	(cos.f64 (-.f64 lambda1 lambda2))

simplify69.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4859	1102
1	4859	1102

prune402.0ms (2.5%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	64	12	76
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	65	12	77

Merged error: 6.1b

Counts

77 → 12

Compiler

Compiled 7154 to 3720 computations (48% saved)

localize34.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(*.f64 (sin.f64 lambda1) (cos.f64 lambda2))
0.2b	(.f64 (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (*.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)))
3.5b	(cos.f64 (-.f64 lambda1 lambda2))

rewrite39.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64_2165`
13×	`pow1_binary64_2204` `add-exp-log_binary64_2181` `add-cbrt-cube_binary64_2179`
10×	`add-cube-cbrt_binary64_2178` `*-un-lft-identity_binary64_2143`
9×	`associate-r_binary64_2083`
7×	`associate-l_binary64_2084`
5×	`cbrt-unprod_binary64_2176` `pow-prod-down_binary64_2214` `prod-exp_binary64_2192`
4×	`add-log-exp_binary64_2182` `cos-sum_binary64_2277`
3×	`cos-diff_binary64_2280` `associate-l/_binary64_2086` `cancel-sign-sub-inv_binary64_2109` `-commutative_binary64_2074`
2×	`sin-cos-mult_binary64_2299` `unswap-sqr_binary64_2111`
1×	`flip--_binary64_2118` `distribute-rgt-in_binary64_2093` `sub-neg_binary64_2136` `flip3--_binary64_2147` `distribute-lft-in_binary64_2092`

Counts

4 → 72

Calls

4 calls:

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

series579.0ms (3.6%)

Counts

4 → 12

Calls

4 calls:

264.0ms	(.f64 (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2))
214.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
70.0ms	(*.f64 (sin.f64 lambda1) (cos.f64 lambda2))
31.0ms	(cos.f64 (-.f64 lambda1 lambda2))

simplify48.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	5127	1472

prune244.0ms (1.5%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	82	2	84
Fresh	3	8	11
Picked	1	0	1
Done	0	0	0
Total	86	10	96

Merged error: 0.1b

Counts

96 → 10

Compiler

Compiled 5515 to 1916 computations (65.3% saved)

localize37.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite51.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`pow1_binary64_2204` `add-exp-log_binary64_2181` `add-cbrt-cube_binary64_2179`
18×	`cbrt-unprod_binary64_2176` `pow-prod-down_binary64_2214` `prod-exp_binary64_2192`
12×	`add-sqr-sqrt_binary64_2165`
8×	`associate-r_binary64_2083` `associate-l_binary64_2084` `add-cube-cbrt_binary64_2178` `*-un-lft-identity_binary64_2143`
4×	`add-log-exp_binary64_2182` `sin-cos-mult_binary64_2299` `associate-l/_binary64_2086` `-commutative_binary64_2074`
3×	`sin-mult_binary64_2298`
2×	`cos-mult_binary64_2297` `frac-times_binary64_2153` `associate-*r/_binary64_2085` `unswap-sqr_binary64_2111`
1×	`flip--_binary64_2118` `flip3--_binary64_2147`

Counts

4 → 89

Calls

4 calls:

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

series767.0ms (4.8%)

Counts

4 → 12

Calls

4 calls:

253.0ms	(.f64 (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2))
234.0ms	(.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 phi1) (cos.f64 phi2)))
210.0ms	(.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (sin.f64 phi1) (cos.f64 phi2)))
70.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))

simplify72.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5153	1911

prune584.0ms (3.6%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	95	6	101
Fresh	6	3	9
Picked	1	0	1
Done	0	0	0
Total	102	9	111

Merged error: 0.0b

Counts

111 → 9

Compiler

Compiled 13037 to 5229 computations (59.9% saved)

localize39.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.5b	(*.f64 (cbrt.f64 (sin.f64 lambda1)) (cbrt.f64 (sin.f64 lambda1)))
0.6b	(cbrt.f64 (sin.f64 lambda1))
0.6b	(cbrt.f64 (sin.f64 lambda1))
0.6b	(cbrt.f64 (sin.f64 lambda1))

rewrite30.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`cbrt-prod_binary64_2174`
23×	`add-sqr-sqrt_binary64_2165`
15×	`add-cube-cbrt_binary64_2178` `*-un-lft-identity_binary64_2143`
11×	`pow1_binary64_2204`
9×	`pow1/3_binary64_2225`
6×	`associate-r_binary64_2083` `add-exp-log_binary64_2181` `associate-l_binary64_2084` `swap-sqr_binary64_2110`
4×	`add-log-exp_binary64_2182` `unswap-sqr_binary64_2111` `add-cbrt-cube_binary64_2179`
2×	`pow-sqr_binary64_2116` `pow-prod-up_binary64_2213` `pow-prod-down_binary64_2214`
1×	`pow2_binary64_2224` `pow-plus_binary64_2206` `cbrt-unprod_binary64_2176` `prod-exp_binary64_2192` `*-commutative_binary64_2074`

Counts

4 → 73

Calls

4 calls:

8.0ms	(*.f64 (cbrt.f64 (sin.f64 lambda1)) (cbrt.f64 (sin.f64 lambda1)))
2.0ms	(cbrt.f64 (sin.f64 lambda1))
2.0ms	(cbrt.f64 (sin.f64 lambda1))
2.0ms	(cbrt.f64 (sin.f64 lambda1))

series546.0ms (3.4%)

Counts

4 → 12

Calls

4 calls:

170.0ms	(*.f64 (cbrt.f64 (sin.f64 lambda1)) (cbrt.f64 (sin.f64 lambda1)))
137.0ms	(cbrt.f64 (sin.f64 lambda1))
121.0ms	(cbrt.f64 (sin.f64 lambda1))
118.0ms	(cbrt.f64 (sin.f64 lambda1))

simplify82.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	4872	797
1	4872	797

prune181.0ms (1.1%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	85	0	85
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	85	9	94

Merged error: 0.0b

Counts

94 → 9

Compiler

Compiled 5738 to 1161 computations (79.8% saved)

regimes190.0ms (1.2%)

Compiler: Compiled 2304 to 1270 computations (44.9% saved)

bsearch0.0ms (0%)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	170	89
1	170	89

end0.0ms (0%)

sample8.5s (53%)

Algorithm

1×

intervals

Results

6.2s	5412×	body	1024	valid
796.0ms	1237×	body	512	valid
505.0ms	189×	body	2048	valid
152.0ms	801×	body	128	valid
134.0ms	361×	body	256	valid

Compiler

Compiled 518 to 282 computations (45.6% saved)

Details

analyze2.7s (16.5%)

sample266.0ms (1.7%)

simplify189.0ms (1.2%)

prune4.0ms (0%)

localize24.0ms (0.2%)

rewrite35.0ms (0.2%)

series410.0ms (2.5%)

simplify69.0ms (0.4%)

prune402.0ms (2.5%)

localize34.0ms (0.2%)

rewrite39.0ms (0.2%)

series579.0ms (3.6%)

simplify48.0ms (0.3%)

prune244.0ms (1.5%)

localize37.0ms (0.2%)

rewrite51.0ms (0.3%)

series767.0ms (4.8%)

simplify72.0ms (0.4%)

prune584.0ms (3.6%)

localize39.0ms (0.2%)

rewrite30.0ms (0.2%)

series546.0ms (3.4%)

simplify82.0ms (0.5%)

prune181.0ms (1.1%)

regimes190.0ms (1.2%)

bsearch0.0ms (0%)

simplify5.0ms (0%)

end0.0ms (0%)

sample8.5s (53%)

Profiling