Details

analyze2.6s (16.4%)

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 (1.6%)

Algorithm

1×

intervals

Results

184.0ms	167×	body	1024	valid
24.0ms	40×	body	512	valid
23.0ms	7×	body	2048	valid
5.0ms	29×	body	128	valid
5.0ms	13×	body	256	valid

Compiler

Compiled 49 to 39 computations (20.4% saved)

simplify23.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (15.0ms)

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)

localize25.0ms (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	(sin.f64 (-.f64 lambda1 lambda2))
3.5b	(cos.f64 (-.f64 lambda1 lambda2))

rewrite36.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `add-sqr-sqrt_binary64`
9×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
6×	`associate-r_binary64` `cancel-sign-sub-inv_binary64`
4×	`pow-prod-down_binary64` `add-log-exp_binary64` `cbrt-unprod_binary64` `sin-sum_binary64` `associate-l_binary64` `prod-exp_binary64` `cos-sum_binary64`
3×	`cos-diff_binary64`
2×	`sub-neg_binary64` `sin-cos-mult_binary64` `*-commutative_binary64`
1×	`sin-diff_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `associate-*l/_binary64`

Counts

4 → 64

Calls

4 calls:

9.0ms	(*.f64 (sin.f64 (-.f64 lambda1 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	(sin.f64 (-.f64 lambda1 lambda2))

series420.0ms (2.7%)

Counts

4 → 12

Calls

4 calls:

212.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
135.0ms	(*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2))
38.0ms	(cos.f64 (-.f64 lambda1 lambda2))
35.0ms	(sin.f64 (-.f64 lambda1 lambda2))

simplify67.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4860	1102
1	4860	1102

prune484.0ms (3.1%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	62	14	76
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	63	14	77

Merged error: 7.1b

Counts

77 → 14

Compiler

Compiled 9315 to 4890 computations (47.5% saved)

localize34.0ms (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 (cos.f64 lambda2) (sin.f64 lambda1))
0.2b	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
3.5b	(cos.f64 (-.f64 lambda1 lambda2))

rewrite37.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64`
13×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
10×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
9×	`associate-r_binary64`
7×	`associate-l_binary64`
5×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `prod-exp_binary64`
4×	`add-log-exp_binary64` `cos-sum_binary64`
3×	`cancel-sign-sub-inv_binary64` `cos-diff_binary64` `associate-l/_binary64` `-commutative_binary64`
2×	`unswap-sqr_binary64`
1×	`sub-neg_binary64` `flip3--_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `sin-cos-mult_binary64` `flip--_binary64`

Counts

4 → 71

Calls

4 calls:

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

series597.0ms (3.8%)

Counts

4 → 12

Calls

4 calls:

267.0ms	(.f64 (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2))
216.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
82.0ms	(*.f64 (cos.f64 lambda2) (sin.f64 lambda1))
32.0ms	(cos.f64 (-.f64 lambda1 lambda2))

simplify47.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	5122	1458

prune204.0ms (1.3%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	81	2	83
Fresh	7	6	13
Picked	1	0	1
Done	0	0	0
Total	89	8	97

Merged error: 0.1b

Counts

97 → 8

Compiler

Compiled 4949 to 1477 computations (70.2% saved)

localize33.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite50.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`add-sqr-sqrt_binary64`
15×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
12×	`associate-r_binary64`
11×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
10×	`associate-l_binary64`
6×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `prod-exp_binary64`
4×	`add-log-exp_binary64` `sin-cos-mult_binary64` `*-commutative_binary64`
3×	`associate-r/_binary64` `unswap-sqr_binary64` `sin-mult_binary64` `frac-times_binary64` `associate-l/_binary64`
2×	`flip3-+_binary64` `cos-mult_binary64` `frac-add_binary64` `flip-+_binary64`
1×	`flip3--_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `flip--_binary64`

Counts

4 → 84

Calls

4 calls:

13.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))
8.0ms	(.f64 (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2))
6.0ms	(*.f64 (cos.f64 lambda2) (sin.f64 lambda1))
6.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))

series788.0ms (5%)

Counts

4 → 12

Calls

4 calls:

378.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))
268.0ms	(.f64 (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2))
73.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
68.0ms	(*.f64 (cos.f64 lambda2) (sin.f64 lambda1))

simplify65.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5030	2099

prune421.0ms (2.7%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	91	5	96
Fresh	1	6	7
Picked	0	1	1
Done	0	0	0
Total	92	12	104

Merged error: 0.0b

Counts

104 → 12

Compiler

Compiled 10432 to 3798 computations (63.6% saved)

localize38.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.5b	(*.f64 (cbrt.f64 (sin.f64 lambda1)) (cbrt.f64 (sin.f64 lambda1)))
0.7b	(cbrt.f64 (sin.f64 lambda1))
0.7b	(cbrt.f64 (sin.f64 lambda1))
0.7b	(cbrt.f64 (sin.f64 lambda1))

rewrite26.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`cbrt-prod_binary64`
23×	`add-sqr-sqrt_binary64`
15×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
11×	`pow1_binary64`
9×	`pow1/3_binary64`
6×	`swap-sqr_binary64` `associate-r_binary64` `add-exp-log_binary64` `associate-l_binary64`
4×	`add-log-exp_binary64` `add-cbrt-cube_binary64` `unswap-sqr_binary64`
2×	`pow-prod-down_binary64` `pow-prod-up_binary64` `pow-sqr_binary64`
1×	`cbrt-unprod_binary64` `pow-plus_binary64` `prod-exp_binary64` `pow2_binary64` `*-commutative_binary64`

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))

series536.0ms (3.4%)

Counts

4 → 12

Calls

4 calls:

173.0ms	(*.f64 (cbrt.f64 (sin.f64 lambda1)) (cbrt.f64 (sin.f64 lambda1)))
125.0ms	(cbrt.f64 (sin.f64 lambda1))
122.0ms	(cbrt.f64 (sin.f64 lambda1))
116.0ms	(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	4871	797
1	4871	797

prune179.0ms (1.1%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	84	1	85
Fresh	0	10	10
Picked	1	0	1
Done	0	1	1
Total	85	12	97

Merged error: 0.0b

Counts

97 → 12

Compiler

Compiled 5417 to 1275 computations (76.5% saved)

regimes227.0ms (1.4%)

Compiler: Compiled 2864 to 1610 computations (43.8% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	136	63
1	136	63

end0.0ms (0%)

sample8.5s (53.9%)

Algorithm

1×

intervals

Results

6.2s	5451×	body	1024	valid
777.0ms	1229×	body	512	valid
494.0ms	182×	body	2048	valid
154.0ms	416×	body	256	valid
123.0ms	722×	body	128	valid

Compiler

Compiled 601 to 338 computations (43.8% saved)

Details

analyze2.6s (16.4%)

sample256.0ms (1.6%)

simplify23.0ms (0.1%)

prune4.0ms (0%)

localize25.0ms (0.2%)

rewrite36.0ms (0.2%)

series420.0ms (2.7%)

simplify67.0ms (0.4%)

prune484.0ms (3.1%)

localize34.0ms (0.2%)

rewrite37.0ms (0.2%)

series597.0ms (3.8%)

simplify47.0ms (0.3%)

prune204.0ms (1.3%)

localize33.0ms (0.2%)

rewrite50.0ms (0.3%)

series788.0ms (5%)

simplify65.0ms (0.4%)

prune421.0ms (2.7%)

localize38.0ms (0.2%)

rewrite26.0ms (0.2%)

series536.0ms (3.4%)

simplify82.0ms (0.5%)

prune179.0ms (1.1%)

regimes227.0ms (1.4%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample8.5s (53.9%)

Profiling