Details

analyze2.7s (17.2%)

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)

sample258.0ms (1.6%)

Algorithm

1×

intervals

Results

190.0ms	162×	body	1024	valid
31.0ms	50×	body	512	valid
11.0ms	4×	body	2048	valid
6.0ms	14×	body	256	valid
5.0ms	26×	body	128	valid

Compiler

Compiled 49 to 39 computations (20.4% saved)

simplify21.0ms (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: 11.3b

Counts

2 → 1

Compiler

Compiled 48 to 34 computations (29.2% saved)

localize30.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2))
0.2b	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
2.7b	(sin.f64 (-.f64 lambda1 lambda2))
2.8b	(cos.f64 (-.f64 lambda1 lambda2))

rewrite31.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 58

Calls

4 calls:

8.0ms	(*.f64 (sin.f64 (-.f64 lambda1 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))
4.0ms	(sin.f64 (-.f64 lambda1 lambda2))

series415.0ms (2.7%)

Counts

4 → 12

Calls

4 calls:

224.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
126.0ms	(*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2))
35.0ms	(sin.f64 (-.f64 lambda1 lambda2))
29.0ms	(cos.f64 (-.f64 lambda1 lambda2))

simplify80.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	4896	994
1	4896	994

prune115.0ms (0.7%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	56	14	70
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	57	14	71

Merged error: 5.0b

Counts

71 → 14

Compiler

Compiled 2430 to 550 computations (77.4% saved)

localize35.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(*.f64 (cos.f64 lambda1) (sin.f64 lambda2))
0.1b	(*.f64 (cos.f64 lambda2) (sin.f64 lambda1))
0.2b	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
2.8b	(cos.f64 (-.f64 lambda1 lambda2))

rewrite31.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 66

Calls

4 calls:

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

series387.0ms (2.5%)

Counts

4 → 12

Calls

4 calls:

222.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
69.0ms	(*.f64 (cos.f64 lambda1) (sin.f64 lambda2))
66.0ms	(*.f64 (cos.f64 lambda2) (sin.f64 lambda1))
30.0ms	(cos.f64 (-.f64 lambda1 lambda2))

simplify90.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 0 (76.0ms)

Iter	Nodes	Cost
0	4854	1035
1	4854	1035

prune118.0ms (0.8%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	73	5	78
Fresh	5	8	13
Picked	1	0	1
Done	0	0	0
Total	79	13	92

Merged error: 0.1b

Counts

92 → 13

Compiler

Compiled 3214 to 644 computations (80% saved)

localize36.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(*.f64 (cos.f64 lambda2) (sin.f64 lambda1))
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)))

rewrite44.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
18×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `prod-exp_binary64`
12×	`add-sqr-sqrt_binary64`
8×	`-un-lft-identity_binary64` `associate-r_binary64` `add-cube-cbrt_binary64` `associate-l*_binary64`
4×	`add-log-exp_binary64` `sin-cos-mult_binary64` `*-commutative_binary64`
3×	`sin-mult_binary64`
2×	`cos-mult_binary64` `associate-r/_binary64` `unswap-sqr_binary64` `frac-times_binary64` `associate-l/_binary64`

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 lambda2) (sin.f64 lambda1))

series603.0ms (3.9%)

Counts

4 → 12

Calls

4 calls:

246.0ms	(.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 phi1) (cos.f64 phi2)))
214.0ms	(.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (sin.f64 phi1) (cos.f64 phi2)))
73.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
70.0ms	(*.f64 (cos.f64 lambda2) (sin.f64 lambda1))

simplify56.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	4976	1542
1	4976	1542

prune174.0ms (1.1%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	94	5	99
Fresh	3	9	12
Picked	1	0	1
Done	0	0	0
Total	98	14	112

Merged error: 0.0b

Counts

112 → 14

Compiler

Compiled 5292 to 814 computations (84.6% saved)

localize38.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (cbrt.f64 (pow.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) 3)) (*.f64 (sin.f64 phi1) (cos.f64 phi2)))
0.2b	(.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 phi1) (cos.f64 phi2)))
0.3b	(pow.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)) 3)
26.9b	(cbrt.f64 (pow.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)) 3))

rewrite45.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`pow1_binary64` `add-exp-log_binary64`
22×	`add-cbrt-cube_binary64`
16×	`cbrt-prod_binary64`
12×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `associate-l_binary64` `prod-exp_binary64`
8×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
4×	`add-log-exp_binary64` `cube-div_binary64` `sin-mult_binary64` `sin-cos-mult_binary64`
3×	`cbrt-div_binary64` `pow-unpow_binary64` `sqr-pow_binary64` `unpow-prod-down_binary64` `cube-prod_binary64` `unpow3_binary64` `cube-mult_binary64`
2×	`associate-r_binary64` `cos-mult_binary64` `associate-r/_binary64` `pow-pow_binary64` `rem-cube-cbrt_binary64` `frac-times_binary64` `pow-exp_binary64` `associate-l/_binary64` `*-commutative_binary64`
1×	`pow-to-exp_binary64` `rem-cbrt-cube_binary64` `pow1/3_binary64`

Counts

4 → 95

Calls

4 calls:

10.0ms	(.f64 (cbrt.f64 (pow.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) 3)) (*.f64 (sin.f64 phi1) (cos.f64 phi2)))
10.0ms	(.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 phi1) (cos.f64 phi2)))
5.0ms	(pow.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)) 3)
3.0ms	(cbrt.f64 (pow.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)) 3))

series660.0ms (4.2%)

Counts

4 → 12

Calls

4 calls:

236.0ms	(.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 phi1) (cos.f64 phi2)))
217.0ms	(.f64 (cbrt.f64 (pow.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) 3)) (*.f64 (sin.f64 phi1) (cos.f64 phi2)))
128.0ms	(pow.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)) 3)
79.0ms	(cbrt.f64 (pow.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)) 3))

simplify69.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5007	1732

prune158.0ms (1%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	106	1	107
Fresh	1	12	13
Picked	0	1	1
Done	0	0	0
Total	107	14	121

Merged error: 0.0b

Counts

121 → 14

Compiler

Compiled 5380 to 841 computations (84.4% saved)

regimes249.0ms (1.6%)

Compiler: Compiled 3074 to 1839 computations (40.2% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	141	78
1	141	78

end0.0ms (0%)

sample9.2s (58.8%)

Algorithm

1×

intervals

Results

6.6s	5347×	body	1024	valid
910.0ms	1295×	body	512	valid
499.0ms	177×	body	2048	valid
156.0ms	808×	body	128	valid
154.0ms	373×	body	256	valid

Compiler

Compiled 644 to 384 computations (40.4% saved)

Details

analyze2.7s (17.2%)

sample258.0ms (1.6%)

simplify21.0ms (0.1%)

prune4.0ms (0%)

localize30.0ms (0.2%)

rewrite31.0ms (0.2%)

series415.0ms (2.7%)

simplify80.0ms (0.5%)

prune115.0ms (0.7%)

localize35.0ms (0.2%)

rewrite31.0ms (0.2%)

series387.0ms (2.5%)

simplify90.0ms (0.6%)

prune118.0ms (0.8%)

localize36.0ms (0.2%)

rewrite44.0ms (0.3%)

series603.0ms (3.9%)

simplify56.0ms (0.4%)

prune174.0ms (1.1%)

localize38.0ms (0.2%)

rewrite45.0ms (0.3%)

series660.0ms (4.2%)

simplify69.0ms (0.4%)

prune158.0ms (1%)

regimes249.0ms (1.6%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample9.2s (58.8%)

Profiling