Details

analyze8.0s (7.9%)

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
0%	99.8%	0.2%	9
0%	99.8%	0.2%	10
0.8%	99%	0.2%	11
1.2%	98.6%	0.2%	12
1.8%	98%	0.2%	13
2%	97.7%	0.2%	14

Compiler

Compiled 20 to 18 computations (10% saved)

sample792.0ms (0.8%)

Algorithm

1×

intervals

Results

479.0ms	169×	body	1024	valid
114.0ms	47×	body	512	valid
36.0ms	6×	body	2048	valid
23.0ms	19×	body	256	valid
8.0ms	15×	body	128	valid

Compiler

Compiled 39 to 40 computations (-2.6% saved)

simplify168.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (9.0ms)

Iter	Nodes	Cost
0	96	31
1	96	31

prune6.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 15.1b

Counts

2 → 1

Compiler

Compiled 38 to 34 computations (10.5% saved)

localize47.0ms (0%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
0.2b	(*.f64 (sin.f64 phi1) (sin.f64 phi2))
1.3b	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
2.7b	(cos.f64 (-.f64 lambda1 lambda2))

rewrite44.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`add-cbrt-cube_binary64_114` `add-exp-log_binary64_116` `pow1_binary64_139`
10×	`add-sqr-sqrt_binary64_100`
8×	`add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
6×	`associate-r_binary64_18`
4×	`associate-l_binary64_19` `add-log-exp_binary64_117` `cbrt-unprod_binary64_111` `prod-exp_binary64_127` `pow-prod-down_binary64_149` `cos-sum_binary64_212`
3×	`cancel-sign-sub-inv_binary64_44` `cos-diff_binary64_215`
2×	`*-commutative_binary64_9`
1×	`distribute-lft-in_binary64_27` `distribute-rgt-in_binary64_28` `acos-asin_binary64_259` `associate-*l/_binary64_21` `unswap-sqr_binary64_46` `sin-mult_binary64_233` `cos-mult_binary64_232` `sub-neg_binary64_71`

Counts

4 → 60

Calls

4 calls:

13.0ms	(.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
9.0ms	(*.f64 (sin.f64 phi1) (sin.f64 phi2))
9.0ms	(cos.f64 (-.f64 lambda1 lambda2))
2.0ms	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))

series377.0ms (0.4%)

Counts

4 → 12

Calls

4 calls:

203.0ms	(.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
77.0ms	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
67.0ms	(*.f64 (sin.f64 phi1) (sin.f64 phi2))
30.0ms	(cos.f64 (-.f64 lambda1 lambda2))

simplify189.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 0 (150.0ms)

Iter	Nodes	Cost
0	4864	1228
1	4864	1228

prune1.3s (1.3%)

Pruning

32 alts after pruning (31 fresh and 1 done)

	Pruned	Kept	Total
New	41	31	72
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	41	32	73

Merged error: 5.0b

Counts

73 → 32

Compiler

Compiled 2559 to 934 computations (63.5% saved)

localize102.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
0.2b	(.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))
0.2b	(*.f64 (sin.f64 phi1) (sin.f64 phi2))
1.4b	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))

rewrite123.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`add-cbrt-cube_binary64_114` `add-sqr-sqrt_binary64_100` `add-exp-log_binary64_116` `pow1_binary64_139`
9×	`add-cube-cbrt_binary64_113` `associate-r_binary64_18` `*-un-lft-identity_binary64_78`
7×	`associate-l_binary64_19`
6×	`cos-mult_binary64_232`
5×	`cbrt-unprod_binary64_111` `prod-exp_binary64_127` `pow-prod-down_binary64_149`
4×	`add-log-exp_binary64_117` `sin-mult_binary64_233`
3×	`-commutative_binary64_9` `frac-times_binary64_88` `associate-r/_binary64_20`
2×	`frac-add_binary64_86` `flip-+_binary64_52` `unswap-sqr_binary64_46` `flip3-+_binary64_81`
1×	`distribute-lft-in_binary64_27` `distribute-rgt-in_binary64_28` `acos-asin_binary64_259` `associate-*l/_binary64_21`

Counts

4 → 73

Calls

4 calls:

39.0ms	(.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))
21.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
17.0ms	(*.f64 (sin.f64 phi1) (sin.f64 phi2))
10.0ms	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))

series1.3s (1.3%)

Counts

4 → 12

Calls

4 calls:

673.0ms	(.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))
293.0ms	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
157.0ms	(*.f64 (sin.f64 phi1) (sin.f64 phi2))
155.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))

simplify268.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 0 (103.0ms)

Iter	Nodes	Cost
0	5052	2013

prune1.5s (1.5%)

Pruning

70 alts after pruning (68 fresh and 2 done)

	Pruned	Kept	Total
New	45	40	85
Fresh	2	28	30
Picked	0	1	1
Done	0	1	1
Total	47	70	117

Merged error: 4.9b

Counts

117 → 70

Compiler

Compiled 5074 to 2017 computations (60.2% saved)

localize53.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (sin.f64 lambda1) (neg.f64 (sin.f64 lambda2)))
0.2b	(.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (neg.f64 (sin.f64 lambda2)))))
0.2b	(*.f64 (sin.f64 phi1) (sin.f64 phi2))
1.4b	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (neg.f64 (sin.f64 lambda2)))))))

rewrite75.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`associate-r_binary64_18`
15×	`add-sqr-sqrt_binary64_100`
13×	`add-cbrt-cube_binary64_114` `add-exp-log_binary64_116` `pow1_binary64_139`
11×	`add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
7×	`associate-l_binary64_19`
5×	`cbrt-unprod_binary64_111` `prod-exp_binary64_127` `pow-prod-down_binary64_149`
4×	`add-log-exp_binary64_117`
3×	`*-commutative_binary64_9` `distribute-lft-neg-in_binary64_35` `cos-mult_binary64_232` `distribute-rgt-neg-in_binary64_36`
2×	`distribute-lft-in_binary64_27` `flip3--_binary64_82` `distribute-rgt-in_binary64_28` `frac-times_binary64_88` `flip--_binary64_53` `unswap-sqr_binary64_46` `associate-*r/_binary64_20` `cancel-sign-sub-inv_binary64_44` `sub-neg_binary64_71`
1×	`neg-mul-1_binary64_74` `acos-asin_binary64_259` `associate-*l/_binary64_21` `sin-mult_binary64_233` `distribute-rgt-neg-out_binary64_38`

Counts

4 → 80

Calls

4 calls:

21.0ms	(.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (neg.f64 (sin.f64 lambda2)))))
14.0ms	(*.f64 (sin.f64 lambda1) (neg.f64 (sin.f64 lambda2)))
9.0ms	(*.f64 (sin.f64 phi1) (sin.f64 phi2))
2.0ms	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (neg.f64 (sin.f64 lambda2)))))))

series749.0ms (0.7%)

Counts

4 → 12

Calls

4 calls:

427.0ms	(.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (neg.f64 (sin.f64 lambda2)))))
124.0ms	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (neg.f64 (sin.f64 lambda2)))))))
107.0ms	(*.f64 (sin.f64 phi1) (sin.f64 phi2))
90.0ms	(*.f64 (sin.f64 lambda1) (neg.f64 (sin.f64 lambda2)))

simplify254.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 0 (118.0ms)

Iter	Nodes	Cost
0	5034	2101

prune3.1s (3.1%)

Pruning

90 alts after pruning (87 fresh and 3 done)

	Pruned	Kept	Total
New	67	25	92
Fresh	5	62	67
Picked	0	1	1
Done	0	2	2
Total	72	90	162

Merged error: 4.9b

Counts

162 → 90

Compiler

Compiled 6076 to 2550 computations (58% saved)

localize57.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (log.f64 (exp.f64 (.f64 (sin.f64 lambda1) (neg.f64 (sin.f64 lambda2)))))))
0.2b	(*.f64 (sin.f64 phi1) (sin.f64 phi2))
1.4b	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (log.f64 (exp.f64 (*.f64 (sin.f64 lambda1) (neg.f64 (sin.f64 lambda2)))))))))
2.8b	(log.f64 (exp.f64 (*.f64 (sin.f64 lambda1) (neg.f64 (sin.f64 lambda2)))))

rewrite62.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`pow1_binary64_139`
13×	`log-pow_binary64_167`
12×	`add-sqr-sqrt_binary64_100` `cancel-sign-sub-inv_binary64_44`
11×	`add-cbrt-cube_binary64_114` `add-exp-log_binary64_116`
10×	`distribute-lft-in_binary64_27` `add-cube-cbrt_binary64_113` `distribute-rgt-in_binary64_28` `*-un-lft-identity_binary64_78`
9×	`add-log-exp_binary64_117`
6×	`associate-r_binary64_18`
5×	`exp-to-pow_binary64_140` `exp-prod_binary64_130`
4×	`associate-l_binary64_19` `cbrt-unprod_binary64_111` `prod-exp_binary64_127` `exp-neg_binary64_125` `cancel-sign-sub_binary64_43` `pow-prod-down_binary64_149` `distribute-rgt-neg-out_binary64_38`
3×	`log-prod_binary64_164` `log-div_binary64_165` `cos-mult_binary64_232`
2×	`-commutative_binary64_9` `flip3--_binary64_82` `associate--r-_binary64_17` `frac-times_binary64_88` `flip--_binary64_53` `associate-r/_binary64_20` `sub-neg_binary64_71`
1×	`acos-asin_binary64_259` `log-rec_binary64_166` `associate-*l/_binary64_21` `rem-log-exp_binary64_119` `unswap-sqr_binary64_46` `sin-mult_binary64_233`

Counts

4 → 86

Calls

4 calls:

26.0ms	(.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (log.f64 (exp.f64 (.f64 (sin.f64 lambda1) (neg.f64 (sin.f64 lambda2)))))))
9.0ms	(*.f64 (sin.f64 phi1) (sin.f64 phi2))
4.0ms	(log.f64 (exp.f64 (*.f64 (sin.f64 lambda1) (neg.f64 (sin.f64 lambda2)))))
2.0ms	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (log.f64 (exp.f64 (*.f64 (sin.f64 lambda1) (neg.f64 (sin.f64 lambda2)))))))))

series1.2s (1.2%)

Counts

4 → 12

Calls

4 calls:

823.0ms	(.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (log.f64 (exp.f64 (.f64 (sin.f64 lambda1) (neg.f64 (sin.f64 lambda2)))))))
173.0ms	(log.f64 (exp.f64 (*.f64 (sin.f64 lambda1) (neg.f64 (sin.f64 lambda2)))))
108.0ms	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (log.f64 (exp.f64 (*.f64 (sin.f64 lambda1) (neg.f64 (sin.f64 lambda2)))))))))
67.0ms	(*.f64 (sin.f64 phi1) (sin.f64 phi2))

simplify245.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 0 (184.0ms)

Iter	Nodes	Cost
0	4874	2575
1	4874	2575

prune2.5s (2.5%)

Pruning

108 alts after pruning (104 fresh and 4 done)

	Pruned	Kept	Total
New	73	25	98
Fresh	7	79	86
Picked	0	1	1
Done	0	3	3
Total	80	108	188

Merged error: 4.9b

Counts

188 → 108

Compiler

Compiled 3300 to 454 computations (86.2% saved)

regimes18.7s (18.6%)

Compiler: Compiled 69088 to 50890 computations (26.3% saved)

bsearch20.9s (20.7%)

simplify27.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	64	49
1	64	49

end0.0ms (0%)

sample38.7s (38.4%)

Algorithm

1×

intervals

Results

15.1s	5502×	body	1024	valid
2.1s	1393×	body	512	valid
1.4s	277×	body	2048	valid
474.0ms	522×	body	256	valid
115.0ms	306×	body	128	valid
3.0ms	2×	body	1024	invalid

Compiler

Compiled 6833 to 5039 computations (26.3% saved)

Pareto

0.0

Details

analyze8.0s (7.9%)

sample792.0ms (0.8%)

simplify168.0ms (0.2%)

prune6.0ms (0%)

localize47.0ms (0%)

rewrite44.0ms (0%)

series377.0ms (0.4%)

simplify189.0ms (0.2%)

prune1.3s (1.3%)

localize102.0ms (0.1%)

rewrite123.0ms (0.1%)

series1.3s (1.3%)

simplify268.0ms (0.3%)

prune1.5s (1.5%)

localize53.0ms (0.1%)

rewrite75.0ms (0.1%)

series749.0ms (0.7%)

simplify254.0ms (0.3%)

prune3.1s (3.1%)

localize57.0ms (0.1%)

rewrite62.0ms (0.1%)

series1.2s (1.2%)

simplify245.0ms (0.2%)

prune2.5s (2.5%)

regimes18.7s (18.6%)

bsearch20.9s (20.7%)

simplify27.0ms (0%)

end0.0ms (0%)

sample38.7s (38.4%)

Profiling