Details

analyze2.9s (13.3%)

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)

sample210.0ms (1%)

Algorithm

1×

intervals

Results

152.0ms	182×	body	1024	valid
24.0ms	47×	body	512	valid
11.0ms	6×	body	2048	valid
5.0ms	14×	body	256	valid
1.0ms	7×	body	128	valid

Compiler

Compiled 39 to 40 computations (-2.6% saved)

simplify101.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	96	31
1	96	31

prune9.0ms (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: 15.4b

Counts

2 → 1

Compiler

Compiled 38 to 34 computations (10.5% saved)

localize20.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (sin.f64 phi1) (sin.f64 phi2))
0.2b	(.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
0.7b	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
3.0b	(cos.f64 (-.f64 lambda1 lambda2))

rewrite23.0ms (0.1%)

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:

7.0ms	(.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
5.0ms	(*.f64 (sin.f64 phi1) (sin.f64 phi2))
5.0ms	(cos.f64 (-.f64 lambda1 lambda2))
1.0ms	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))

series781.0ms (3.5%)

Counts

4 → 55

Calls

4 calls:

477.0ms	(.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
138.0ms	(*.f64 (sin.f64 phi1) (sin.f64 phi2))
104.0ms	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
61.0ms	(cos.f64 (-.f64 lambda1 lambda2))

Compiler

Compiled 2159 to 1781 computations (17.5% saved)

simplify82.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	5000	2290

prune144.0ms (0.7%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	100	15	115
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	101	15	116

Merged error: 3.0b

Counts

116 → 15

Compiler

Compiled 3186 to 1028 computations (67.7% saved)

localize25.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (sin.f64 phi1) (sin.f64 phi2))
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))))
0.7b	(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))))))

rewrite29.0ms (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:

11.0ms	(.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))
5.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
5.0ms	(*.f64 (sin.f64 phi1) (sin.f64 phi2))
1.0ms	(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))))))

series1.4s (6.5%)

Counts

4 → 55

Calls

4 calls:

929.0ms	(.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))
172.0ms	(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))))))
170.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
156.0ms	(*.f64 (sin.f64 phi1) (sin.f64 phi2))

Compiler

Compiled 3062 to 2334 computations (23.8% saved)

simplify84.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5028	3606

prune192.0ms (0.9%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	119	9	128
Fresh	7	7	14
Picked	1	0	1
Done	0	0	0
Total	127	16	143

Merged error: 2.9b

Counts

143 → 16

Compiler

Compiled 4819 to 1337 computations (72.3% saved)

localize28.0ms (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)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))
0.4b	(exp.f64 (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)))))))
0.6b	(log.f64 (exp.f64 (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))))))))
0.7b	(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))))))

rewrite25.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`pow1_binary64_139`
9×	`add-cbrt-cube_binary64_114` `add-exp-log_binary64_116`
8×	`add-sqr-sqrt_binary64_100` `add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
6×	`exp-prod_binary64_130` `cos-mult_binary64_232`
5×	`add-log-exp_binary64_117`
4×	`log-pow_binary64_167`
3×	`cbrt-unprod_binary64_111` `prod-exp_binary64_127` `acos-asin_binary64_259` `frac-times_binary64_88` `associate-r_binary64_18` `log-prod_binary64_164` `pow-prod-down_binary64_149` `associate-*r/_binary64_20`
2×	`frac-add_binary64_86` `flip-+_binary64_52` `exp-diff_binary64_126` `sin-mult_binary64_233` `flip3-+_binary64_81`
1×	`distribute-lft-in_binary64_27` `-commutative_binary64_9` `associate-l_binary64_19` `rem-exp-log_binary64_118` `distribute-rgt-in_binary64_28` `associate-l/_binary64_21` `rem-log-exp_binary64_119` `log-div_binary64_165`

Counts

4 → 63

Calls

4 calls:

11.0ms	(.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))
3.0ms	(log.f64 (exp.f64 (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))))))))
2.0ms	(exp.f64 (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)))))))
1.0ms	(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))))))

series2.6s (11.9%)

Counts

4 → 58

Calls

4 calls:

1.1s	(log.f64 (exp.f64 (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))))))))
948.0ms	(.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))
354.0ms	(exp.f64 (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)))))))
175.0ms	(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))))))

Compiler

Compiled 3952 to 3017 computations (23.7% saved)

simplify95.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5082	5241

prune195.0ms (0.9%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	112	9	121
Fresh	7	8	15
Picked	1	0	1
Done	0	0	0
Total	120	17	137

Merged error: 2.9b

Counts

137 → 17

Compiler

Compiled 5156 to 1386 computations (73.1% saved)

localize28.0ms (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))))
0.4b	(asin.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))))))
0.7b	(-.f64 (/.f64 PI.f64 2) (asin.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)))))))

rewrite34.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`add-sqr-sqrt_binary64_100`
11×	`add-cbrt-cube_binary64_114` `add-exp-log_binary64_116` `pow1_binary64_139`
10×	`*-un-lft-identity_binary64_78`
8×	`add-cube-cbrt_binary64_113`
6×	`add-log-exp_binary64_117` `associate-r_binary64_18` `cos-mult_binary64_232`
4×	`associate-l_binary64_19` `cbrt-unprod_binary64_111` `prod-exp_binary64_127` `pow-prod-down_binary64_149`
3×	`frac-times_binary64_88` `sin-mult_binary64_233` `associate-*r/_binary64_20` `cancel-sign-sub-inv_binary64_44`
2×	`*-commutative_binary64_9` `frac-add_binary64_86` `flip-+_binary64_52` `difference-of-squares_binary64_47` `asin-acos_binary64_258` `flip3-+_binary64_81`
1×	`distribute-lft-in_binary64_27` `distribute-lft-out--_binary64_30` `flip3--_binary64_82` `diff-log_binary64_170` `distribute-rgt-in_binary64_28` `times-frac_binary64_84` `associate--r-_binary64_17` `flip--_binary64_53` `associate-*l/_binary64_21` `unswap-sqr_binary64_46` `sub-neg_binary64_71`

Counts

4 → 72

Calls

4 calls:

11.0ms	(.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))
8.0ms	(-.f64 (/.f64 PI.f64 2) (asin.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)))))))
5.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
1.0ms	(asin.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))))))

series1.5s (6.7%)

Counts

4 → 58

Calls

4 calls:

899.0ms	(.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))
242.0ms	(-.f64 (/.f64 PI.f64 2) (asin.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)))))))
164.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
164.0ms	(asin.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))))))

Compiler

Compiled 3810 to 2973 computations (22% saved)

simplify78.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5200	5082

prune173.0ms (0.8%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	125	5	130
Fresh	8	8	16
Picked	1	0	1
Done	0	0	0
Total	134	13	147

Merged error: 2.8b

Counts

147 → 13

Compiler

Compiled 5071 to 1407 computations (72.3% saved)

regimes2.1s (9.6%)

Compiler: Compiled 29456 to 19512 computations (33.8% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	31	43
1	31	43

end0.0ms (0%)

sample9.1s (41.4%)

Algorithm

1×

intervals

Results

4.7s	5515×	body	1024	valid
793.0ms	1433×	body	512	valid
526.0ms	267×	body	2048	valid
180.0ms	519×	body	256	valid
46.0ms	266×	body	128	valid
1.0ms	1×	body	1024	invalid

Compiler

Compiled 2885 to 1904 computations (34% saved)

Details

analyze2.9s (13.3%)

sample210.0ms (1%)

simplify101.0ms (0.5%)

prune9.0ms (0%)

localize20.0ms (0.1%)

rewrite23.0ms (0.1%)

series781.0ms (3.5%)

simplify82.0ms (0.4%)

prune144.0ms (0.7%)

localize25.0ms (0.1%)

rewrite29.0ms (0.1%)

series1.4s (6.5%)

simplify84.0ms (0.4%)

prune192.0ms (0.9%)

localize28.0ms (0.1%)

rewrite25.0ms (0.1%)

series2.6s (11.9%)

simplify95.0ms (0.4%)

prune195.0ms (0.9%)

localize28.0ms (0.1%)

rewrite34.0ms (0.2%)

series1.5s (6.7%)

simplify78.0ms (0.4%)

prune173.0ms (0.8%)

regimes2.1s (9.6%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample9.1s (41.4%)

Profiling