Details

analyze3.6s (20%)

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
1.2%	98.6%	0.2%	11
1.4%	98.4%	0.2%	12
10.8%	88.9%	0.2%	13
10.8%	88.9%	0.2%	14

Compiler

Compiled 34 to 24 computations (29.4% saved)

sample253.0ms (1.4%)

Algorithm

1×

intervals

Results

183.0ms	136×	body	1024	valid
24.0ms	32×	body	512	valid
20.0ms	70×	body	128	valid
8.0ms	18×	body	256	valid

Compiler

Compiled 67 to 52 computations (22.4% saved)

simplify208.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	463	55
1	463	55

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: 0.1b

Counts

2 → 1

Compiler

Compiled 66 to 46 computations (30.3% saved)

localize32.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (sin.f64 theta) (sin.f64 delta))
0.3b	(.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))))
0.3b	(asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))
0.5b	(-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))))

rewrite26.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`add-sqr-sqrt_binary64_1123`
8×	`*-un-lft-identity_binary64_1101` `add-exp-log_binary64_1139` `pow1_binary64_1162` `add-cube-cbrt_binary64_1136` `add-cbrt-cube_binary64_1137`
6×	`add-log-exp_binary64_1140` `associate-r_binary64_1041` `associate-l_binary64_1042`
2×	`*-commutative_binary64_1032` `cbrt-unprod_binary64_1134` `prod-exp_binary64_1150` `pow-prod-down_binary64_1172` `unswap-sqr_binary64_1069` `sin-mult_binary64_1256`
1×	`diff-log_binary64_1193` `sub-neg_binary64_1094` `flip--_binary64_1076` `flip3--_binary64_1105` `asin-acos_binary64_1281` `cancel-sign-sub-inv_binary64_1067`

Counts

4 → 58

Calls

4 calls:

6.0ms	(.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))))
6.0ms	(*.f64 (sin.f64 theta) (sin.f64 delta))
5.0ms	(-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))))
1.0ms	(asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))

series657.0ms (3.7%)

Counts

4 → 12

Calls

4 calls:

314.0ms	(-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))))
232.0ms	(.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))))
74.0ms	(*.f64 (sin.f64 theta) (sin.f64 delta))
37.0ms	(asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))

simplify89.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	4895	2133
1	4895	2133

prune115.0ms (0.6%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	63	7	70
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	64	7	71

Merged error: 0.0b

Counts

71 → 7

Compiler

Compiled 3126 to 537 computations (82.8% saved)

localize36.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(.f64 (sin.f64 phi1) (sin.f64 (-.f64 (/.f64 PI.f64 2) (acos.f64 (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))))
0.3b	(acos.f64 (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))
0.5b	(-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (-.f64 (/.f64 PI.f64 2) (acos.f64 (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))))))
3.9b	(-.f64 (/.f64 PI.f64 2) (acos.f64 (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))

rewrite49.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`sin-sum_binary64_1234`
18×	`add-sqr-sqrt_binary64_1123`
16×	`cancel-sign-sub-inv_binary64_1067`
13×	`*-un-lft-identity_binary64_1101`
11×	`add-cube-cbrt_binary64_1136`
10×	`associate--r+_binary64_1037` `distribute-lft-in_binary64_1050` `distribute-rgt-in_binary64_1051`
8×	`add-log-exp_binary64_1140`
6×	`add-exp-log_binary64_1139` `pow1_binary64_1162` `sub-neg_binary64_1094` `acos-asin_binary64_1282` `add-cbrt-cube_binary64_1137`
5×	`associate--r-_binary64_1040`
3×	`associate-r_binary64_1041` `associate-l_binary64_1042`
2×	`diff-log_binary64_1193` `difference-of-squares_binary64_1070` `flip--_binary64_1076` `flip3--_binary64_1105`
1×	`*-commutative_binary64_1032` `cbrt-unprod_binary64_1134` `prod-exp_binary64_1150` `distribute-lft-out--_binary64_1053` `times-frac_binary64_1107` `pow-prod-down_binary64_1172` `unswap-sqr_binary64_1069` `sin-mult_binary64_1256`

Counts

4 → 77

Calls

4 calls:

17.0ms	(.f64 (sin.f64 phi1) (sin.f64 (-.f64 (/.f64 PI.f64 2) (acos.f64 (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))))
10.0ms	(-.f64 (/.f64 PI.f64 2) (acos.f64 (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))
7.0ms	(-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (-.f64 (/.f64 PI.f64 2) (acos.f64 (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))))))
1.0ms	(acos.f64 (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))

series924.0ms (5.2%)

Counts

4 → 12

Calls

4 calls:

445.0ms	(-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (-.f64 (/.f64 PI.f64 2) (acos.f64 (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))))))
354.0ms	(.f64 (sin.f64 phi1) (sin.f64 (-.f64 (/.f64 PI.f64 2) (acos.f64 (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))))
89.0ms	(-.f64 (/.f64 PI.f64 2) (acos.f64 (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))
36.0ms	(acos.f64 (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))

simplify82.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5065	3463

prune139.0ms (0.8%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	89	0	89
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	89	7	96

Merged error: 0.0b

Counts

96 → 7

Compiler

Compiled 4379 to 919 computations (79% saved)

localize35.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))))
0.3b	(asin.f64 (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))
0.5b	(-.f64 (cos.f64 delta) (log.f64 (exp.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))))))
2.8b	(log.f64 (exp.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))))))

rewrite30.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`add-sqr-sqrt_binary64_1123`
12×	`*-un-lft-identity_binary64_1101`
9×	`pow1_binary64_1162` `add-cube-cbrt_binary64_1136`
7×	`add-log-exp_binary64_1140` `log-pow_binary64_1190`
6×	`add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137` `log-prod_binary64_1187` `cancel-sign-sub-inv_binary64_1067`
3×	`associate--r+_binary64_1037` `associate-r_binary64_1041` `associate-l_binary64_1042`
2×	`distribute-lft-out--_binary64_1053` `exp-prod_binary64_1153` `exp-to-pow_binary64_1163`
1×	`diff-log_binary64_1193` `*-commutative_binary64_1032` `cbrt-unprod_binary64_1134` `difference-of-squares_binary64_1070` `prod-exp_binary64_1150` `sub-neg_binary64_1094` `rem-log-exp_binary64_1142` `flip--_binary64_1076` `flip3--_binary64_1105` `asin-acos_binary64_1281` `pow-prod-down_binary64_1172` `unswap-sqr_binary64_1069` `sin-mult_binary64_1256`

Counts

4 → 64

Calls

4 calls:

8.0ms	(-.f64 (cos.f64 delta) (log.f64 (exp.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))))))
6.0ms	(.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))))
3.0ms	(log.f64 (exp.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))))))
1.0ms	(asin.f64 (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))

series1.2s (6.9%)

Counts

4 → 12

Calls

4 calls:

521.0ms	(-.f64 (cos.f64 delta) (log.f64 (exp.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))))))
433.0ms	(log.f64 (exp.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))))))
250.0ms	(.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))))
33.0ms	(asin.f64 (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))

simplify86.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4889	2821
1	4889	2821

prune112.0ms (0.6%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	75	1	76
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	76	7	83

Merged error: 0.0b

Counts

83 → 7

Compiler

Compiled 3405 to 548 computations (83.9% saved)

localize37.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (sin.f64 theta) (sin.f64 delta))
0.3b	(asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))
0.5b	(-.f64 (cos.f64 delta) (log.f64 (pow.f64 (exp.f64 (sin.f64 phi1)) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))))))
2.8b	(log.f64 (pow.f64 (exp.f64 (sin.f64 phi1)) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))))

rewrite31.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`add-sqr-sqrt_binary64_1123`
14×	`log-prod_binary64_1187`
13×	`*-un-lft-identity_binary64_1101`
11×	`add-cube-cbrt_binary64_1136`
7×	`associate--r+_binary64_1037` `add-exp-log_binary64_1139`
6×	`unpow-prod-down_binary64_1180` `pow1_binary64_1162` `add-cbrt-cube_binary64_1137`
5×	`add-log-exp_binary64_1140`
4×	`cancel-sign-sub-inv_binary64_1067`
3×	`rem-log-exp_binary64_1142` `asin-acos_binary64_1281` `associate-r_binary64_1041` `associate-l_binary64_1042`
2×	`pow-sub_binary64_1177` `log-pow_binary64_1190` `log-div_binary64_1188` `sqr-pow_binary64_1073` `sin-diff_binary64_1237`
1×	`diff-log_binary64_1193` `*-commutative_binary64_1032` `pow-exp_binary64_1169` `cbrt-unprod_binary64_1134` `difference-of-squares_binary64_1070` `prod-exp_binary64_1150` `sub-neg_binary64_1094` `distribute-lft-out--_binary64_1053` `flip--_binary64_1076` `flip3--_binary64_1105` `associate--r-_binary64_1040` `pow-prod-down_binary64_1172` `unswap-sqr_binary64_1069` `pow-to-exp_binary64_1170` `sin-mult_binary64_1256`

Counts

4 → 71

Calls

4 calls:

10.0ms	(-.f64 (cos.f64 delta) (log.f64 (pow.f64 (exp.f64 (sin.f64 phi1)) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))))))
5.0ms	(*.f64 (sin.f64 theta) (sin.f64 delta))
5.0ms	(log.f64 (pow.f64 (exp.f64 (sin.f64 phi1)) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))))
1.0ms	(asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))

series1.1s (6.3%)

Counts

4 → 12

Calls

4 calls:

547.0ms	(-.f64 (cos.f64 delta) (log.f64 (pow.f64 (exp.f64 (sin.f64 phi1)) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))))))
485.0ms	(log.f64 (pow.f64 (exp.f64 (sin.f64 phi1)) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))))
72.0ms	(*.f64 (sin.f64 theta) (sin.f64 delta))
33.0ms	(asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))

simplify96.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	4874	2622
1	4874	2622

prune104.0ms (0.6%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	83	0	83
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	83	7	90

Merged error: 0.0b

Counts

90 → 7

Compiler

Compiled 3552 to 419 computations (88.2% saved)

regimes372.0ms (2.1%)

Compiler: Compiled 4702 to 2926 computations (37.8% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	57	55
1	57	55

end0.0ms (0%)

sample8.5s (47.2%)

Algorithm

1×

intervals

Results

5.7s	3929×	body	1024	valid
1.1s	1372×	body	512	valid
442.0ms	2163×	body	128	valid
251.0ms	526×	body	256	valid
34.0ms	10×	body	2048	valid

Compiler

Compiled 719 to 450 computations (37.4% saved)

Details

analyze3.6s (20%)

sample253.0ms (1.4%)

simplify208.0ms (1.2%)

prune4.0ms (0%)

localize32.0ms (0.2%)

rewrite26.0ms (0.1%)

series657.0ms (3.7%)

simplify89.0ms (0.5%)

prune115.0ms (0.6%)

localize36.0ms (0.2%)

rewrite49.0ms (0.3%)

series924.0ms (5.2%)

simplify82.0ms (0.5%)

prune139.0ms (0.8%)

localize35.0ms (0.2%)

rewrite30.0ms (0.2%)

series1.2s (6.9%)

simplify86.0ms (0.5%)

prune112.0ms (0.6%)

localize37.0ms (0.2%)

rewrite31.0ms (0.2%)

series1.1s (6.3%)

simplify96.0ms (0.5%)

prune104.0ms (0.6%)

regimes372.0ms (2.1%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample8.5s (47.2%)

Profiling