Details

analyze3.6s (19.9%)

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
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)

sample299.0ms (1.7%)

Algorithm

1×

intervals

Results

189.0ms	110×	body	1280	valid
59.0ms	61×	body	640	valid
15.0ms	54×	body	80	valid
14.0ms	20×	body	320	valid
5.0ms	11×	body	160	valid

Compiler

Compiled 67 to 52 computations (22.4% saved)

simplify80.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	464	55
1	464	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: 0.2b

Counts

2 → 1

Compiler

Compiled 66 to 46 computations (30.3% saved)

localize31.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1))
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)))))))

rewrite23.0ms (0.1%)

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×	`add-log-exp_binary64` `associate-r_binary64`
4×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `associate-l_binary64` `prod-exp_binary64` `insert-posit16`
2×	`sin-mult_binary64` `*-commutative_binary64`
1×	`sub-neg_binary64` `asin-acos_binary64` `flip3--_binary64` `diff-log_binary64` `unswap-sqr_binary64` `flip--_binary64` `associate-*l/_binary64`

Counts

4 → 61

Calls

4 calls:

8.0ms	(.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1))
7.0ms	(.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))))))
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)))))))
2.0ms	(asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))

series869.0ms (4.8%)

Counts

4 → 12

Calls

4 calls:

391.0ms	(-.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)))))))
296.0ms	(.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))))))
142.0ms	(.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1))
40.0ms	(asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))

simplify132.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 0 (98.0ms)

Iter	Nodes	Cost
0	4881	2229
1	4881	2229

prune144.0ms (0.8%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	64	9	73
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	65	9	74

Merged error: 0.1b

Counts

74 → 9

Compiler

Compiled 3383 to 608 computations (82% saved)

localize31.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (sin.f64 theta) (.f64 (cos.f64 phi1) (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)))))))

rewrite24.0ms (0.1%)

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×	`add-log-exp_binary64` `associate-l_binary64`
4×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `associate-r_binary64` `prod-exp_binary64` `insert-posit16`
2×	`*-commutative_binary64`
1×	`sub-neg_binary64` `asin-acos_binary64` `flip3--_binary64` `diff-log_binary64` `unswap-sqr_binary64` `sin-mult_binary64` `flip--_binary64`

Counts

4 → 60

Calls

4 calls:

8.0ms	(.f64 (sin.f64 theta) (.f64 (cos.f64 phi1) (sin.f64 delta)))
7.0ms	(.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))))))
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)))))))
2.0ms	(asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))

series860.0ms (4.8%)

Counts

4 → 12

Calls

4 calls:

388.0ms	(-.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)))))))
293.0ms	(.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))))))
138.0ms	(.f64 (sin.f64 theta) (.f64 (cos.f64 phi1) (sin.f64 delta)))
41.0ms	(asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))

simplify166.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 0 (132.0ms)

Iter	Nodes	Cost
0	4882	2205
1	4882	2205

prune121.0ms (0.7%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	67	5	72
Fresh	2	6	8
Picked	1	0	1
Done	0	0	0
Total	70	11	81

Merged error: 0.1b

Counts

81 → 11

Compiler

Compiled 3416 to 640 computations (81.3% saved)

localize30.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite32.0ms (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` `add-cube-cbrt_binary64` `associate-l*_binary64`
7×	`associate-r_binary64`
6×	`add-log-exp_binary64`
5×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `prod-exp_binary64`
4×	`insert-posit16`
3×	`*-commutative_binary64`
2×	`associate--r+_binary64` `associate-*r/_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64`
1×	`flip3-+_binary64` `sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `flip--_binary64` `flip-+_binary64`

Counts

4 → 75

Calls

4 calls:

11.0ms	(.f64 (sin.f64 phi1) (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))
8.0ms	(.f64 (sin.f64 theta) (.f64 (cos.f64 phi1) (sin.f64 delta)))
6.0ms	(*.f64 (cos.f64 phi1) (sin.f64 delta))
5.0ms	(-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))

series891.0ms (4.9%)

Counts

4 → 12

Calls

4 calls:

386.0ms	(-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))
298.0ms	(.f64 (sin.f64 phi1) (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))
134.0ms	(.f64 (sin.f64 theta) (.f64 (cos.f64 phi1) (sin.f64 delta)))
73.0ms	(*.f64 (cos.f64 phi1) (sin.f64 delta))

simplify101.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	5565	2061

prune153.0ms (0.8%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	77	10	87
Fresh	9	1	10
Picked	1	0	1
Done	0	0	0
Total	87	11	98

Merged error: 0.1b

Counts

98 → 11

Compiler

Compiled 3763 to 740 computations (80.3% saved)

localize27.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (sin.f64 theta) (.f64 (cos.f64 phi1) (sin.f64 delta)))
0.3b	(.f64 (.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)) (sin.f64 phi1))
0.3b	(pow.f64 (sin.f64 phi1) 2)
0.7b	(-.f64 (cos.f64 delta) (*.f64 (cos.f64 delta) (pow.f64 (sin.f64 phi1) 2)))

rewrite30.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`pow1_binary64` `add-exp-log_binary64`
18×	`add-cbrt-cube_binary64`
9×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `prod-exp_binary64`
8×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
6×	`add-log-exp_binary64`
4×	`associate-r_binary64` `associate-l_binary64` `insert-posit16`
3×	`pow-unpow_binary64` `unpow-prod-down_binary64`
2×	`*-commutative_binary64`
1×	`pow-to-exp_binary64` `sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `unpow2_binary64` `pow-pow_binary64` `sqr-pow_binary64` `flip--_binary64` `pow-exp_binary64`

Counts

4 → 72

Calls

4 calls:

11.0ms	(.f64 (.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)) (sin.f64 phi1))
8.0ms	(.f64 (sin.f64 theta) (.f64 (cos.f64 phi1) (sin.f64 delta)))
5.0ms	(-.f64 (cos.f64 delta) (*.f64 (cos.f64 delta) (pow.f64 (sin.f64 phi1) 2)))
3.0ms	(pow.f64 (sin.f64 phi1) 2)

series488.0ms (2.7%)

Counts

4 → 12

Calls

4 calls:

194.0ms	(.f64 (.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)) (sin.f64 phi1))
135.0ms	(-.f64 (cos.f64 delta) (*.f64 (cos.f64 delta) (pow.f64 (sin.f64 phi1) 2)))
132.0ms	(.f64 (sin.f64 theta) (.f64 (cos.f64 phi1) (sin.f64 delta)))
28.0ms	(pow.f64 (sin.f64 phi1) 2)

simplify152.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (123.0ms)

Iter	Nodes	Cost
0	4921	1269
1	4921	1269

prune117.0ms (0.6%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	82	2	84
Fresh	3	7	10
Picked	0	1	1
Done	0	0	0
Total	85	10	95

Merged error: 0.1b

Counts

95 → 10

Compiler

Compiled 3072 to 783 computations (74.5% saved)

regimes179.0ms (1%)

Compiler: Compiled 2335 to 1275 computations (45.4% saved)

bsearch0.0ms (0%)

simplify9.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	110	54
1	110	54

end0.0ms (0%)

sample9.5s (52.4%)

Algorithm

1×

intervals

Results

5.7s	3144×	body	1280	valid
1.9s	1873×	body	640	valid
469.0ms	679×	body	320	valid
398.0ms	1961×	body	80	valid
151.0ms	343×	body	160	valid

Compiler

Compiled 532 to 296 computations (44.4% saved)

Details

analyze3.6s (19.9%)

sample299.0ms (1.7%)

simplify80.0ms (0.4%)

prune4.0ms (0%)

localize31.0ms (0.2%)

rewrite23.0ms (0.1%)

series869.0ms (4.8%)

simplify132.0ms (0.7%)

prune144.0ms (0.8%)

localize31.0ms (0.2%)

rewrite24.0ms (0.1%)

series860.0ms (4.8%)

simplify166.0ms (0.9%)

prune121.0ms (0.7%)

localize30.0ms (0.2%)

rewrite32.0ms (0.2%)

series891.0ms (4.9%)

simplify101.0ms (0.6%)

prune153.0ms (0.8%)

localize27.0ms (0.1%)

rewrite30.0ms (0.2%)

series488.0ms (2.7%)

simplify152.0ms (0.8%)

prune117.0ms (0.6%)

regimes179.0ms (1%)

bsearch0.0ms (0%)

simplify9.0ms (0%)

end0.0ms (0%)

sample9.5s (52.4%)

Profiling