Details

analyze3.9s (26.1%)

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

sample303.0ms (2%)

Algorithm

1×

intervals

Results

183.0ms	103×	body	1280	valid
58.0ms	54×	body	640	valid
22.0ms	24×	body	320	valid
12.0ms	64×	body	80	valid
5.0ms	11×	body	160	valid

simplify29.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	462	33
1	462	33

prune13.0ms (0.1%)

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

localize32.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(atan2 (* (* (sin theta) (sin delta)) (cos phi1)) (- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))
0.3b	(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
0.3b	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
0.6b	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

rewrite16.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
6×	`pow1` `add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `add-log-exp`
3×	`associate-r` `associate-l`
1×	`sub-neg` `asin-acos` `flip3--` `diff-log` `pow-prod-down` `prod-exp` `*-commutative` `flip--` `cbrt-unprod` `sin-mult` `unswap-sqr`

Counts

4 → 45

Calls

4 calls:

7.0ms	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))
5.0ms	(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
1.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
1.0ms	(atan2 (* (* (sin theta) (sin delta)) (cos phi1)) (- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))

series101.0ms (0.7%)

Counts

4 → 12

Calls

4 calls:

46.0ms	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))
38.0ms	(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
12.0ms	(atan2 (* (* (sin theta) (sin delta)) (cos phi1)) (- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))
5.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))

simplify52.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

57 → 57

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4908	1415
1	4908	1415

prune162.0ms (1.1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	49	8	57
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	50	8	58

Merged error: 0.1b

Counts

58 → 8

localize27.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(* (cos delta) (sin phi1))
0.2b	(atan2 (* (* (sin theta) (sin delta)) (cos phi1)) (- (cos delta) (* (sin phi1) (+ (* (cos delta) (sin phi1)) (* (* (cos phi1) (sin delta)) (cos theta))))))
0.3b	(* (sin phi1) (+ (* (cos delta) (sin phi1)) (* (* (cos phi1) (sin delta)) (cos theta))))
0.6b	(- (cos delta) (* (sin phi1) (+ (* (cos delta) (sin phi1)) (* (* (cos phi1) (sin delta)) (cos theta)))))

rewrite19.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
8×	`pow1` `add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
6×	`associate-r` `associate-l` `add-log-exp`
2×	`distribute-rgt-in` `distribute-lft-in` `associate-r/` `pow-prod-down` `prod-exp` `-commutative` `cbrt-unprod` `associate--r+` `unswap-sqr`
1×	`sub-neg` `flip3--` `flip3-+` `diff-log` `flip--` `flip-+`

Counts

4 → 60

Calls

4 calls:

8.0ms	(* (sin phi1) (+ (* (cos delta) (sin phi1)) (* (* (cos phi1) (sin delta)) (cos theta))))
5.0ms	(* (cos delta) (sin phi1))
4.0ms	(- (cos delta) (* (sin phi1) (+ (* (cos delta) (sin phi1)) (* (* (cos phi1) (sin delta)) (cos theta)))))
1.0ms	(atan2 (* (* (sin theta) (sin delta)) (cos phi1)) (- (cos delta) (* (sin phi1) (+ (* (cos delta) (sin phi1)) (* (* (cos phi1) (sin delta)) (cos theta))))))

series103.0ms (0.7%)

Counts

4 → 12

Calls

4 calls:

47.0ms	(- (cos delta) (* (sin phi1) (+ (* (cos delta) (sin phi1)) (* (* (cos phi1) (sin delta)) (cos theta)))))
36.0ms	(* (sin phi1) (+ (* (cos delta) (sin phi1)) (* (* (cos phi1) (sin delta)) (cos theta))))
11.0ms	(atan2 (* (* (sin theta) (sin delta)) (cos phi1)) (- (cos delta) (* (sin phi1) (+ (* (cos delta) (sin phi1)) (* (* (cos phi1) (sin delta)) (cos theta))))))
9.0ms	(* (cos delta) (sin phi1))

simplify38.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	4990	1345
1	4990	1345

prune149.0ms (1%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	67	5	72
Fresh	7	0	7
Picked	1	0	1
Done	0	0	0
Total	75	5	80

Merged error: 0.0b

Counts

80 → 5

localize27.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(* (sin theta) (sin delta))
0.2b	(atan2 (* (* (sin theta) (sin delta)) (cos phi1)) (- (* (cos delta) (* (cos phi1) (cos phi1))) (* (sin phi1) (* (* (cos phi1) (sin delta)) (cos theta)))))
0.3b	(* (sin phi1) (* (* (cos phi1) (sin delta)) (cos theta)))
0.3b	(* (cos phi1) (cos phi1))

rewrite20.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`pow1`
17×	`add-exp-log` `add-cbrt-cube`
15×	`add-sqr-sqrt`
11×	`add-cube-cbrt` `*-un-lft-identity`
9×	`associate-l`
8×	`pow-prod-down` `prod-exp` `cbrt-unprod`
7×	`associate-r`
4×	`add-log-exp`
3×	`swap-sqr` `*-commutative`
2×	`unswap-sqr`
1×	`pow2` `sqr-cos-a` `pow-plus` `pow-sqr` `cos-mult` `pow-prod-up` `sin-mult`

Counts

4 → 74

Calls

4 calls:

8.0ms	(* (sin phi1) (* (* (cos phi1) (sin delta)) (cos theta)))
4.0ms	(* (sin theta) (sin delta))
4.0ms	(* (cos phi1) (cos phi1))
1.0ms	(atan2 (* (* (sin theta) (sin delta)) (cos phi1)) (- (* (cos delta) (* (cos phi1) (cos phi1))) (* (sin phi1) (* (* (cos phi1) (sin delta)) (cos theta)))))

series48.0ms (0.3%)

Counts

4 → 12

Calls

4 calls:

25.0ms	(* (sin phi1) (* (* (cos phi1) (sin delta)) (cos theta)))
10.0ms	(atan2 (* (* (sin theta) (sin delta)) (cos phi1)) (- (* (cos delta) (* (cos phi1) (cos phi1))) (* (sin phi1) (* (* (cos phi1) (sin delta)) (cos theta)))))
9.0ms	(* (sin theta) (sin delta))
3.0ms	(* (cos phi1) (cos phi1))

simplify51.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5064	833

prune183.0ms (1.2%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	82	4	86
Fresh	1	3	4
Picked	1	0	1
Done	0	0	0
Total	84	7	91

Merged error: 0.0b

Counts

91 → 7

localize30.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(* (sin theta) (sin delta))
0.2b	(atan2 (* (* (sin theta) (sin delta)) (cos phi1)) (- (* (cos delta) (* (cos phi1) (cos phi1))) (* (* (sin phi1) (* (cos phi1) (sin delta))) (cos theta))))
0.2b	(* (sin phi1) (* (cos phi1) (sin delta)))
0.3b	(* (cos phi1) (cos phi1))

rewrite17.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`pow1`
15×	`add-sqr-sqrt`
13×	`add-exp-log` `add-cbrt-cube`
11×	`add-cube-cbrt` `*-un-lft-identity`
9×	`associate-l`
7×	`associate-r`
5×	`pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`add-log-exp`
3×	`swap-sqr` `*-commutative`
2×	`unswap-sqr`
1×	`pow2` `sqr-cos-a` `pow-plus` `pow-sqr` `cos-mult` `pow-prod-up` `sin-mult`

Counts

4 → 71

Calls

4 calls:

6.0ms	(* (sin phi1) (* (cos phi1) (sin delta)))
4.0ms	(* (sin theta) (sin delta))
4.0ms	(* (cos phi1) (cos phi1))
1.0ms	(atan2 (* (* (sin theta) (sin delta)) (cos phi1)) (- (* (cos delta) (* (cos phi1) (cos phi1))) (* (* (sin phi1) (* (cos phi1) (sin delta))) (cos theta))))

series36.0ms (0.2%)

Counts

4 → 12

Calls

4 calls:

14.0ms	(* (sin phi1) (* (cos phi1) (sin delta)))
10.0ms	(atan2 (* (* (sin theta) (sin delta)) (cos phi1)) (- (* (cos delta) (* (cos phi1) (cos phi1))) (* (* (sin phi1) (* (cos phi1) (sin delta))) (cos theta))))
9.0ms	(* (sin theta) (sin delta))
3.0ms	(* (cos phi1) (cos phi1))

simplify55.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4904	737
1	4904	737

prune121.0ms (0.8%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	83	0	83
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	83	7	90

Merged error: 0.0b

Counts

90 → 7

regimes487.0ms (3.2%)

Accuracy

Total 0.0b remaining (46.9%)

Threshold costs 0.0b (46.9%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	85	31
1	85	31

end0.0ms (0%)

sample9.0s (59.8%)

Algorithm

1×

intervals

Results

5.5s	3056×	body	1280	valid
1.9s	1824×	body	640	valid
538.0ms	754×	body	320	valid
417.0ms	2045×	body	80	valid
146.0ms	321×	body	160	valid

Details

analyze3.9s (26.1%)

sample303.0ms (2%)

simplify29.0ms (0.2%)

prune13.0ms (0.1%)

localize32.0ms (0.2%)

rewrite16.0ms (0.1%)

series101.0ms (0.7%)

simplify52.0ms (0.3%)

prune162.0ms (1.1%)

localize27.0ms (0.2%)

rewrite19.0ms (0.1%)

series103.0ms (0.7%)

simplify38.0ms (0.3%)

prune149.0ms (1%)

localize27.0ms (0.2%)

rewrite20.0ms (0.1%)

series48.0ms (0.3%)

simplify51.0ms (0.3%)

prune183.0ms (1.2%)

localize30.0ms (0.2%)

rewrite17.0ms (0.1%)

series36.0ms (0.2%)

simplify55.0ms (0.4%)

prune121.0ms (0.8%)

regimes487.0ms (3.2%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample9.0s (59.8%)

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