Details

analyze1.9s (20.1%)

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
9.4%	90.4%	0.2%	9
9.4%	90.4%	0.2%	10
10.9%	88.9%	0.2%	11
10.9%	88.9%	0.2%	12
10.9%	88.9%	0.2%	13
10.9%	88.9%	0.2%	14

sample183.0ms (1.9%)

Algorithm

1×

intervals

Results

112.0ms	112×	body	1280	valid
38.0ms	73×	body	640	valid
10.0ms	27×	body	320	valid
4.0ms	30×	body	80	valid
3.0ms	14×	body	160	valid

simplify15.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (13.0ms)

Iter	Nodes	Cost
0	270	20
1	270	20

prune9.0ms (0.1%)

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: 0.9b

Counts

2 → 1

localize21.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
0.5b	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
3.9b	(sin (- lambda1 lambda2))
4.2b	(cos (- lambda1 lambda2))

rewrite13.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`add-log-exp`
4×	`pow1` `add-exp-log` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
3×	`cos-diff`
2×	`sub-neg` `associate-+r+`
1×	`+-commutative` `distribute-rgt-in` `cos-sum` `distribute-lft-in` `flip3-+` `sin-sum` `sum-log` `sin-diff` `flip-+`

Counts

4 → 38

Calls

4 calls:

4.0ms	(cos (- lambda1 lambda2))
4.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
4.0ms	(sin (- lambda1 lambda2))
1.0ms	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))

series44.0ms (0.5%)

Counts

4 → 12

Calls

4 calls:

27.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
7.0ms	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
5.0ms	(sin (- lambda1 lambda2))
4.0ms	(cos (- lambda1 lambda2))

simplify44.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

50 → 50

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	4947	591
1	4947	591

prune150.0ms (1.6%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	38	12	50
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	39	12	51

Merged error: 0.7b

Counts

51 → 12

localize31.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(* (cos lambda1) (sin lambda2))
0.2b	(atan2 (* (cos phi2) (- (* (cos lambda2) (sin lambda1)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
0.5b	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
4.2b	(cos (- lambda1 lambda2))

rewrite14.0ms (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×	`cos-diff` `associate-r` `associate-l`
2×	`associate-+r+`
1×	`+-commutative` `distribute-rgt-in` `sub-neg` `cos-sum` `distribute-lft-in` `flip3-+` `pow-prod-down` `prod-exp` `sum-log` `*-commutative` `cbrt-unprod` `flip-+` `unswap-sqr`

Counts

4 → 47

Calls

4 calls:

4.0ms	(* (cos lambda1) (sin lambda2))
4.0ms	(cos (- lambda1 lambda2))
4.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
1.0ms	(atan2 (* (cos phi2) (- (* (cos lambda2) (sin lambda1)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))

series48.0ms (0.5%)

Counts

4 → 12

Calls

4 calls:

24.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
11.0ms	(* (cos lambda1) (sin lambda2))
10.0ms	(atan2 (* (cos phi2) (- (* (cos lambda2) (sin lambda1)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
4.0ms	(cos (- lambda1 lambda2))

simplify76.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

59 → 59

Iterations

Useful iterations: 0 (70.0ms)

Iter	Nodes	Cost
0	5109	730

prune141.0ms (1.5%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	58	1	59
Fresh	1	10	11
Picked	1	0	1
Done	0	0	0
Total	60	11	71

Merged error: 0.1b

Counts

71 → 11

localize32.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(* (cos lambda1) (sin lambda2))
0.2b	(* (sin lambda1) (sin lambda2))
0.3b	(atan2 (* (cos phi2) (- (* (cos lambda2) (sin lambda1)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
0.4b	(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

rewrite15.0ms (0.2%)

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×	`associate-+r+` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`+-commutative` `distribute-rgt-in` `distribute-lft-in` `flip3-+` `sum-log` `flip-+` `sin-mult`

Counts

4 → 57

Calls

4 calls:

5.0ms	(* (sin lambda1) (sin lambda2))
4.0ms	(* (cos lambda1) (sin lambda2))
4.0ms	(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))
1.0ms	(atan2 (* (cos phi2) (- (* (cos lambda2) (sin lambda1)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

series84.0ms (0.9%)

Counts

4 → 12

Calls

4 calls:

51.0ms	(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))
14.0ms	(atan2 (* (cos phi2) (- (* (cos lambda2) (sin lambda1)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
9.0ms	(* (cos lambda1) (sin lambda2))
9.0ms	(* (sin lambda1) (sin lambda2))

simplify46.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	4961	985
1	4961	985

prune143.0ms (1.5%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	68	1	69
Fresh	1	9	10
Picked	1	0	1
Done	0	0	0
Total	70	10	80

Merged error: 0.0b

Counts

80 → 10

localize35.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (* (cos lambda1) (sin lambda2))) (cbrt (* (cos lambda1) (sin lambda2))))
0.6b	(cbrt (* (cos lambda1) (sin lambda2)))
0.6b	(cbrt (* (cos lambda1) (sin lambda2)))
0.6b	(cbrt (* (cos lambda1) (sin lambda2)))

rewrite17.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`pow1`
10×	`add-sqr-sqrt`
9×	`pow1/3`
8×	`add-cube-cbrt` `*-un-lft-identity`
7×	`cbrt-prod`
6×	`add-exp-log`
4×	`swap-sqr` `associate-r` `associate-l` `add-cbrt-cube` `add-log-exp`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 58

Calls

4 calls:

6.0ms	(* (cbrt (* (cos lambda1) (sin lambda2))) (cbrt (* (cos lambda1) (sin lambda2))))
3.0ms	(cbrt (* (cos lambda1) (sin lambda2)))
3.0ms	(cbrt (* (cos lambda1) (sin lambda2)))
3.0ms	(cbrt (* (cos lambda1) (sin lambda2)))

series87.0ms (0.9%)

Counts

4 → 12

Calls

4 calls:

28.0ms	(* (cbrt (* (cos lambda1) (sin lambda2))) (cbrt (* (cos lambda1) (sin lambda2))))
22.0ms	(cbrt (* (cos lambda1) (sin lambda2)))
19.0ms	(cbrt (* (cos lambda1) (sin lambda2)))
19.0ms	(cbrt (* (cos lambda1) (sin lambda2)))

simplify45.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5097	525

prune101.0ms (1.1%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	69	1	70
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	69	11	80

Merged error: 0.0b

Counts

80 → 11

regimes587.0ms (6.1%)

Accuracy

Total 0.4b remaining (73.9%)

Threshold costs 0.4b (73.9%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	62	49
1	62	49

end0.0ms (0%)

sample5.7s (59.2%)

Algorithm

1×

intervals

Results

3.4s	3508×	body	1280	valid
1.3s	2331×	body	640	valid
382.0ms	1027×	body	320	valid
107.0ms	442×	body	160	valid
84.0ms	692×	body	80	valid

Details

analyze1.9s (20.1%)

sample183.0ms (1.9%)

simplify15.0ms (0.2%)

prune9.0ms (0.1%)

localize21.0ms (0.2%)

rewrite13.0ms (0.1%)

series44.0ms (0.5%)

simplify44.0ms (0.5%)

prune150.0ms (1.6%)

localize31.0ms (0.3%)

rewrite14.0ms (0.1%)

series48.0ms (0.5%)

simplify76.0ms (0.8%)

prune141.0ms (1.5%)

localize32.0ms (0.3%)

rewrite15.0ms (0.2%)

series84.0ms (0.9%)

simplify46.0ms (0.5%)

prune143.0ms (1.5%)

localize35.0ms (0.4%)

rewrite17.0ms (0.2%)

series87.0ms (0.9%)

simplify45.0ms (0.5%)

prune101.0ms (1.1%)

regimes587.0ms (6.1%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample5.7s (59.2%)

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