Details

analyze2.9s (20.3%)

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
7.8%	92%	0.2%	9
7.8%	92%	0.2%	10
10.1%	89.7%	0.2%	11
10.1%	89.7%	0.2%	12
13.9%	85.9%	0.2%	13
13.9%	85.9%	0.2%	14

sample375.0ms (2.6%)

Algorithm

1×

intervals

Results

264.0ms	144×	body	1280	valid
75.0ms	70×	body	640	valid
11.0ms	15×	body	320	valid
4.0ms	20×	body	80	valid
3.0ms	7×	body	160	valid

simplify14.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (13.0ms)

Iter	Nodes	Cost
0	384	24
1	384	24

prune10.0ms (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: 14.9b

Counts

2 → 1

localize24.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(* (sin (- lambda1 lambda2)) (cos phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
3.8b	(sin (- lambda1 lambda2))
3.9b	(cos (- lambda1 lambda2))

rewrite21.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`pow1` `add-exp-log` `add-cbrt-cube`
9×	`add-sqr-sqrt`
7×	`add-cube-cbrt` `*-un-lft-identity`
6×	`associate-r`
4×	`associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `add-log-exp`
3×	`cos-diff`
2×	`sub-neg` `*-commutative` `sin-cos-mult`
1×	`distribute-rgt-in` `cos-sum` `distribute-lft-in` `sin-sum` `associate-*l/` `sin-diff` `unswap-sqr`

Counts

4 → 58

Calls

4 calls:

6.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
6.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
4.0ms	(cos (- lambda1 lambda2))
4.0ms	(sin (- lambda1 lambda2))

series49.0ms (0.3%)

Counts

4 → 12

Calls

4 calls:

23.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
14.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
7.0ms	(sin (- lambda1 lambda2))
4.0ms	(cos (- lambda1 lambda2))

simplify46.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	4879	620
1	4879	620

prune198.0ms (1.4%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	54	16	70
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	55	16	71

Merged error: 6.8b

Counts

71 → 16

localize33.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(* (cos lambda1) (sin lambda2))
0.2b	(* (- (* (cos lambda2) (sin lambda1)) (* (cos lambda1) (sin lambda2))) (cos phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
3.9b	(cos (- lambda1 lambda2))

rewrite21.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`pow1` `add-exp-log` `add-sqr-sqrt` `add-cbrt-cube`
9×	`add-cube-cbrt` `-un-lft-identity` `associate-r*`
7×	`associate-l`
5×	`pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`add-log-exp`
3×	`cos-diff` `associate-l/` `-commutative`
2×	`unswap-sqr`
1×	`distribute-rgt-in` `sub-neg` `cos-sum` `flip3--` `distribute-lft-in` `sin-cos-mult` `flip--`

Counts

4 → 68

Calls

4 calls:

6.0ms	(* (- (* (cos lambda2) (sin lambda1)) (* (cos lambda1) (sin lambda2))) (cos phi2))
6.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
4.0ms	(* (cos lambda1) (sin lambda2))
4.0ms	(cos (- lambda1 lambda2))

series66.0ms (0.5%)

Counts

4 → 12

Calls

4 calls:

30.0ms	(* (- (* (cos lambda2) (sin lambda1)) (* (cos lambda1) (sin lambda2))) (cos phi2))
23.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
9.0ms	(* (cos lambda1) (sin lambda2))
4.0ms	(cos (- lambda1 lambda2))

simplify27.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 0 (20.0ms)

Iter	Nodes	Cost
0	5076	860

prune209.0ms (1.4%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	75	5	80
Fresh	8	7	15
Picked	1	0	1
Done	0	0	0
Total	84	12	96

Merged error: 0.1b

Counts

96 → 12

localize34.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(* (- (* (cos lambda2) (sin lambda1)) (* (cos lambda1) (sin lambda2))) (cos phi2))
0.2b	(* (sin lambda1) (sin lambda2))
0.2b	(* (* (sin lambda1) (sin lambda2)) (* (sin phi1) (cos phi2)))
0.2b	(* (* (cos lambda1) (cos lambda2)) (* (sin phi1) (cos phi2)))

rewrite31.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`pow1` `add-exp-log` `add-cbrt-cube`
18×	`pow-prod-down` `prod-exp` `cbrt-unprod`
12×	`add-sqr-sqrt`
8×	`add-cube-cbrt` `-un-lft-identity` `associate-r` `associate-l*`
4×	`associate-l/` `-commutative` `sin-cos-mult` `add-log-exp`
3×	`sin-mult`
2×	`frac-times` `associate-*r/` `cos-mult` `unswap-sqr`
1×	`flip3--` `flip--`

Counts

4 → 89

Calls

4 calls:

9.0ms	(* (* (cos lambda1) (cos lambda2)) (* (sin phi1) (cos phi2)))
8.0ms	(* (* (sin lambda1) (sin lambda2)) (* (sin phi1) (cos phi2)))
6.0ms	(* (- (* (cos lambda2) (sin lambda1)) (* (cos lambda1) (sin lambda2))) (cos phi2))
4.0ms	(* (sin lambda1) (sin lambda2))

series94.0ms (0.6%)

Counts

4 → 12

Calls

4 calls:

30.0ms	(* (- (* (cos lambda2) (sin lambda1)) (* (cos lambda1) (sin lambda2))) (cos phi2))
28.0ms	(* (* (cos lambda1) (cos lambda2)) (* (sin phi1) (cos phi2)))
26.0ms	(* (* (sin lambda1) (sin lambda2)) (* (sin phi1) (cos phi2)))
9.0ms	(* (sin lambda1) (sin lambda2))

simplify43.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5122	1164

prune210.0ms (1.4%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	96	5	101
Fresh	3	8	11
Picked	1	0	1
Done	0	0	0
Total	100	13	113

Merged error: 0.1b

Counts

113 → 13

localize37.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(* (- (* (cos lambda2) (sin lambda1)) (* (cos lambda1) (sin lambda2))) (cos phi2))
0.2b	(* (sin lambda1) (sin lambda2))
0.2b	(* (* (cos lambda1) (cos lambda2)) (* (sin phi1) (cos phi2)))
3.0b	(log (exp (* (sin lambda1) (sin lambda2))))

rewrite23.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`pow1`
20×	`add-exp-log` `add-cbrt-cube`
13×	`add-sqr-sqrt`
10×	`pow-prod-down` `prod-exp` `cbrt-unprod`
9×	`add-cube-cbrt` `*-un-lft-identity`
7×	`associate-r` `associate-l`
5×	`add-log-exp`
3×	`log-prod` `associate-l/` `log-pow` `-commutative`
2×	`cos-mult` `sin-cos-mult` `unswap-sqr`
1×	`frac-times` `exp-prod` `flip3--` `exp-to-pow` `associate-*r/` `rem-log-exp` `flip--` `sin-mult`

Counts

4 → 78

Calls

4 calls:

8.0ms	(* (* (cos lambda1) (cos lambda2)) (* (sin phi1) (cos phi2)))
6.0ms	(* (- (* (cos lambda2) (sin lambda1)) (* (cos lambda1) (sin lambda2))) (cos phi2))
5.0ms	(* (sin lambda1) (sin lambda2))
2.0ms	(log (exp (* (sin lambda1) (sin lambda2))))

series77.0ms (0.5%)

Counts

4 → 12

Calls

4 calls:

30.0ms	(* (* (cos lambda1) (cos lambda2)) (* (sin phi1) (cos phi2)))
28.0ms	(* (- (* (cos lambda2) (sin lambda1)) (* (cos lambda1) (sin lambda2))) (cos phi2))
9.0ms	(log (exp (* (sin lambda1) (sin lambda2))))
9.0ms	(* (sin lambda1) (sin lambda2))

simplify28.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 0 (21.0ms)

Iter	Nodes	Cost
0	5244	946

prune125.0ms (0.9%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	89	1	90
Fresh	0	12	12
Picked	0	1	1
Done	0	0	0
Total	89	14	103

Merged error: 0.1b

Counts

103 → 14

regimes721.0ms (5%)

Accuracy

Total 0.1b remaining (65.6%)

Threshold costs 0.1b (65.6%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	139	46
1	139	46

end0.0ms (0%)

sample9.1s (62.4%)

Algorithm

1×

intervals

Results

6.7s	4623×	body	1280	valid
1.6s	1951×	body	640	valid
299.0ms	565×	body	320	valid
104.0ms	651×	body	80	valid
71.0ms	210×	body	160	valid

Details

analyze2.9s (20.3%)

sample375.0ms (2.6%)

simplify14.0ms (0.1%)

prune10.0ms (0.1%)

localize24.0ms (0.2%)

rewrite21.0ms (0.1%)

series49.0ms (0.3%)

simplify46.0ms (0.3%)

prune198.0ms (1.4%)

localize33.0ms (0.2%)

rewrite21.0ms (0.1%)

series66.0ms (0.5%)

simplify27.0ms (0.2%)

prune209.0ms (1.4%)

localize34.0ms (0.2%)

rewrite31.0ms (0.2%)

series94.0ms (0.6%)

simplify43.0ms (0.3%)

prune210.0ms (1.4%)

localize37.0ms (0.3%)

rewrite23.0ms (0.2%)

series77.0ms (0.5%)

simplify28.0ms (0.2%)

prune125.0ms (0.9%)

regimes721.0ms (5%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample9.1s (62.4%)

Profiling