Details

analyze3.6s (24.3%)

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
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

sample294.0ms (2%)

Algorithm

1×

intervals

Results

170.0ms	97×	body	1280	valid
69.0ms	64×	body	640	valid
19.0ms	27×	body	320	valid
12.0ms	60×	body	80	valid
3.0ms	8×	body	160	valid

simplify24.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	462	33
1	462	33

prune23.0ms (0.2%)

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: 0.1b

Counts

2 → 2

localize33.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(* (sin theta) (sin delta))
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))))
0.4b	(- (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

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×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `sin-mult` `unswap-sqr`
1×	`sub-neg` `asin-acos` `flip3--` `diff-log` `flip--`

Counts

4 → 57

Calls

4 calls:

5.0ms	(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
4.0ms	(* (sin theta) (sin delta))
4.0ms	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))
2.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))

series91.0ms (0.6%)

Counts

4 → 12

Calls

4 calls:

44.0ms	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))
33.0ms	(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
9.0ms	(* (sin theta) (sin delta))
5.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))

simplify49.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	4892	1209
1	4892	1209

prune166.0ms (1.1%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	62	7	69
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	64	7	71

Merged error: 0.0b

Counts

71 → 7

localize37.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.3b	(* (sin phi1) (sin (- (/ PI 2) (acos (+ (* (cos delta) (sin phi1)) (* (cos phi1) (* (sin delta) (cos theta))))))))
0.3b	(* (sin theta) (sin delta))
0.4b	(- (cos delta) (* (sin phi1) (sin (- (/ PI 2) (acos (+ (* (cos delta) (sin phi1)) (* (cos phi1) (* (sin delta) (cos theta)))))))))
2.9b	(- (/ PI 2) (acos (+ (* (cos delta) (sin phi1)) (* (cos phi1) (* (sin delta) (cos theta))))))

rewrite30.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`add-sqr-sqrt`
10×	`*-un-lft-identity`
8×	`pow1` `add-exp-log` `add-cube-cbrt` `sin-sum` `add-cbrt-cube` `add-log-exp`
6×	`sub-neg` `associate-r` `associate-l`
5×	`acos-asin` `associate--r-`
4×	`distribute-rgt-in` `distribute-lft-in` `associate--r+`
2×	`flip3--` `diff-log` `pow-prod-down` `prod-exp` `*-commutative` `flip--` `cbrt-unprod` `sin-mult` `difference-of-squares` `unswap-sqr`
1×	`times-frac` `distribute-lft-out--`

Counts

4 → 72

Calls

4 calls:

11.0ms	(* (sin phi1) (sin (- (/ PI 2) (acos (+ (* (cos delta) (sin phi1)) (* (cos phi1) (* (sin delta) (cos theta))))))))
8.0ms	(- (/ PI 2) (acos (+ (* (cos delta) (sin phi1)) (* (cos phi1) (* (sin delta) (cos theta))))))
4.0ms	(- (cos delta) (* (sin phi1) (sin (- (/ PI 2) (acos (+ (* (cos delta) (sin phi1)) (* (cos phi1) (* (sin delta) (cos theta)))))))))
4.0ms	(* (sin theta) (sin delta))

series101.0ms (0.7%)

Counts

4 → 12

Calls

4 calls:

47.0ms	(- (cos delta) (* (sin phi1) (sin (- (/ PI 2) (acos (+ (* (cos delta) (sin phi1)) (* (cos phi1) (* (sin delta) (cos theta)))))))))
36.0ms	(* (sin phi1) (sin (- (/ PI 2) (acos (+ (* (cos delta) (sin phi1)) (* (cos phi1) (* (sin delta) (cos theta))))))))
10.0ms	(- (/ PI 2) (acos (+ (* (cos delta) (sin phi1)) (* (cos phi1) (* (sin delta) (cos theta))))))
9.0ms	(* (sin theta) (sin delta))

simplify83.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (73.0ms)

Iter	Nodes	Cost
0	4818	1692
1	4818	1692

prune179.0ms (1.2%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	84	0	84
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	84	7	91

Merged error: 0.0b

Counts

91 → 7

localize35.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(asin (+ (* (cos delta) (sin phi1)) (* (cos phi1) (* (sin delta) (cos theta)))))
0.4b	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (cos delta) (sin phi1)) (* (cos phi1) (* (sin delta) (cos theta))))))))
0.5b	(cbrt (pow (- (cos delta) (* (sin phi1) (sin (asin (+ (* (cos delta) (sin phi1)) (* (cos phi1) (* (sin delta) (cos theta)))))))) 3))
0.6b	(pow (- (cos delta) (* (sin phi1) (sin (asin (+ (* (cos delta) (sin phi1)) (* (cos phi1) (* (sin delta) (cos theta)))))))) 3)

rewrite14.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`cbrt-prod`
10×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`unpow-prod-down` `cube-prod` `add-log-exp`
5×	`pow1` `add-exp-log` `add-cbrt-cube`
4×	`cube-div`
3×	`pow-unpow` `flip3--` `flip--`
2×	`cube-mult` `cbrt-div` `unpow3` `sqr-pow`
1×	`pow-to-exp` `sub-neg` `asin-acos` `pow-pow` `pow1/3` `diff-log` `pow-exp` `rem-cbrt-cube` `rem-cube-cbrt`

Counts

4 → 67

Calls

4 calls:

4.0ms	(pow (- (cos delta) (* (sin phi1) (sin (asin (+ (* (cos delta) (sin phi1)) (* (cos phi1) (* (sin delta) (cos theta)))))))) 3)
4.0ms	(cbrt (pow (- (cos delta) (* (sin phi1) (sin (asin (+ (* (cos delta) (sin phi1)) (* (cos phi1) (* (sin delta) (cos theta)))))))) 3))
4.0ms	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (cos delta) (sin phi1)) (* (cos phi1) (* (sin delta) (cos theta))))))))
1.0ms	(asin (+ (* (cos delta) (sin phi1)) (* (cos phi1) (* (sin delta) (cos theta)))))

series167.0ms (1.1%)

Counts

4 → 12

Calls

4 calls:

78.0ms	(pow (- (cos delta) (* (sin phi1) (sin (asin (+ (* (cos delta) (sin phi1)) (* (cos phi1) (* (sin delta) (cos theta)))))))) 3)
43.0ms	(cbrt (pow (- (cos delta) (* (sin phi1) (sin (asin (+ (* (cos delta) (sin phi1)) (* (cos phi1) (* (sin delta) (cos theta)))))))) 3))
41.0ms	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (cos delta) (sin phi1)) (* (cos phi1) (* (sin delta) (cos theta))))))))
5.0ms	(asin (+ (* (cos delta) (sin phi1)) (* (cos phi1) (* (sin delta) (cos theta)))))

simplify47.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5032	2279

prune172.0ms (1.2%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	79	0	79
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	79	7	86

Merged error: 0.0b

Counts

86 → 7

localize41.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (asin (+ (* (cos delta) (sin phi1)) (* (cos phi1) (* (sin delta) (cos theta)))))) (cbrt (asin (+ (* (cos delta) (sin phi1)) (* (cos phi1) (* (sin delta) (cos theta)))))))
0.6b	(cbrt (asin (+ (* (cos delta) (sin phi1)) (* (cos phi1) (* (sin delta) (cos theta))))))
0.6b	(cbrt (asin (+ (* (cos delta) (sin phi1)) (* (cos phi1) (* (sin delta) (cos theta))))))
0.6b	(cbrt (asin (+ (* (cos delta) (sin phi1)) (* (cos phi1) (* (sin delta) (cos theta))))))

rewrite11.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 73

Calls

4 calls:

5.0ms	(* (cbrt (asin (+ (* (cos delta) (sin phi1)) (* (cos phi1) (* (sin delta) (cos theta)))))) (cbrt (asin (+ (* (cos delta) (sin phi1)) (* (cos phi1) (* (sin delta) (cos theta)))))))
1.0ms	(cbrt (asin (+ (* (cos delta) (sin phi1)) (* (cos phi1) (* (sin delta) (cos theta))))))
1.0ms	(cbrt (asin (+ (* (cos delta) (sin phi1)) (* (cos phi1) (* (sin delta) (cos theta))))))
1.0ms	(cbrt (asin (+ (* (cos delta) (sin phi1)) (* (cos phi1) (* (sin delta) (cos theta))))))

series116.0ms (0.8%)

Counts

4 → 12

Calls

4 calls:

38.0ms	(* (cbrt (asin (+ (* (cos delta) (sin phi1)) (* (cos phi1) (* (sin delta) (cos theta)))))) (cbrt (asin (+ (* (cos delta) (sin phi1)) (* (cos phi1) (* (sin delta) (cos theta)))))))
28.0ms	(cbrt (asin (+ (* (cos delta) (sin phi1)) (* (cos phi1) (* (sin delta) (cos theta))))))
25.0ms	(cbrt (asin (+ (* (cos delta) (sin phi1)) (* (cos phi1) (* (sin delta) (cos theta))))))
25.0ms	(cbrt (asin (+ (* (cos delta) (sin phi1)) (* (cos phi1) (* (sin delta) (cos theta))))))

simplify55.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5038	1717

prune135.0ms (0.9%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	85	0	85
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	85	7	92

Merged error: 0.0b

Counts

92 → 7

regimes469.0ms (3.2%)

Accuracy

Total 0.1b remaining (41.8%)

Threshold costs 0.1b (41.8%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	68	37
1	68	37

end0.0ms (0%)

sample8.8s (59.5%)

Algorithm

1×

intervals

Results

5.4s	3092×	body	1280	valid
1.9s	1898×	body	640	valid
487.0ms	717×	body	320	valid
414.0ms	1988×	body	80	valid
135.0ms	305×	body	160	valid

Details

analyze3.6s (24.3%)

sample294.0ms (2%)

simplify24.0ms (0.2%)

prune23.0ms (0.2%)

localize33.0ms (0.2%)

rewrite16.0ms (0.1%)

series91.0ms (0.6%)

simplify49.0ms (0.3%)

prune166.0ms (1.1%)

localize37.0ms (0.3%)

rewrite30.0ms (0.2%)

series101.0ms (0.7%)

simplify83.0ms (0.6%)

prune179.0ms (1.2%)

localize35.0ms (0.2%)

rewrite14.0ms (0.1%)

series167.0ms (1.1%)

simplify47.0ms (0.3%)

prune172.0ms (1.2%)

localize41.0ms (0.3%)

rewrite11.0ms (0.1%)

series116.0ms (0.8%)

simplify55.0ms (0.4%)

prune135.0ms (0.9%)

regimes469.0ms (3.2%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample8.8s (59.5%)

Profiling