Details

sample977.0ms

Algorithm

intervals

Results

793.0ms	98×	body	1280	valid
93.0ms	58×	body	640	valid
26.0ms	25×	body	320	valid
21.0ms	66×	body	80	valid
6.0ms	9×	body	160	valid

simplify96.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	22	33
1	35	33
2	56	33
3	60	33
done	60	33

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

localize69.0ms

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))))))))
0.2b	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
0.2b	(* (sin phi1) (sin (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)))))))

rewrite53.0ms

Algorithm

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 → 46

Calls

4 calls:

0.0ms	(atan2 (* (* (sin theta) (sin delta)) (cos phi1)) (- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))
3.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
24.0ms	(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
13.0ms	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

series534.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(atan2 (* (* (sin theta) (sin delta)) (cos phi1)) (- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))
15.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
199.0ms	(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
303.0ms	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

simplify773.0ms

Counts

58 → 58

Iterations

Useful iterations: done (768.0ms)

Iter	Nodes	Cost
0	119	1686
1	250	1623
2	814	1447
done	5001	1435

prune564.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize66.0ms

Local error

Found 4 expressions with local error:

0.2b	(atan2 (* (* (sin theta) (sin delta)) (cos phi1)) (- (cos delta) (* (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta))) (sin phi1))))
0.2b	(* (sin delta) (* (cos phi1) (cos theta)))
0.2b	(* (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta))) (sin phi1))
0.4b	(- (cos delta) (* (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta))) (sin phi1)))

rewrite122.0ms

Algorithm

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-l` `add-log-exp`
4×	`associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod`
3×	`associate-*l/`
2×	`associate-r/` `cos-mult` `-commutative`
1×	`sub-neg` `flip3--` `flip3-+` `diff-log` `frac-add` `sin-cos-mult` `flip--` `flip-+` `unswap-sqr`

Counts

4 → 59

Calls

4 calls:

0.0ms	(atan2 (* (* (sin theta) (sin delta)) (cos phi1)) (- (cos delta) (* (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta))) (sin phi1))))
27.0ms	(* (sin delta) (* (cos phi1) (cos theta)))
86.0ms	(* (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta))) (sin phi1))
7.0ms	(- (cos delta) (* (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta))) (sin phi1)))

series609.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(atan2 (* (* (sin theta) (sin delta)) (cos phi1)) (- (cos delta) (* (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta))) (sin phi1))))
101.0ms	(* (sin delta) (* (cos phi1) (cos theta)))
207.0ms	(* (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta))) (sin phi1))
284.0ms	(- (cos delta) (* (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta))) (sin phi1)))

simplify1.2s

Counts

71 → 71

Iterations

Useful iterations: 2 (246.0ms)

Iter	Nodes	Cost
0	150	1641
1	378	1563
2	1634	1396
done	5002	1396

prune585.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize46.0ms

Local error

Found 4 expressions with local error:

0.2b	(atan2 (* (sin delta) (* (cos phi1) (sin theta))) (- (cos delta) (+ (* (pow (sin phi1) 2) (cos delta)) (* (sin phi1) (* (cos phi1) (* (cos theta) (sin delta)))))))
0.2b	(* (sin phi1) (* (cos phi1) (* (cos theta) (sin delta))))
0.2b	(pow (sin phi1) 2)
0.4b	(- (cos delta) (+ (* (pow (sin phi1) 2) (cos delta)) (* (sin phi1) (* (cos phi1) (* (cos theta) (sin delta))))))

rewrite167.0ms

Algorithm

rewrite-expression-head

Rules

14×	`pow1` `add-exp-log`
13×	`add-cbrt-cube`
9×	`add-sqr-sqrt` `*-un-lft-identity` `add-log-exp`
7×	`add-cube-cbrt`
6×	`pow-prod-down` `prod-exp` `cbrt-unprod`
3×	`unpow-prod-down` `pow-unpow` `associate-l`
2×	`diff-log`
1×	`pow-to-exp` `sub-neg` `flip3--` `pow-pow` `associate-r` `pow-exp` `sum-log` `*-commutative` `flip--` `associate--r+` `distribute-lft-out--` `unpow2` `difference-of-squares` `sqr-pow`

Counts

4 → 62

Calls

4 calls:

1.0ms	(atan2 (* (sin delta) (* (cos phi1) (sin theta))) (- (cos delta) (+ (* (pow (sin phi1) 2) (cos delta)) (* (sin phi1) (* (cos phi1) (* (cos theta) (sin delta)))))))
109.0ms	(* (sin phi1) (* (cos phi1) (* (cos theta) (sin delta))))
8.0ms	(pow (sin phi1) 2)
46.0ms	(- (cos delta) (+ (* (pow (sin phi1) 2) (cos delta)) (* (sin phi1) (* (cos phi1) (* (cos theta) (sin delta))))))

series516.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(atan2 (* (sin delta) (* (cos phi1) (sin theta))) (- (cos delta) (+ (* (pow (sin phi1) 2) (cos delta)) (* (sin phi1) (* (cos phi1) (* (cos theta) (sin delta)))))))
124.0ms	(* (sin phi1) (* (cos phi1) (* (cos theta) (sin delta))))
42.0ms	(pow (sin phi1) 2)
322.0ms	(- (cos delta) (+ (* (pow (sin phi1) 2) (cos delta)) (* (sin phi1) (* (cos phi1) (* (cos theta) (sin delta))))))

simplify933.0ms

Counts

74 → 74

Iterations

Useful iterations: done (929.0ms)

Iter	Nodes	Cost
0	146	1537
1	383	1484
2	1579	1275
done	5001	1206

prune490.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize69.0ms

Local error

Found 4 expressions with local error:

0.2b	(atan2 (* (sin delta) (* (cos phi1) (sin theta))) (- (- (cos delta) (* (pow (sin phi1) 2) (cos delta))) (* (sin phi1) (* (cos phi1) (* (cos theta) (sin delta))))))
0.2b	(* (sin phi1) (* (cos phi1) (* (cos theta) (sin delta))))
0.2b	(pow (sin phi1) 2)
0.5b	(- (cos delta) (* (pow (sin phi1) 2) (cos delta)))

rewrite113.0ms

Algorithm

rewrite-expression-head

Rules

14×	`pow1` `add-exp-log`
13×	`add-cbrt-cube`
8×	`*-un-lft-identity`
7×	`add-sqr-sqrt` `add-cube-cbrt`
6×	`pow-prod-down` `prod-exp` `cbrt-unprod` `add-log-exp`
3×	`unpow-prod-down` `pow-unpow` `associate-l`
1×	`pow-to-exp` `sub-neg` `flip3--` `distribute-rgt-out--` `pow-pow` `diff-log` `associate-r` `pow-exp` `*-commutative` `flip--` `unpow2` `sqr-pow`

Counts

4 → 59

Calls

4 calls:

1.0ms	(atan2 (* (sin delta) (* (cos phi1) (sin theta))) (- (- (cos delta) (* (pow (sin phi1) 2) (cos delta))) (* (sin phi1) (* (cos phi1) (* (cos theta) (sin delta))))))
89.0ms	(* (sin phi1) (* (cos phi1) (* (cos theta) (sin delta))))
8.0ms	(pow (sin phi1) 2)
13.0ms	(- (cos delta) (* (pow (sin phi1) 2) (cos delta)))

series281.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(atan2 (* (sin delta) (* (cos phi1) (sin theta))) (- (- (cos delta) (* (pow (sin phi1) 2) (cos delta))) (* (sin phi1) (* (cos phi1) (* (cos theta) (sin delta))))))
128.0ms	(* (sin phi1) (* (cos phi1) (* (cos theta) (sin delta))))
22.0ms	(pow (sin phi1) 2)
96.0ms	(- (cos delta) (* (pow (sin phi1) 2) (cos delta)))

simplify1.1s

Counts

71 → 71

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	141	1174
1	372	1128
2	1516	950
done	5001	892

prune407.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

regimes315.0ms

Accuracy

0% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	20	31
1	27	31
done	27	31

end0.0ms

sample21.2s

Algorithm

intervals

Results

12.9s	3122×	body	1280	valid
5.0s	1890×	body	640	valid
1.3s	1984×	body	80	valid
972.0ms	700×	body	320	valid
284.0ms	304×	body	160	valid