Details

sample575.0ms

Algorithm

intervals

Results

342.0ms	101×	body	1280	valid
124.0ms	59×	body	640	valid
30.0ms	26×	body	320	valid
19.0ms	58×	body	80	valid
9.0ms	12×	body	160	valid

simplify94.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	62
3	62
2	56
1	35
0	22

prune56.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize526.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (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))))
0.5b	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 58

Calls

4 calls:

18.0ms	(* (sin theta) (sin delta))
20.0ms	(* (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))))
12.0ms	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

series567.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(* (sin theta) (sin delta))
214.0ms	(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
9.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
274.0ms	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

simplify753.0ms

Counts

70 → 70

Iterations

Iter	Nodes
done	5001
2	1120
1	312
0	144

prune875.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

localize220.0ms

Local error

Found 4 expressions with local error:

0.3b	(asin (+ (* (* (cos theta) (cos phi1)) (sin delta)) (* (sin phi1) (cos delta))))
0.3b	(asin (+ (* (* (cos theta) (cos phi1)) (sin delta)) (* (sin phi1) (cos delta))))
0.3b	(asin (+ (* (* (cos theta) (cos phi1)) (sin delta)) (* (sin phi1) (cos delta))))
0.4b	(- (* (cos delta) (cos delta)) (* (* (pow (sin phi1) 2) (sin (asin (+ (* (* (cos theta) (cos phi1)) (sin delta)) (* (sin phi1) (cos delta)))))) (sin (asin (+ (* (* (cos theta) (cos phi1)) (sin delta)) (* (sin phi1) (cos delta)))))))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-log-exp`
4×	`add-sqr-sqrt` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
3×	`asin-acos`
1×	`sqr-cos` `sub-neg` `flip3--` `diff-log` `associate--l+` `flip--`

Counts

4 → 37

Calls

4 calls:

4.0ms	(asin (+ (* (* (cos theta) (cos phi1)) (sin delta)) (* (sin phi1) (cos delta))))
4.0ms	(asin (+ (* (* (cos theta) (cos phi1)) (sin delta)) (* (sin phi1) (cos delta))))
4.0ms	(asin (+ (* (* (cos theta) (cos phi1)) (sin delta)) (* (sin phi1) (cos delta))))
45.0ms	(- (* (cos delta) (cos delta)) (* (* (pow (sin phi1) 2) (sin (asin (+ (* (* (cos theta) (cos phi1)) (sin delta)) (* (sin phi1) (cos delta)))))) (sin (asin (+ (* (* (cos theta) (cos phi1)) (sin delta)) (* (sin phi1) (cos delta)))))))

series918.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(asin (+ (* (* (cos theta) (cos phi1)) (sin delta)) (* (sin phi1) (cos delta))))
16.0ms	(asin (+ (* (* (cos theta) (cos phi1)) (sin delta)) (* (sin phi1) (cos delta))))
15.0ms	(asin (+ (* (* (cos theta) (cos phi1)) (sin delta)) (* (sin phi1) (cos delta))))
878.0ms	(- (* (cos delta) (cos delta)) (* (* (pow (sin phi1) 2) (sin (asin (+ (* (* (cos theta) (cos phi1)) (sin delta)) (* (sin phi1) (cos delta)))))) (sin (asin (+ (* (* (cos theta) (cos phi1)) (sin delta)) (* (sin phi1) (cos delta)))))))

simplify706.0ms

Counts

49 → 49

Iterations

Iter	Nodes
done	5001
2	1227
1	264
0	102

prune869.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

localize105.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sin delta) (* (cos phi1) (sin theta)))
0.3b	(* (sin phi1) (sin (asin (+ (* (cos delta) (sin phi1)) (* (cos theta) (* (cos phi1) (sin delta)))))))
0.3b	(asin (+ (* (cos delta) (sin phi1)) (* (cos theta) (* (cos phi1) (sin delta)))))
0.5b	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (cos delta) (sin phi1)) (* (cos theta) (* (cos phi1) (sin delta))))))))

rewrite77.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 57

Calls

4 calls:

40.0ms	(* (sin delta) (* (cos phi1) (sin theta)))
21.0ms	(* (sin phi1) (sin (asin (+ (* (cos delta) (sin phi1)) (* (cos theta) (* (cos phi1) (sin delta)))))))
3.0ms	(asin (+ (* (cos delta) (sin phi1)) (* (cos theta) (* (cos phi1) (sin delta)))))
10.0ms	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (cos delta) (sin phi1)) (* (cos theta) (* (cos phi1) (sin delta))))))))

series672.0ms

Counts

4 → 12

Calls

4 calls:

116.0ms	(* (sin delta) (* (cos phi1) (sin theta)))
268.0ms	(* (sin phi1) (sin (asin (+ (* (cos delta) (sin phi1)) (* (cos theta) (* (cos phi1) (sin delta)))))))
16.0ms	(asin (+ (* (cos delta) (sin phi1)) (* (cos theta) (* (cos phi1) (sin delta)))))
273.0ms	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (cos delta) (sin phi1)) (* (cos theta) (* (cos phi1) (sin delta))))))))

simplify619.0ms

Counts

69 → 69

Iterations

Iter	Nodes
done	5001
2	1214
1	328
0	149

prune907.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.1b

localize160.0ms

Local error

Found 4 expressions with local error:

0.3b	(asin (+ (* (cos theta) (* (sin delta) (cos phi1))) (* (sin phi1) (cos delta))))
0.4b	(- (pow (cos delta) 2) (* (* (sin (asin (+ (* (cos theta) (* (sin delta) (cos phi1))) (* (sin phi1) (cos delta))))) (pow (sin phi1) 2)) (sin (asin (+ (* (cos theta) (* (sin delta) (cos phi1))) (* (sin phi1) (cos delta)))))))
0.5b	(cbrt (pow (- (pow (cos delta) 2) (* (* (sin (asin (+ (* (cos theta) (* (sin delta) (cos phi1))) (* (sin phi1) (cos delta))))) (pow (sin phi1) 2)) (sin (asin (+ (* (cos theta) (* (sin delta) (cos phi1))) (* (sin phi1) (cos delta))))))) 3))
0.5b	(pow (- (pow (cos delta) 2) (* (* (sin (asin (+ (* (cos theta) (* (sin delta) (cos phi1))) (* (sin phi1) (cos delta))))) (pow (sin phi1) 2)) (sin (asin (+ (* (cos theta) (* (sin delta) (cos phi1))) (* (sin phi1) (cos delta))))))) 3)

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 68

Calls

4 calls:

2.0ms	(asin (+ (* (cos theta) (* (sin delta) (cos phi1))) (* (sin phi1) (cos delta))))
13.0ms	(- (pow (cos delta) 2) (* (* (sin (asin (+ (* (cos theta) (* (sin delta) (cos phi1))) (* (sin phi1) (cos delta))))) (pow (sin phi1) 2)) (sin (asin (+ (* (cos theta) (* (sin delta) (cos phi1))) (* (sin phi1) (cos delta)))))))
12.0ms	(cbrt (pow (- (pow (cos delta) 2) (* (* (sin (asin (+ (* (cos theta) (* (sin delta) (cos phi1))) (* (sin phi1) (cos delta))))) (pow (sin phi1) 2)) (sin (asin (+ (* (cos theta) (* (sin delta) (cos phi1))) (* (sin phi1) (cos delta))))))) 3))
15.0ms	(pow (- (pow (cos delta) 2) (* (* (sin (asin (+ (* (cos theta) (* (sin delta) (cos phi1))) (* (sin phi1) (cos delta))))) (pow (sin phi1) 2)) (sin (asin (+ (* (cos theta) (* (sin delta) (cos phi1))) (* (sin phi1) (cos delta))))))) 3)

series3.6s

Counts

4 → 12

Calls

4 calls:

15.0ms	(asin (+ (* (cos theta) (* (sin delta) (cos phi1))) (* (sin phi1) (cos delta))))
843.0ms	(- (pow (cos delta) 2) (* (* (sin (asin (+ (* (cos theta) (* (sin delta) (cos phi1))) (* (sin phi1) (cos delta))))) (pow (sin phi1) 2)) (sin (asin (+ (* (cos theta) (* (sin delta) (cos phi1))) (* (sin phi1) (cos delta)))))))
957.0ms	(cbrt (pow (- (pow (cos delta) 2) (* (* (sin (asin (+ (* (cos theta) (* (sin delta) (cos phi1))) (* (sin phi1) (cos delta))))) (pow (sin phi1) 2)) (sin (asin (+ (* (cos theta) (* (sin delta) (cos phi1))) (* (sin phi1) (cos delta))))))) 3))
1.8s	(pow (- (pow (cos delta) 2) (* (* (sin (asin (+ (* (cos theta) (* (sin delta) (cos phi1))) (* (sin phi1) (cos delta))))) (pow (sin phi1) 2)) (sin (asin (+ (* (cos theta) (* (sin delta) (cos phi1))) (* (sin phi1) (cos delta))))))) 3)

simplify1.8s

Counts

80 → 80

Iterations

Iter	Nodes
done	5000
2	2836
1	498
0	171

prune1.3s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

regimes816.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 0.2b

bsearch0.0ms

simplify10.0ms

Iterations

Iter	Nodes
done	57
1	57
0	43

end0.0ms

sample20.4s

Algorithm

intervals

Results

13.3s	3104×	body	1280	valid
3.6s	1865×	body	640	valid
1.1s	2039×	body	80	valid
940.0ms	667×	body	320	valid
720.0ms	325×	body	160	valid