Details

sample1.0s

Algorithm

intervals

Results

434.0ms	25×	body	320	valid
341.0ms	89×	body	1280	valid
133.0ms	60×	body	640	valid
32.0ms	75×	body	80	valid
7.0ms	7×	body	160	valid

simplify45.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	55
3	55
2	54
1	35
0	22

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

localize67.0ms

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))))))
0.4b	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
0.6b	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

rewrite34.0ms

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`
4×	`insert-posit16`
2×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `sin-mult` `unswap-sqr`
1×	`asin-acos` `sub-neg` `flip3--` `diff-log` `flip--`

Counts

4 → 62

Calls

4 calls:

14.0ms	(* (sin theta) (sin delta))
12.0ms	(* (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))))
6.0ms	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

series535.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(* (sin theta) (sin delta))
194.0ms	(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
12.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
272.0ms	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

simplify1.1s

Counts

74 → 74

Iterations

Iter	Nodes
done	2000
3	2000
2	734
1	317
0	148

prune1.7s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize85.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos theta) (sin delta))
0.2b	(* (sin theta) (sin delta))
0.3b	(* (sin phi1) (+ (* (sin phi1) (cos delta)) (* (cos phi1) (* (cos theta) (sin delta)))))
0.6b	(- (cos delta) (* (sin phi1) (+ (* (sin phi1) (cos delta)) (* (cos phi1) (* (cos theta) (sin delta))))))

rewrite136.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
10×	`pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
9×	`associate-r` `associate-l`
6×	`add-log-exp`
4×	`insert-posit16`
3×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
2×	`distribute-rgt-in` `distribute-lft-in` `associate-*r/` `associate--r+`
1×	`sub-neg` `flip3-+` `flip3--` `diff-log` `flip-+` `flip--` `sin-mult`

Counts

4 → 77

Calls

4 calls:

21.0ms	(* (cos theta) (sin delta))
22.0ms	(* (sin theta) (sin delta))
80.0ms	(* (sin phi1) (+ (* (sin phi1) (cos delta)) (* (cos phi1) (* (cos theta) (sin delta)))))
11.0ms	(- (cos delta) (* (sin phi1) (+ (* (sin phi1) (cos delta)) (* (cos phi1) (* (cos theta) (sin delta))))))

series642.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(* (cos theta) (sin delta))
64.0ms	(* (sin theta) (sin delta))
235.0ms	(* (sin phi1) (+ (* (sin phi1) (cos delta)) (* (cos phi1) (* (cos theta) (sin delta)))))
283.0ms	(- (cos delta) (* (sin phi1) (+ (* (sin phi1) (cos delta)) (* (cos phi1) (* (cos theta) (sin delta))))))

simplify1.5s

Counts

89 → 89

Iterations

Iter	Nodes
done	2000
3	2000
2	1508
1	450
0	163

prune1.9s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize99.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin theta) (sin delta))
0.2b	(* (sin phi1) (* (sin phi1) (cos delta)))
0.2b	(* (sin phi1) (* (cos phi1) (* (cos theta) (sin delta))))
0.6b	(- (cos delta) (+ (* (sin phi1) (* (sin phi1) (cos delta))) (* (sin phi1) (* (cos phi1) (* (cos theta) (sin delta))))))

rewrite215.0ms

Algorithm

rewrite-expression-head

Rules

20×	`pow1` `add-cbrt-cube` `add-exp-log`
12×	`add-sqr-sqrt`
10×	`*-un-lft-identity` `pow-prod-down` `prod-exp` `cbrt-unprod`
9×	`associate-l` `add-log-exp`
8×	`add-cube-cbrt`
5×	`associate-r`
4×	`insert-posit16`
3×	`*-commutative`
2×	`diff-log`
1×	`sum-log` `sub-neg` `flip3--` `associate-*r/` `sin-cos-mult` `flip--` `sin-mult` `associate--r+` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

4 → 79

Calls

4 calls:

23.0ms	(* (sin theta) (sin delta))
47.0ms	(* (sin phi1) (* (sin phi1) (cos delta)))
108.0ms	(* (sin phi1) (* (cos phi1) (* (cos theta) (sin delta))))
35.0ms	(- (cos delta) (+ (* (sin phi1) (* (sin phi1) (cos delta))) (* (sin phi1) (* (cos phi1) (* (cos theta) (sin delta))))))

series569.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(* (sin theta) (sin delta))
81.0ms	(* (sin phi1) (* (sin phi1) (cos delta)))
145.0ms	(* (sin phi1) (* (cos phi1) (* (cos theta) (sin delta))))
277.0ms	(- (cos delta) (+ (* (sin phi1) (* (sin phi1) (cos delta))) (* (sin phi1) (* (cos phi1) (* (cos theta) (sin delta))))))

simplify1.5s

Counts

91 → 91

Iterations

Iter	Nodes
done	2004
3	2004
2	1806
1	452
0	176

prune1.7s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize113.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin theta) (sin delta))
0.3b	(* (sin phi1) (+ (* (sin phi1) (cos delta)) (* (cos phi1) (log (exp (* (cos theta) (sin delta)))))))
0.6b	(- (cos delta) (* (sin phi1) (+ (* (sin phi1) (cos delta)) (* (cos phi1) (log (exp (* (cos theta) (sin delta))))))))
2.4b	(log (exp (* (cos theta) (sin delta))))

rewrite77.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt`
9×	`pow1` `*-un-lft-identity` `add-cube-cbrt`
8×	`add-cbrt-cube` `add-exp-log`
7×	`add-log-exp`
6×	`associate-r` `associate-l`
4×	`insert-posit16`
3×	`log-prod` `log-pow`
2×	`distribute-rgt-in` `distribute-lft-in` `pow-prod-down` `prod-exp` `associate-r/` `-commutative` `cbrt-unprod` `associate--r+` `unswap-sqr`
1×	`exp-prod` `sub-neg` `flip3-+` `flip3--` `exp-to-pow` `diff-log` `rem-log-exp` `flip-+` `flip--` `sin-mult`

Counts

4 → 73

Calls

4 calls:

11.0ms	(* (sin theta) (sin delta))
46.0ms	(* (sin phi1) (+ (* (sin phi1) (cos delta)) (* (cos phi1) (log (exp (* (cos theta) (sin delta)))))))
12.0ms	(- (cos delta) (* (sin phi1) (+ (* (sin phi1) (cos delta)) (* (cos phi1) (log (exp (* (cos theta) (sin delta))))))))
7.0ms	(log (exp (* (cos theta) (sin delta))))

series545.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(* (sin theta) (sin delta))
197.0ms	(* (sin phi1) (+ (* (sin phi1) (cos delta)) (* (cos phi1) (log (exp (* (cos theta) (sin delta)))))))
240.0ms	(- (cos delta) (* (sin phi1) (+ (* (sin phi1) (cos delta)) (* (cos phi1) (log (exp (* (cos theta) (sin delta))))))))
51.0ms	(log (exp (* (cos theta) (sin delta))))

simplify1.3s

Counts

85 → 85

Iterations

Iter	Nodes
done	2006
3	2006
2	1349
1	420
0	161

prune1.8s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.0b

regimes702.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
done	30
1	30
0	21

end0.0ms

sample25.9s

Algorithm

intervals

Results

16.0s	3154×	body	1280	valid
6.1s	1833×	body	640	valid
1.7s	2026×	body	80	valid
1.4s	679×	body	320	valid
366.0ms	308×	body	160	valid