Details

sample924.0ms

Algorithm

intervals

Results

492.0ms	110×	body	1280	valid
220.0ms	64×	body	640	valid
79.0ms	54×	body	80	valid
58.0ms	8×	body	160	valid
39.0ms	20×	body	320	valid

simplify55.0ms

Counts

1 → 1

Iterations

Iter	Nodes
4	55
3	55
2	54
1	35
0	22

prune18.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

localize117.0ms

Local error

Found 4 expressions with local error:

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

rewrite40.0ms

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:

11.0ms	(* (sin theta) (sin delta))
2.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
13.0ms	(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
14.0ms	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

series626.0ms

Counts

4 → 12

Calls

4 calls:

85.0ms	(* (sin theta) (sin delta))
13.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
228.0ms	(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
299.0ms	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

simplify1.1s

Counts

74 → 74

Iterations

Iter	Nodes
3	2021
2	728
1	315
0	148

prune1.8s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize81.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (sin theta) (sin delta)) (cos phi1))
0.2b	(* (sin theta) (sin delta))
0.3b	(* (sin phi1) (+ (* (cos delta) (sin phi1)) (* (* (sin delta) (cos phi1)) (cos theta))))
0.5b	(- (cos delta) (* (sin phi1) (+ (* (cos delta) (sin phi1)) (* (* (sin delta) (cos phi1)) (cos theta)))))

rewrite92.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 78

Calls

4 calls:

40.0ms	(* (* (sin theta) (sin delta)) (cos phi1))
18.0ms	(* (sin theta) (sin delta))
27.0ms	(* (sin phi1) (+ (* (cos delta) (sin phi1)) (* (* (sin delta) (cos phi1)) (cos theta))))
6.0ms	(- (cos delta) (* (sin phi1) (+ (* (cos delta) (sin phi1)) (* (* (sin delta) (cos phi1)) (cos theta)))))

series690.0ms

Counts

4 → 12

Calls

4 calls:

122.0ms	(* (* (sin theta) (sin delta)) (cos phi1))
58.0ms	(* (sin theta) (sin delta))
247.0ms	(* (sin phi1) (+ (* (cos delta) (sin phi1)) (* (* (sin delta) (cos phi1)) (cos theta))))
263.0ms	(- (cos delta) (* (sin phi1) (+ (* (cos delta) (sin phi1)) (* (* (sin delta) (cos phi1)) (cos theta)))))

simplify8.3s

Counts

90 → 90

Iterations

Iter	Nodes
3	12714
2	1757
1	446
0	161

prune1.8s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize55.0ms

Local error

Found 4 expressions with local error:

0.2b	(atan2 (* (sin theta) (* (sin delta) (cos phi1))) (- (cos delta) (* (sin phi1) (+ (* (cos delta) (sin phi1)) (* (* (sin delta) (cos phi1)) (cos theta))))))
0.2b	(* (sin theta) (* (sin delta) (cos phi1)))
0.3b	(* (sin phi1) (+ (* (cos delta) (sin phi1)) (* (* (sin delta) (cos phi1)) (cos theta))))
0.5b	(- (cos delta) (* (sin phi1) (+ (* (cos delta) (sin phi1)) (* (* (sin delta) (cos phi1)) (cos theta)))))

rewrite98.0ms

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` `insert-posit16`
3×	`associate-*r/`
2×	`distribute-rgt-in` `distribute-lft-in` `*-commutative` `associate--r+`
1×	`sub-neg` `flip3-+` `flip3--` `diff-log` `flip-+` `sin-cos-mult` `flip--` `unswap-sqr`

Counts

4 → 66

Calls

4 calls:

0.0ms	(atan2 (* (sin theta) (* (sin delta) (cos phi1))) (- (cos delta) (* (sin phi1) (+ (* (cos delta) (sin phi1)) (* (* (sin delta) (cos phi1)) (cos theta))))))
23.0ms	(* (sin theta) (* (sin delta) (cos phi1)))
54.0ms	(* (sin phi1) (+ (* (cos delta) (sin phi1)) (* (* (sin delta) (cos phi1)) (cos theta))))
20.0ms	(- (cos delta) (* (sin phi1) (+ (* (cos delta) (sin phi1)) (* (* (sin delta) (cos phi1)) (cos theta)))))

series625.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(atan2 (* (sin theta) (* (sin delta) (cos phi1))) (- (cos delta) (* (sin phi1) (+ (* (cos delta) (sin phi1)) (* (* (sin delta) (cos phi1)) (cos theta))))))
125.0ms	(* (sin theta) (* (sin delta) (cos phi1)))
223.0ms	(* (sin phi1) (+ (* (cos delta) (sin phi1)) (* (* (sin delta) (cos phi1)) (cos theta))))
263.0ms	(- (cos delta) (* (sin phi1) (+ (* (cos delta) (sin phi1)) (* (* (sin delta) (cos phi1)) (cos theta)))))

simplify4.8s

Counts

78 → 78

Iterations

Iter	Nodes
3	10062
2	1678
1	451
0	167

prune1.7s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize104.0ms

Local error

Found 4 expressions with local error:

0.2b	(atan2 (* (sin delta) (* (sin theta) (cos phi1))) (- (cos delta) (* (sin phi1) (+ (* (cos delta) (sin phi1)) (* (* (sin delta) (cos phi1)) (cos theta))))))
0.2b	(* (sin delta) (* (sin theta) (cos phi1)))
0.3b	(* (sin phi1) (+ (* (cos delta) (sin phi1)) (* (* (sin delta) (cos phi1)) (cos theta))))
0.5b	(- (cos delta) (* (sin phi1) (+ (* (cos delta) (sin phi1)) (* (* (sin delta) (cos phi1)) (cos theta)))))

rewrite73.0ms

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` `insert-posit16`
3×	`associate-*r/`
2×	`distribute-rgt-in` `distribute-lft-in` `*-commutative` `associate--r+`
1×	`sub-neg` `flip3-+` `flip3--` `diff-log` `flip-+` `sin-cos-mult` `flip--` `unswap-sqr`

Counts

4 → 66

Calls

4 calls:

0.0ms	(atan2 (* (sin delta) (* (sin theta) (cos phi1))) (- (cos delta) (* (sin phi1) (+ (* (cos delta) (sin phi1)) (* (* (sin delta) (cos phi1)) (cos theta))))))
29.0ms	(* (sin delta) (* (sin theta) (cos phi1)))
36.0ms	(* (sin phi1) (+ (* (cos delta) (sin phi1)) (* (* (sin delta) (cos phi1)) (cos theta))))
6.0ms	(- (cos delta) (* (sin phi1) (+ (* (cos delta) (sin phi1)) (* (* (sin delta) (cos phi1)) (cos theta)))))

series650.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(atan2 (* (sin delta) (* (sin theta) (cos phi1))) (- (cos delta) (* (sin phi1) (+ (* (cos delta) (sin phi1)) (* (* (sin delta) (cos phi1)) (cos theta))))))
130.0ms	(* (sin delta) (* (sin theta) (cos phi1)))
238.0ms	(* (sin phi1) (+ (* (cos delta) (sin phi1)) (* (* (sin delta) (cos phi1)) (cos theta))))
260.0ms	(- (cos delta) (* (sin phi1) (+ (* (cos delta) (sin phi1)) (* (* (sin delta) (cos phi1)) (cos theta)))))

simplify5.1s

Counts

78 → 78

Iterations

Iter	Nodes
3	11248
2	1741
1	446
0	166

prune1.6s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

regimes749.0ms

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
2	26
1	26
0	19

end0.0ms

sample24.5s

Algorithm

intervals

Results

14.2s	3041×	body	1280	valid
6.2s	1926×	body	640	valid
1.4s	2019×	body	80	valid
1.3s	682×	body	320	valid
894.0ms	332×	body	160	valid