Details

sample431.0ms

Algorithm

intervals

Results

202.0ms	110×	body	1280	valid
154.0ms	79×	body	640	valid
29.0ms	29×	body	320	valid
8.0ms	16×	body	160	valid
5.0ms	22×	body	80	valid

simplify16.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (12.0ms)

Iter	Nodes	Cost
0	14	20
1	20	20
2	23	19
done	23	19

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.5b

localize31.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos phi2) (sin (- lambda1 lambda2)))
0.6b	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
3.2b	(sin (- lambda1 lambda2))
3.4b	(cos (- lambda1 lambda2))

rewrite565.0ms

Algorithm

rewrite-expression-head

Rules

36×	`prod-diff`
33×	`add-sqr-sqrt` `sin-sum`
31×	`add-cube-cbrt` `*-un-lft-identity`
12×	`distribute-rgt-in` `distribute-lft-in`
11×	`cos-sum`
6×	`pow1` `add-exp-log` `add-cbrt-cube` `add-log-exp`
4×	`expm1-log1p-u` `sub-neg` `log1p-expm1-u`
3×	`cos-diff` `fma-def` `associate-r` `associate-l`
2×	`associate-+r+`
1×	`+-commutative` `flip3-+` `pow-prod-down` `prod-exp` `sum-log` `sin-diff` `*-commutative` `cbrt-unprod` `flip-+` `unswap-sqr`

Counts

4 → 102

Calls

4 calls:

54.0ms	(* (cos phi2) (sin (- lambda1 lambda2)))
14.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
30.0ms	(sin (- lambda1 lambda2))
457.0ms	(cos (- lambda1 lambda2))

series338.0ms

Counts

4 → 12

Calls

4 calls:

111.0ms	(* (cos phi2) (sin (- lambda1 lambda2)))
151.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
40.0ms	(sin (- lambda1 lambda2))
35.0ms	(cos (- lambda1 lambda2))

simplify5.7s

Counts

114 → 114

Iterations

Useful iterations: 4 (4.3s)

Iter	Nodes	Cost
0	242	2795
1	472	2124
2	994	1681
3	2087	1511
4	4462	1150
done	5000	1150

prune604.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 1.2b

localize41.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin lambda1) (cos lambda2))
0.2b	(* (cos phi2) (* (sin lambda1) (cos lambda2)))
0.6b	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
3.4b	(cos (- lambda1 lambda2))

rewrite93.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
14×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1` `add-exp-log` `cos-sum` `add-cbrt-cube`
9×	`prod-diff`
6×	`associate-l` `add-log-exp`
4×	`expm1-log1p-u` `associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod` `log1p-expm1-u`
3×	`cos-diff` `fma-def`
2×	`associate-+r+` `*-commutative` `sin-cos-mult`
1×	`+-commutative` `distribute-rgt-in` `sub-neg` `distribute-lft-in` `flip3-+` `associate-*r/` `sum-log` `flip-+` `unswap-sqr`

Counts

4 → 81

Calls

4 calls:

13.0ms	(* (sin lambda1) (cos lambda2))
47.0ms	(* (cos phi2) (* (sin lambda1) (cos lambda2)))
14.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
16.0ms	(cos (- lambda1 lambda2))

series367.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(* (sin lambda1) (cos lambda2))
112.0ms	(* (cos phi2) (* (sin lambda1) (cos lambda2)))
166.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
20.0ms	(cos (- lambda1 lambda2))

simplify3.1s

Counts

93 → 93

Iterations

Useful iterations: done (3.1s)

Iter	Nodes	Cost
0	207	1306
1	430	1123
2	1080	919
3	2941	875
done	5001	819

prune684.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize69.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin lambda1) (cos lambda2))
0.2b	(* (sin lambda1) (sin lambda2))
0.2b	(* (cos phi2) (* (sin lambda1) (cos lambda2)))
0.5b	(fma (* (cos lambda1) (cos lambda2)) (cos phi2) (cos phi1))

rewrite77.0ms

Algorithm

rewrite-expression-head

Rules

13×	`pow1` `add-exp-log` `add-sqr-sqrt` `add-cbrt-cube`
9×	`add-cube-cbrt` `-un-lft-identity` `associate-l*`
7×	`associate-r`
5×	`pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`*-commutative`
2×	`sin-cos-mult` `unswap-sqr`
1×	`associate-*r/` `fma-udef` `sin-mult`

Counts

4 → 73

Calls

4 calls:

21.0ms	(* (sin lambda1) (cos lambda2))
13.0ms	(* (sin lambda1) (sin lambda2))
39.0ms	(* (cos phi2) (* (sin lambda1) (cos lambda2)))
1.0ms	(fma (* (cos lambda1) (cos lambda2)) (cos phi2) (cos phi1))

series468.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(* (sin lambda1) (cos lambda2))
75.0ms	(* (sin lambda1) (sin lambda2))
121.0ms	(* (cos phi2) (* (sin lambda1) (cos lambda2)))
201.0ms	(fma (* (cos lambda1) (cos lambda2)) (cos phi2) (cos phi1))

simplify6.4s

Counts

85 → 85

Iterations

Useful iterations: 4 (5.0s)

Iter	Nodes	Cost
0	127	792
1	273	778
2	776	669
3	2199	668
4	4514	667
done	5000	667

prune696.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

localize70.0ms

Local error

Found 4 expressions with local error:

1.9b	(- (* (cos (- lambda1 lambda2)) (cos phi2)) (cos phi1))
3.4b	(cos (- lambda1 lambda2))
3.4b	(cos (- lambda1 lambda2))
3.4b	(cos (- lambda1 lambda2))

rewrite84.0ms

Algorithm

rewrite-expression-head

Rules

33×	`cos-sum`
30×	`prod-diff`
23×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`add-log-exp`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `sub-neg` `add-cbrt-cube` `log1p-expm1-u`
3×	`cos-diff`
1×	`flip3--` `fma-neg` `diff-log` `flip--`

Counts

4 → 81

Calls

4 calls:

23.0ms	(- (* (cos (- lambda1 lambda2)) (cos phi2)) (cos phi1))
14.0ms	(cos (- lambda1 lambda2))
17.0ms	(cos (- lambda1 lambda2))
26.0ms	(cos (- lambda1 lambda2))

series237.0ms

Counts

4 → 12

Calls

4 calls:

161.0ms	(- (* (cos (- lambda1 lambda2)) (cos phi2)) (cos phi1))
23.0ms	(cos (- lambda1 lambda2))
28.0ms	(cos (- lambda1 lambda2))
26.0ms	(cos (- lambda1 lambda2))

simplify5.2s

Counts

93 → 93

Iterations

Useful iterations: 4 (3.5s)

Iter	Nodes	Cost
0	151	2119
1	278	1581
2	571	1247
3	1562	1104
4	4881	831
done	5000	831

prune652.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

regimes637.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	24	40
1	34	40
done	34	40

end0.0ms

sample12.4s

Algorithm

intervals

Results

7.1s	3516×	body	1280	valid
2.8s	2346×	body	640	valid
1.5s	988×	body	320	valid
236.0ms	410×	body	160	valid
228.0ms	740×	body	80	valid