Details

sample469.0ms

Algorithm

intervals

Results

334.0ms	155×	body	1280	valid
83.0ms	55×	body	640	valid
15.0ms	20×	body	320	valid
4.0ms	21×	body	80	valid
3.0ms	5×	body	160	valid

simplify107.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	24
1	28	24
2	47	24
3	78	24
4	99	24
5	100	24
done	100	24

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.0b

localize423.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin phi1) (cos phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
5.4b	(sin (- lambda1 lambda2))
5.6b	(cos (- lambda1 lambda2))

rewrite136.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 86

Calls

4 calls:

20.0ms	(* (sin phi1) (cos phi2))
69.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
24.0ms	(sin (- lambda1 lambda2))
17.0ms	(cos (- lambda1 lambda2))

series277.0ms

Counts

4 → 12

Calls

4 calls:

74.0ms	(* (sin phi1) (cos phi2))
147.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
34.0ms	(sin (- lambda1 lambda2))
22.0ms	(cos (- lambda1 lambda2))

simplify1.1s

Counts

98 → 98

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	208	1720
1	427	1395
2	1647	1111
done	5000	1056

prune540.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.1b

localize49.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos phi1) (sin phi2))
0.2b	(* (sin phi1) (cos phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
5.6b	(cos (- lambda1 lambda2))

rewrite83.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
13×	`pow1` `add-exp-log` `add-cbrt-cube`
11×	`cos-sum`
9×	`associate-r` `prod-diff`
7×	`associate-l`
5×	`pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`cos-diff` `*-commutative`
2×	`sin-cos-mult` `unswap-sqr`
1×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `associate-*l/`

Counts

4 → 85

Calls

4 calls:

13.0ms	(* (cos phi1) (sin phi2))
16.0ms	(* (sin phi1) (cos phi2))
36.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
15.0ms	(cos (- lambda1 lambda2))

series249.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(* (cos phi1) (sin phi2))
54.0ms	(* (sin phi1) (cos phi2))
121.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
23.0ms	(cos (- lambda1 lambda2))

simplify1.2s

Counts

97 → 97

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	210	1312
1	446	1141
2	1921	944
done	5001	911

prune778.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.0b

localize41.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos phi1) (sin phi2))
0.2b	(* (sin phi1) (cos phi2))
0.2b	(* (sin lambda2) (sin lambda1))
0.2b	(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda2) (sin lambda1))))

rewrite126.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt`
15×	`pow1` `add-exp-log` `add-cbrt-cube`
12×	`associate-r`
11×	`add-cube-cbrt` `*-un-lft-identity`
10×	`associate-l`
6×	`pow-prod-down` `prod-exp` `cbrt-unprod`
5×	`sin-cos-mult`
4×	`expm1-log1p-u` `*-commutative` `log1p-expm1-u` `add-log-exp`
3×	`frac-times` `associate-*r/` `sin-mult` `unswap-sqr`
2×	`flip3-+` `frac-add` `cos-mult` `flip-+`
1×	`distribute-rgt-in` `distribute-lft-in` `associate-*l/`

Counts

4 → 91

Calls

4 calls:

15.0ms	(* (cos phi1) (sin phi2))
20.0ms	(* (sin phi1) (cos phi2))
17.0ms	(* (sin lambda2) (sin lambda1))
70.0ms	(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda2) (sin lambda1))))

series434.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(* (cos phi1) (sin phi2))
60.0ms	(* (sin phi1) (cos phi2))
62.0ms	(* (sin lambda2) (sin lambda1))
234.0ms	(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda2) (sin lambda1))))

simplify2.2s

Counts

103 → 103

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	191	1327
1	537	1257
2	3215	1119
done	5000	1115

prune885.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize82.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin phi1) (cos phi2))
0.2b	(* (sin lambda2) (sin lambda1))
0.2b	(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda2) (sin lambda1))))
0.3b	(log1p (* (cos phi1) (sin phi2)))

rewrite154.0ms

Algorithm

rewrite-expression-head

Rules

13×	`pow1` `add-exp-log` `add-sqr-sqrt` `add-cbrt-cube`
9×	`add-cube-cbrt` `-un-lft-identity` `associate-r*`
7×	`associate-l`
5×	`expm1-log1p-u` `pow-prod-down` `prod-exp` `sin-cos-mult` `cbrt-unprod`
4×	`log1p-expm1-u` `add-log-exp`
3×	`frac-times` `associate-r/` `-commutative` `sin-mult`
2×	`flip3-+` `frac-add` `cos-mult` `flip-+` `unswap-sqr`
1×	`distribute-rgt-in` `log1p-udef` `distribute-lft-in` `log1p-expm1` `associate-*l/`

Counts

4 → 82

Calls

4 calls:

22.0ms	(* (sin phi1) (cos phi2))
24.0ms	(* (sin lambda2) (sin lambda1))
104.0ms	(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda2) (sin lambda1))))
1.0ms	(log1p (* (cos phi1) (sin phi2)))

series527.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(* (sin phi1) (cos phi2))
69.0ms	(* (sin lambda2) (sin lambda1))
284.0ms	(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda2) (sin lambda1))))
102.0ms	(log1p (* (cos phi1) (sin phi2)))

simplify1.9s

Counts

94 → 94

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	175	1272
1	493	1200
2	2881	1061
done	5001	1052

prune784.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

regimes598.0ms

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	28	42
1	37	42
done	37	42

end0.0ms

sample18.8s

Algorithm

intervals

Results

13.1s	4677×	body	1280	valid
3.9s	1905×	body	640	valid
855.0ms	550×	body	320	valid
202.0ms	659×	body	80	valid
106.0ms	209×	body	160	valid