Details

sample453.0ms

Algorithm

intervals

Results

316.0ms	148×	body	1280	valid
94.0ms	62×	body	640	valid
11.0ms	18×	body	320	valid
5.0ms	24×	body	80	valid
2.0ms	4×	body	160	valid

simplify128.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.9b

localize46.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin (- lambda1 lambda2)) (cos phi2))
0.3b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
4.1b	(cos (- lambda1 lambda2))
4.2b	(sin (- lambda1 lambda2))

rewrite147.0ms

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:

50.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
49.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
20.0ms	(cos (- lambda1 lambda2))
25.0ms	(sin (- lambda1 lambda2))

series263.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
139.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
26.0ms	(cos (- lambda1 lambda2))
25.0ms	(sin (- lambda1 lambda2))

simplify1.0s

Counts

98 → 98

Iterations

Useful iterations: done (1.0s)

Iter	Nodes	Cost
0	210	1766
1	434	1442
2	1761	1146
done	5000	1095

prune566.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 5.4b

localize50.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2))
0.2b	(* (cos lambda1) (sin (- lambda2)))
0.3b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
4.1b	(cos (- lambda1 lambda2))

rewrite145.0ms

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` `associate-l/` `-commutative`
2×	`unswap-sqr`
1×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `flip3-+` `sin-neg` `distribute-rgt-neg-out` `sin-cos-mult` `flip-+`

Counts

4 → 87

Calls

4 calls:

67.0ms	(* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2))
21.0ms	(* (cos lambda1) (sin (- lambda2)))
39.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
14.0ms	(cos (- lambda1 lambda2))

series376.0ms

Counts

4 → 12

Calls

4 calls:

163.0ms	(* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2))
70.0ms	(* (cos lambda1) (sin (- lambda2)))
118.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
26.0ms	(cos (- lambda1 lambda2))

simplify1.6s

Counts

99 → 99

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	226	1642
1	514	1430
2	2324	1200
done	5000	1170

prune758.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize57.0ms

Local error

Found 4 expressions with local error:

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

rewrite147.0ms

Algorithm

rewrite-expression-head

Rules

32×	`pow1` `add-exp-log` `add-cbrt-cube`
18×	`pow-prod-down` `prod-exp` `cbrt-unprod`
12×	`add-sqr-sqrt`
8×	`add-cube-cbrt` `-un-lft-identity` `associate-r` `associate-l*`
4×	`expm1-log1p-u` `*-commutative` `sin-cos-mult` `log1p-expm1-u` `add-log-exp`
3×	`sin-mult`
2×	`frac-times` `associate-r/` `associate-l/` `cos-mult` `unswap-sqr`
1×	`sin-neg` `distribute-rgt-neg-out`

Counts

4 → 96

Calls

4 calls:

46.0ms	(* (* (sin lambda1) (sin lambda2)) (* (sin phi1) (cos phi2)))
12.0ms	(* (sin lambda1) (sin lambda2))
15.0ms	(* (cos lambda1) (sin (- lambda2)))
70.0ms	(* (* (cos lambda1) (cos lambda2)) (* (sin phi1) (cos phi2)))

series358.0ms

Counts

4 → 12

Calls

4 calls:

113.0ms	(* (* (sin lambda1) (sin lambda2)) (* (sin phi1) (cos phi2)))
57.0ms	(* (sin lambda1) (sin lambda2))
56.0ms	(* (cos lambda1) (sin (- lambda2)))
133.0ms	(* (* (cos lambda1) (cos lambda2)) (* (sin phi1) (cos phi2)))

simplify1.4s

Counts

108 → 108

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	179	1334
1	461	1306
2	2336	1066
done	5001	1042

prune785.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize54.0ms

Local error

Found 4 expressions with local error:

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

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 66

Calls

4 calls:

50.0ms	(* (* (cos lambda1) (cos lambda2)) (* (sin phi1) (cos phi2)))
1.0ms	(cbrt (cos lambda1))
1.0ms	(cbrt (cos lambda1))
1.0ms	(cbrt (cos lambda1))

series431.0ms

Counts

4 → 12

Calls

4 calls:

136.0ms	(* (* (cos lambda1) (cos lambda2)) (* (sin phi1) (cos phi2)))
98.0ms	(cbrt (cos lambda1))
97.0ms	(cbrt (cos lambda1))
99.0ms	(cbrt (cos lambda1))

simplify763.0ms

Counts

78 → 78

Iterations

Useful iterations: done (760.0ms)

Iter	Nodes	Cost
0	98	757
1	234	735
2	947	598
done	5001	589

prune511.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

regimes611.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	30	54
1	42	54
done	42	54

end0.0ms

sample17.9s

Algorithm

intervals

Results

13.0s	4561×	body	1280	valid
3.5s	1987×	body	640	valid
539.0ms	574×	body	320	valid
144.0ms	657×	body	80	valid
102.0ms	221×	body	160	valid