Details

sample541.0ms

Algorithm

intervals

Results

348.0ms	148×	body	1280	valid
143.0ms	62×	body	640	valid
14.0ms	18×	body	320	valid
5.0ms	24×	body	80	valid
2.0ms	4×	body	160	valid

simplify97.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	24
1	27	24
2	46	24
3	71	24
4	83	24
5	84	24
done	84	24

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.9b

localize39.0ms

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))

rewrite128.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 60

Calls

4 calls:

29.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
47.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
25.0ms	(cos (- lambda1 lambda2))
24.0ms	(sin (- lambda1 lambda2))

series294.0ms

Counts

4 → 12

Calls

4 calls:

87.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
135.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
32.0ms	(cos (- lambda1 lambda2))
40.0ms	(sin (- lambda1 lambda2))

simplify1.1s

Counts

72 → 72

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	116	760
1	272	748
2	1322	644
done	5000	642

prune599.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 5.4b

localize77.0ms

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))

rewrite171.0ms

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×	`pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`add-log-exp`
3×	`cos-diff` `associate-l/` `-commutative`
2×	`cos-sum` `unswap-sqr`
1×	`distribute-rgt-in` `sub-neg` `flip3--` `distribute-lft-in` `sin-cos-mult` `flip--`

Counts

4 → 69

Calls

4 calls:

86.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
31.0ms	(* (cos lambda1) (sin lambda2))
38.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
14.0ms	(cos (- lambda1 lambda2))

series416.0ms

Counts

4 → 12

Calls

4 calls:

205.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
58.0ms	(* (cos lambda1) (sin lambda2))
129.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
24.0ms	(cos (- lambda1 lambda2))

simplify1.7s

Counts

81 → 81

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	143	1030
1	359	1007
2	1867	877
done	5000	875

prune763.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize83.0ms

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)))

rewrite227.0ms

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×	`*-commutative` `sin-cos-mult` `add-log-exp`
3×	`sin-mult`
2×	`frac-times` `associate-r/` `associate-l/` `cos-mult` `unswap-sqr`

Counts

4 → 87

Calls

4 calls:

98.0ms	(* (* (sin lambda1) (sin lambda2)) (* (sin phi1) (cos phi2)))
24.0ms	(* (sin lambda1) (sin lambda2))
22.0ms	(* (cos lambda1) (sin lambda2))
76.0ms	(* (* (cos lambda1) (cos lambda2)) (* (sin phi1) (cos phi2)))

series526.0ms

Counts

4 → 12

Calls

4 calls:

169.0ms	(* (* (sin lambda1) (sin lambda2)) (* (sin phi1) (cos phi2)))
85.0ms	(* (sin lambda1) (sin lambda2))
64.0ms	(* (cos lambda1) (sin lambda2))
208.0ms	(* (* (cos lambda1) (cos lambda2)) (* (sin phi1) (cos phi2)))

simplify1.4s

Counts

99 → 99

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	158	1229
1	441	1203
2	2239	951
done	5001	943

prune783.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize50.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (pow (* (sin lambda2) (sin lambda1)) 1) (* (sin phi1) (cos phi2)))
0.2b	(* (sin lambda2) (sin lambda1))
0.2b	(* (cos lambda1) (sin lambda2))
0.2b	(* (* (cos lambda1) (cos lambda2)) (* (sin phi1) (cos phi2)))

rewrite205.0ms

Algorithm

rewrite-expression-head

Rules

40×	`add-exp-log`
25×	`add-cbrt-cube`
24×	`prod-exp`
23×	`pow1`
13×	`add-sqr-sqrt` `pow-prod-down` `cbrt-unprod`
12×	`associate-l`
9×	`add-cube-cbrt` `*-un-lft-identity`
8×	`associate-r`
4×	`pow-exp` `*-commutative` `add-log-exp`
3×	`sin-cos-mult`
2×	`pow-to-exp` `associate-*r/` `cos-mult` `unswap-sqr`
1×	`frac-times` `unpow-prod-down` `associate-*l/` `sin-mult` `sqr-pow`

Counts

4 → 89

Calls

4 calls:

67.0ms	(* (pow (* (sin lambda2) (sin lambda1)) 1) (* (sin phi1) (cos phi2)))
29.0ms	(* (sin lambda2) (sin lambda1))
23.0ms	(* (cos lambda1) (sin lambda2))
81.0ms	(* (* (cos lambda1) (cos lambda2)) (* (sin phi1) (cos phi2)))

series440.0ms

Counts

4 → 12

Calls

4 calls:

148.0ms	(* (pow (* (sin lambda2) (sin lambda1)) 1) (* (sin phi1) (cos phi2)))
57.0ms	(* (sin lambda2) (sin lambda1))
47.0ms	(* (cos lambda1) (sin lambda2))
188.0ms	(* (* (cos lambda1) (cos lambda2)) (* (sin phi1) (cos phi2)))

simplify1.3s

Counts

101 → 101

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	176	1264
1	471	1156
2	2380	965
done	5000	955

prune768.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.0b

regimes703.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify7.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	27	46
1	39	44
done	39	44

end0.0ms

sample17.2s

Algorithm

intervals

Results

12.0s	4561×	body	1280	valid
3.7s	1987×	body	640	valid
595.0ms	574×	body	320	valid
188.0ms	657×	body	80	valid
166.0ms	221×	body	160	valid