Details

sample486.0ms

Algorithm

intervals

Results

359.0ms	155×	body	1280	valid
75.0ms	55×	body	640	valid
15.0ms	20×	body	320	valid
4.0ms	21×	body	80	valid
2.0ms	5×	body	160	valid

simplify127.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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: 15.0b

localize55.0ms

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))

rewrite100.0ms

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:

15.0ms	(* (sin phi1) (cos phi2))
61.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
12.0ms	(sin (- lambda1 lambda2))
11.0ms	(cos (- lambda1 lambda2))

series253.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(* (sin phi1) (cos phi2))
132.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
36.0ms	(sin (- lambda1 lambda2))
20.0ms	(cos (- lambda1 lambda2))

simplify1.3s

Counts

72 → 72

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	114	718
1	268	706
2	1407	618
done	5001	608

prune408.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.1b

localize48.0ms

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))

rewrite96.0ms

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` `*-commutative`
2×	`cos-sum` `sin-cos-mult` `unswap-sqr`
1×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `associate-*l/`

Counts

4 → 68

Calls

4 calls:

17.0ms	(* (cos phi1) (sin phi2))
12.0ms	(* (sin phi1) (cos phi2))
49.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
15.0ms	(cos (- lambda1 lambda2))

series272.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(* (cos phi1) (sin phi2))
48.0ms	(* (sin phi1) (cos phi2))
132.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
26.0ms	(cos (- lambda1 lambda2))

simplify1.1s

Counts

80 → 80

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	134	782
1	318	769
2	1626	671
done	5000	659

prune595.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

localize59.0ms

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))))

rewrite161.0ms

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×	`*-commutative` `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 → 83

Calls

4 calls:

28.0ms	(* (cos phi1) (sin phi2))
22.0ms	(* (sin phi1) (cos phi2))
12.0ms	(* (sin lambda2) (sin lambda1))
95.0ms	(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda2) (sin lambda1))))

series451.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(* (cos phi1) (sin phi2))
76.0ms	(* (sin phi1) (cos phi2))
75.0ms	(* (sin lambda2) (sin lambda1))
240.0ms	(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda2) (sin lambda1))))

simplify2.0s

Counts

95 → 95

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	183	1255
1	519	1221
2	3265	1075
done	5001	1065

prune882.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize64.0ms

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)) (log (exp (* (sin lambda2) (sin lambda1))))))
2.9b	(log (exp (* (sin lambda2) (sin lambda1))))

rewrite130.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 77

Calls

4 calls:

22.0ms	(* (sin phi1) (cos phi2))
15.0ms	(* (sin lambda2) (sin lambda1))
68.0ms	(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda2) (cos lambda1)) (log (exp (* (sin lambda2) (sin lambda1))))))
21.0ms	(log (exp (* (sin lambda2) (sin lambda1))))

series441.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(* (sin phi1) (cos phi2))
63.0ms	(* (sin lambda2) (sin lambda1))
251.0ms	(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda2) (cos lambda1)) (log (exp (* (sin lambda2) (sin lambda1))))))
74.0ms	(log (exp (* (sin lambda2) (sin lambda1))))

simplify1.8s

Counts

89 → 89

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	156	1254
1	418	1114
2	2402	984
done	5002	976

prune789.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.0b

regimes1.1s

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: 0 (1.0ms)

Iter	Nodes	Cost
0	28	41
1	38	41
done	38	41

end0.0ms

sample20.0s

Algorithm

intervals

Results

15.4s	4677×	body	1280	valid
3.0s	1905×	body	640	valid
520.0ms	550×	body	320	valid
215.0ms	659×	body	80	valid
209.0ms	209×	body	160	valid