Details

sample574.0ms

Algorithm

intervals

Results

428.0ms	150×	body	1280	valid
84.0ms	59×	body	640	valid
14.0ms	15×	body	320	valid
10.0ms	12×	body	160	valid
5.0ms	20×	body	80	valid

simplify104.0ms

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	72	24
done	72	24

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.5b

localize40.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin (- lambda1 lambda2)) (cos phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
3.9b	(cos (- lambda1 lambda2))
4.0b	(sin (- lambda1 lambda2))

rewrite91.0ms

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:

32.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
33.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
12.0ms	(cos (- lambda1 lambda2))
13.0ms	(sin (- lambda1 lambda2))

series258.0ms

Counts

4 → 12

Calls

4 calls:

94.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
121.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
19.0ms	(cos (- lambda1 lambda2))
25.0ms	(sin (- lambda1 lambda2))

simplify6.6s

Counts

72 → 72

Iterations

Useful iterations: 3 (1.1s)

Iter	Nodes	Cost
0	116	760
1	258	748
2	816	644
3	2194	642
4	3730	642
done	5000	642

prune409.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 7.9b

localize74.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin phi1) (cos phi2))
0.2b	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
3.9b	(cos (- lambda1 lambda2))

rewrite225.0ms

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` `sin-cos-mult` `unswap-sqr`
1×	`distribute-rgt-in` `sub-neg` `flip3--` `distribute-lft-in` `flip--`

Counts

4 → 70

Calls

4 calls:

13.0ms	(* (sin phi1) (cos phi2))
115.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
73.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
22.0ms	(cos (- lambda1 lambda2))

series394.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(* (sin phi1) (cos phi2))
164.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
154.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
25.0ms	(cos (- lambda1 lambda2))

simplify2.9s

Counts

82 → 82

Iterations

Useful iterations: 3 (1.4s)

Iter	Nodes	Cost
0	131	1039
1	321	1026
2	1110	888
3	3637	880
done	5001	880

prune647.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize65.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (sin lambda1) (sin lambda2))
0.2b	(* (sin phi1) (cos phi2))
0.2b	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
0.3b	(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2))))

rewrite200.0ms

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/` `associate-l/` `sin-mult` `unswap-sqr`
2×	`flip3-+` `frac-add` `cos-mult` `flip-+`
1×	`distribute-rgt-in` `flip3--` `distribute-lft-in` `flip--`

Counts

4 → 85

Calls

4 calls:

19.0ms	(* (sin lambda1) (sin lambda2))
15.0ms	(* (sin phi1) (cos phi2))
76.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
87.0ms	(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2))))

series552.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(* (sin lambda1) (sin lambda2))
66.0ms	(* (sin phi1) (cos phi2))
198.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
230.0ms	(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2))))

simplify1.4s

Counts

97 → 97

Iterations

Useful iterations: 2 (385.0ms)

Iter	Nodes	Cost
0	183	1512
1	504	1478
2	2081	1286
done	5000	1286

prune750.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize85.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (sin phi1) (cos phi2)) (- (* (* (cos lambda2) (cos lambda1)) (* (cos lambda2) (cos lambda1))) (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2)))))
0.3b	(/ (* (* (sin phi1) (cos phi2)) (- (* (* (cos lambda2) (cos lambda1)) (* (cos lambda2) (cos lambda1))) (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2))))) (- (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2))))
0.3b	(* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2)))
0.4b	(* (* (cos lambda2) (cos lambda1)) (* (cos lambda2) (cos lambda1)))

rewrite965.0ms

Algorithm

rewrite-expression-head

Rules

87×	`pow1`
78×	`cos-mult` `sin-mult`
74×	`associate-*r/`
66×	`frac-times`
44×	`associate-*l/`
42×	`add-exp-log` `add-cbrt-cube`
37×	`pow-prod-down` `frac-sub`
34×	`sin-cos-mult`
33×	`associate-/l/`
22×	`prod-exp` `cbrt-unprod`
21×	`sub-div`
8×	`pow-sqr` `pow-prod-up`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`associate-r`
5×	`flip3--` `flip--`
4×	`pow-plus` `associate-/r/` `add-log-exp`
3×	`cbrt-undiv` `times-frac` `div-exp` `associate-l` `associate-/r` `-commutative`
2×	`pow2` `distribute-rgt-in` `sub-neg` `distribute-lft-in` `swap-sqr`
1×	`frac-2neg` `clear-num` `div-inv` `associate-/l*` `difference-of-squares`

Counts

4 → 190

Calls

4 calls:

410.0ms	(* (* (sin phi1) (cos phi2)) (- (* (* (cos lambda2) (cos lambda1)) (* (cos lambda2) (cos lambda1))) (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2)))))
380.0ms	(/ (* (* (sin phi1) (cos phi2)) (- (* (* (cos lambda2) (cos lambda1)) (* (cos lambda2) (cos lambda1))) (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2))))) (- (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2))))
97.0ms	(* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2)))
65.0ms	(* (* (cos lambda2) (cos lambda1)) (* (cos lambda2) (cos lambda1)))

series1.3s

Counts

4 → 12

Calls

4 calls:

341.0ms	(* (* (sin phi1) (cos phi2)) (- (* (* (cos lambda2) (cos lambda1)) (* (cos lambda2) (cos lambda1))) (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2)))))
719.0ms	(/ (* (* (sin phi1) (cos phi2)) (- (* (* (cos lambda2) (cos lambda1)) (* (cos lambda2) (cos lambda1))) (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2))))) (- (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2))))
90.0ms	(* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2)))
112.0ms	(* (* (cos lambda2) (cos lambda1)) (* (cos lambda2) (cos lambda1)))

simplify2.4s

Counts

202 → 202

Iterations

Useful iterations: 2 (770.0ms)

Iter	Nodes	Cost
0	306	5917
1	879	5026
2	4165	4304
done	5001	4304

prune2.0s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

regimes397.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	28	62
1	36	62
done	36	62

end0.0ms

sample20.7s

Algorithm

intervals

Results

14.7s	4584×	body	1280	valid
4.2s	1973×	body	640	valid
561.0ms	593×	body	320	valid
291.0ms	654×	body	80	valid
224.0ms	196×	body	160	valid