Details

sample291.0ms

Algorithm

intervals

Results

205.0ms	157×	body	1280	valid
48.0ms	56×	body	640	valid
11.0ms	20×	body	320	valid
3.0ms	10×	body	160	valid
2.0ms	13×	body	80	valid

simplify33.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	24
1	27	24
2	45	24
3	71	24
4	75	24
done	75	24

prune6.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 13.5b

Counts

2 → 1

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin (- lambda1 lambda2)) (cos phi2))
0.3b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
4.5b	(sin (- lambda1 lambda2))
4.6b	(cos (- lambda1 lambda2))

rewrite25.0ms

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:

7.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
7.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
4.0ms	(sin (- lambda1 lambda2))
4.0ms	(cos (- lambda1 lambda2))

series53.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
28.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
5.0ms	(sin (- lambda1 lambda2))
4.0ms	(cos (- lambda1 lambda2))

simplify1.7s

Counts

72 → 72

Iterations

Useful iterations: 3 (283.0ms)

Iter	Nodes	Cost
0	115	760
1	264	748
2	853	644
3	2521	642
4	4665	642
done	5000	642

prune178.0ms

Filtered

50 candidates to 72 candidates (-44.0%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	58	14	72
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	59	14	73

Merged error: 6.0b

Counts

73 → 14

localize36.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
0.2b	(* (sin lambda1) (cos lambda2))
0.3b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
4.6b	(cos (- lambda1 lambda2))

rewrite29.0ms

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:

10.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
5.0ms	(* (sin lambda1) (cos lambda2))
7.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
5.0ms	(cos (- lambda1 lambda2))

series74.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
10.0ms	(* (sin lambda1) (cos lambda2))
26.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
4.0ms	(cos (- lambda1 lambda2))

simplify1.1s

Counts

82 → 82

Iterations

Useful iterations: 3 (438.0ms)

Iter	Nodes	Cost
0	151	1039
1	360	1016
2	1221	882
3	4214	880
done	5000	880

prune193.0ms

Filtered

56 candidates to 82 candidates (-46.4%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	74	8	82
Fresh	8	5	13
Picked	1	0	1
Done	0	0	0
Total	83	13	96

Merged error: 0.1b

Counts

96 → 13

localize35.0ms

Local error

Found 4 expressions with local error:

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

rewrite34.0ms

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:

9.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
5.0ms	(* (sin lambda1) (cos lambda2))
5.0ms	(* (sin lambda1) (sin lambda2))
12.0ms	(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2))))

series103.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
9.0ms	(* (sin lambda1) (cos lambda2))
10.0ms	(* (sin lambda1) (sin lambda2))
52.0ms	(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2))))

simplify597.0ms

Counts

97 → 97

Iterations

Useful iterations: 2 (157.0ms)

Iter	Nodes	Cost
0	194	1512
1	527	1468
2	2048	1286
done	5000	1286

prune220.0ms

Filtered

71 candidates to 97 candidates (-36.6%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	89	8	97
Fresh	7	5	12
Picked	1	0	1
Done	0	0	0
Total	97	13	110

Merged error: 0.0b

Counts

110 → 13

localize47.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2)))
0.3b	(/ (* (* (sin phi1) (cos phi2)) (+ (pow (* (cos lambda2) (cos lambda1)) 3) (pow (* (sin lambda1) (sin lambda2)) 3))) (+ (* (* (cos lambda2) (cos lambda1)) (* (cos lambda2) (cos lambda1))) (- (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2))) (* (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2))))))
0.4b	(* (* (cos lambda2) (cos lambda1)) (* (cos lambda2) (cos lambda1)))
0.5b	(pow (* (cos lambda2) (cos lambda1)) 3)

rewrite86.0ms

Algorithm

rewrite-expression-head

Rules

100×	`cos-mult`
85×	`sin-mult`
58×	`pow1`
51×	`associate-*r/`
50×	`frac-add` `associate-/r/`
49×	`associate-*l/`
45×	`frac-times`
40×	`add-exp-log` `add-cbrt-cube`
27×	`frac-sub`
26×	`pow-prod-down`
20×	`prod-exp` `cbrt-unprod`
15×	`sub-div`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `associate-/l/`
5×	`cube-div`
4×	`pow-sqr` `pow-prod-up` `sin-cos-mult` `add-log-exp`
3×	`cbrt-undiv` `pow-unpow` `flip3--` `flip3-+` `times-frac` `div-exp` `associate-/r*` `flip--` `flip-+`
2×	`pow-pow` `pow-plus` `associate-r` `associate-l` `pow-exp` `*-commutative` `rem-cube-cbrt`
1×	`pow2` `cube-mult` `pow-to-exp` `unpow-prod-down` `frac-2neg` `unpow3` `cube-prod` `swap-sqr` `clear-num` `div-inv` `associate-/l*` `sqr-pow`

Counts

4 → 165

Calls

4 calls:

10.0ms	(* (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2)))
48.0ms	(/ (* (* (sin phi1) (cos phi2)) (+ (pow (* (cos lambda2) (cos lambda1)) 3) (pow (* (sin lambda1) (sin lambda2)) 3))) (+ (* (* (cos lambda2) (cos lambda1)) (* (cos lambda2) (cos lambda1))) (- (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2))) (* (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2))))))
10.0ms	(* (* (cos lambda2) (cos lambda1)) (* (cos lambda2) (cos lambda1)))
5.0ms	(pow (* (cos lambda2) (cos lambda1)) 3)

series341.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(* (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2)))
288.0ms	(/ (* (* (sin phi1) (cos phi2)) (+ (pow (* (cos lambda2) (cos lambda1)) 3) (pow (* (sin lambda1) (sin lambda2)) 3))) (+ (* (* (cos lambda2) (cos lambda1)) (* (cos lambda2) (cos lambda1))) (- (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2))) (* (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2))))))
14.0ms	(* (* (cos lambda2) (cos lambda1)) (* (cos lambda2) (cos lambda1)))
16.0ms	(pow (* (cos lambda2) (cos lambda1)) 3)

simplify384.0ms

Counts

177 → 177

Iterations

Useful iterations: done (376.0ms)

Iter	Nodes	Cost
0	429	8055
1	1262	6787
done	5000	6565

prune274.0ms

Filtered

96 candidates to 177 candidates (-84.4%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	176	1	177
Fresh	0	12	12
Picked	0	1	1
Done	0	0	0
Total	176	14	190

Merged error: 0.0b

Counts

190 → 14

regimes747.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	33	78
1	44	78
done	44	78

end0.0ms

sample8.8s

Algorithm

intervals

Results

6.2s	4729×	body	1280	valid
1.5s	1890×	body	640	valid
327.0ms	563×	body	320	valid
111.0ms	619×	body	80	valid
68.0ms	199×	body	160	valid

Details

sample291.0ms

simplify33.0ms

prune6.0ms

localize25.0ms

rewrite25.0ms

series53.0ms

simplify1.7s

prune178.0ms

localize36.0ms

rewrite29.0ms

series74.0ms

simplify1.1s

prune193.0ms

localize35.0ms

rewrite34.0ms

series103.0ms

simplify597.0ms

prune220.0ms

localize47.0ms

rewrite86.0ms

series341.0ms

simplify384.0ms

prune274.0ms

regimes747.0ms

bsearch0.0ms

simplify3.0ms

end0.0ms

sample8.8s

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