Details

sample509.0ms

Algorithm

intervals

Results

350.0ms	158×	body	1280	valid
115.0ms	57×	body	640	valid
8.0ms	11×	body	320	valid
5.0ms	21×	body	80	valid
4.0ms	9×	body	160	valid

simplify89.0ms

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	72	24
done	72	24

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.3b

localize55.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin (- lambda1 lambda2)) (cos phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
2.9b	(cos (- lambda1 lambda2))
3.0b	(sin (- lambda1 lambda2))

rewrite145.0ms

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:

56.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
38.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
29.0ms	(cos (- lambda1 lambda2))
19.0ms	(sin (- lambda1 lambda2))

series247.0ms

Counts

4 → 12

Calls

4 calls:

87.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
116.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
19.0ms	(cos (- lambda1 lambda2))
25.0ms	(sin (- lambda1 lambda2))

simplify7.1s

Counts

72 → 72

Iterations

Useful iterations: 3 (1.0s)

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

prune496.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 8.1b

localize73.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos phi1) (sin phi2))
0.2b	(* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
2.9b	(cos (- lambda1 lambda2))

rewrite135.0ms

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` `distribute-lft-in` `flip3-+` `sin-cos-mult` `flip-+`

Counts

4 → 69

Calls

4 calls:

20.0ms	(* (cos phi1) (sin phi2))
69.0ms	(* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2))
31.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
11.0ms	(cos (- lambda1 lambda2))

series450.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(* (cos phi1) (sin phi2))
230.0ms	(* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2))
142.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
23.0ms	(cos (- lambda1 lambda2))

simplify4.0s

Counts

81 → 81

Iterations

Useful iterations: 3 (1.8s)

Iter	Nodes	Cost
0	154	1059
1	379	1045
2	1369	901
3	4396	872
done	5000	872

prune723.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize93.0ms

Local error

Found 4 expressions with local error:

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

rewrite224.0ms

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` `sin-mult`
4×	`frac-times` `associate-r/` `cos-mult` `-commutative` `add-log-exp`
3×	`associate-*l/` `unswap-sqr`
2×	`distribute-rgt-in` `sub-neg` `flip3--` `distribute-lft-in` `frac-sub` `flip--` `sub-div`
1×	`flip3-+` `sin-neg` `distribute-rgt-neg-out` `flip-+`

Counts

4 → 89

Calls

4 calls:

12.0ms	(* (cos phi1) (sin phi2))
68.0ms	(* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2))
31.0ms	(* (sin lambda1) (sin (- lambda2)))
110.0ms	(* (* (sin phi1) (cos phi2)) (- (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin (- lambda2)))))

series629.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(* (cos phi1) (sin phi2))
173.0ms	(* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2))
94.0ms	(* (sin lambda1) (sin (- lambda2)))
286.0ms	(* (* (sin phi1) (cos phi2)) (- (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin (- lambda2)))))

simplify1.5s

Counts

101 → 101

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	216	1722
1	546	1674
2	2110	1434
done	5001	1397

prune1.1s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize91.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin lambda1) (sin lambda2))
0.2b	(* (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))) (* (sin phi1) (cos phi2)))
0.5b	(pow (* (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))) (* (sin phi1) (cos phi2))) 3)
18.1b	(cbrt (pow (* (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))) (* (sin phi1) (cos phi2))) 3))

rewrite237.0ms

Algorithm

rewrite-expression-head

Rules

17×	`pow1` `add-exp-log` `add-cbrt-cube`
14×	`cube-div`
12×	`sin-cos-mult`
11×	`add-sqr-sqrt`
9×	`frac-times` `add-cube-cbrt` `-un-lft-identity` `associate-l/`
8×	`cbrt-prod`
7×	`cbrt-div` `pow-prod-down` `prod-exp` `cbrt-unprod` `sin-mult`
6×	`flip3-+` `associate-l` `frac-add` `cos-mult` `flip-+`
4×	`associate-r` `add-log-exp`
3×	`pow-unpow` `pow-pow` `associate-*r/` `pow-exp` `rem-cube-cbrt`
2×	`cube-mult` `unpow-prod-down` `unpow3` `cube-prod` `*-commutative` `sqr-pow`
1×	`pow-to-exp` `pow1/3` `rem-cbrt-cube` `unswap-sqr`

Counts

4 → 100

Calls

4 calls:

16.0ms	(* (sin lambda1) (sin lambda2))
80.0ms	(* (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))) (* (sin phi1) (cos phi2)))
88.0ms	(pow (* (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))) (* (sin phi1) (cos phi2))) 3)
45.0ms	(cbrt (pow (* (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))) (* (sin phi1) (cos phi2))) 3))

series1.1s

Counts

4 → 12

Calls

4 calls:

69.0ms	(* (sin lambda1) (sin lambda2))
273.0ms	(* (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))) (* (sin phi1) (cos phi2)))
435.0ms	(pow (* (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))) (* (sin phi1) (cos phi2))) 3)
313.0ms	(cbrt (pow (* (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))) (* (sin phi1) (cos phi2))) 3))

simplify1.6s

Counts

112 → 112

Iterations

Useful iterations: 2 (506.0ms)

Iter	Nodes	Cost
0	194	2674
1	533	2319
2	2259	2193
done	5002	2193

prune812.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.1b

regimes418.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	34	68
1	43	68
done	43	68

end0.0ms

sample17.7s

Algorithm

intervals

Results

12.3s	4602×	body	1280	valid
3.6s	1994×	body	640	valid
847.0ms	511×	body	320	valid
192.0ms	668×	body	80	valid
146.0ms	225×	body	160	valid