Details

sample508.0ms

Algorithm

intervals

Results

346.0ms	150×	body	1280	valid
114.0ms	61×	body	640	valid
14.0ms	18×	body	320	valid
6.0ms	24×	body	80	valid
2.0ms	3×	body	160	valid

simplify123.0ms

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: 10.8b

localize36.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin (- lambda1 lambda2)) (cos phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
2.5b	(sin (- lambda1 lambda2))
2.6b	(cos (- lambda1 lambda2))

rewrite114.0ms

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:

51.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
32.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
18.0ms	(sin (- lambda1 lambda2))
11.0ms	(cos (- lambda1 lambda2))

series253.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
112.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
28.0ms	(sin (- lambda1 lambda2))
34.0ms	(cos (- lambda1 lambda2))

simplify948.0ms

Counts

72 → 72

Iterations

Useful iterations: done (945.0ms)

Iter	Nodes	Cost
0	116	760
1	272	748
2	1318	644
done	5001	642

prune485.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 4.2b

localize50.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos phi1) (sin phi2))
0.1b	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
2.6b	(cos (- lambda1 lambda2))

rewrite164.0ms

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:

12.0ms	(* (cos phi1) (sin phi2))
70.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
66.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
14.0ms	(cos (- lambda1 lambda2))

series409.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(* (cos phi1) (sin phi2))
218.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
113.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
20.0ms	(cos (- lambda1 lambda2))

simplify1.2s

Counts

81 → 81

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	148	1030
1	375	1017
2	1867	873
done	5000	871

prune772.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize50.0ms

Local error

Found 4 expressions with local error:

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

rewrite179.0ms

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`
4×	`*-commutative` `sin-cos-mult` `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 → 84

Calls

4 calls:

12.0ms	(* (cos phi1) (sin phi2))
71.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
12.0ms	(* (sin lambda2) (sin lambda1))
81.0ms	(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda2) (sin lambda1))))

series492.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(* (cos phi1) (sin phi2))
179.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
53.0ms	(* (sin lambda2) (sin lambda1))
213.0ms	(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda2) (sin lambda1))))

simplify1.8s

Counts

96 → 96

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	198	1503
1	570	1469
2	3300	1287
done	5001	1277

prune638.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize89.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin lambda2) (sin lambda1))
0.2b	(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda2) (sin lambda1))))
0.4b	(pow (* (sin phi2) (cos phi1)) 3)
20.7b	(cbrt (pow (* (sin phi2) (cos phi1)) 3))

rewrite97.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 87

Calls

4 calls:

12.0ms	(* (sin lambda2) (sin lambda1))
63.0ms	(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda2) (sin lambda1))))
14.0ms	(pow (* (sin phi2) (cos phi1)) 3)
5.0ms	(cbrt (pow (* (sin phi2) (cos phi1)) 3))

series393.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(* (sin lambda2) (sin lambda1))
201.0ms	(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda2) (sin lambda1))))
78.0ms	(pow (* (sin phi2) (cos phi1)) 3)
52.0ms	(cbrt (pow (* (sin phi2) (cos phi1)) 3))

simplify2.0s

Counts

99 → 99

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	194	1422
1	576	1295
2	3280	1149
done	5002	1143

prune681.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

regimes442.0ms

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	27	47
1	37	47
done	37	47

end0.0ms

sample17.3s

Algorithm

intervals

Results

13.1s	4594×	body	1280	valid
2.9s	1959×	body	640	valid
463.0ms	545×	body	320	valid
195.0ms	678×	body	80	valid
105.0ms	224×	body	160	valid