Details

sample267.0ms

Algorithm

intervals

Results

188.0ms	151×	body	1280	valid
50.0ms	62×	body	640	valid
7.0ms	17×	body	320	valid
3.0ms	23×	body	80	valid
1.0ms	3×	body	160	valid

simplify9.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	27	15
1	46	15
2	71	15
3	77	15
4	77	15
done	77	15

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.4b

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin phi1) (cos phi2))
0.3b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
2.5b	(sin (- lambda1 lambda2))
2.8b	(cos (- lambda1 lambda2))

rewrite64.0ms

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:

11.0ms	(* (sin phi1) (cos phi2))
32.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
10.0ms	(sin (- lambda1 lambda2))
10.0ms	(cos (- lambda1 lambda2))

series188.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(* (sin phi1) (cos phi2))
98.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
22.0ms	(sin (- lambda1 lambda2))
19.0ms	(cos (- lambda1 lambda2))

simplify112.0ms

Counts

72 → 72

Iterations

Useful iterations: 1 (7.0ms)

Iter	Nodes	Cost
0	254	435
1	1026	372
2	4856	372
3	5001	372
done	5001	372

prune319.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.6b

localize35.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin phi1) (cos phi2))
0.2b	(* (cos lambda1) (sin lambda2))
0.3b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
2.8b	(cos (- lambda1 lambda2))

rewrite65.0ms

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:

12.0ms	(* (sin phi1) (cos phi2))
11.0ms	(* (cos lambda1) (sin lambda2))
28.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
12.0ms	(cos (- lambda1 lambda2))

series204.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(* (sin phi1) (cos phi2))
44.0ms	(* (cos lambda1) (sin lambda2))
95.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
18.0ms	(cos (- lambda1 lambda2))

simplify38.0ms

Counts

80 → 80

Iterations

Useful iterations: 1 (8.0ms)

Iter	Nodes	Cost
0	299	481
1	1250	409
2	5002	409
done	5002	409

prune415.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize35.0ms

Local error

Found 4 expressions with local error:

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

rewrite108.0ms

Algorithm

rewrite-expression-head

Rules

32×	`pow1` `add-exp-log` `add-cbrt-cube`
18×	`pow-prod-down` `prod-exp` `cbrt-unprod`
12×	`add-sqr-sqrt`
8×	`add-cube-cbrt` `-un-lft-identity` `associate-r` `associate-l*`
4×	`*-commutative` `sin-cos-mult` `add-log-exp`
3×	`sin-mult`
2×	`frac-times` `associate-r/` `associate-l/` `cos-mult` `unswap-sqr`

Counts

4 → 87

Calls

4 calls:

11.0ms	(* (cos lambda1) (sin lambda2))
12.0ms	(* (sin lambda1) (sin lambda2))
40.0ms	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))
43.0ms	(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))

series316.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(* (cos lambda1) (sin lambda2))
46.0ms	(* (sin lambda1) (sin lambda2))
117.0ms	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))
105.0ms	(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))

simplify55.0ms

Counts

99 → 99

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	407	779
1	1866	601
2	5002	599
done	5002	599

prune447.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize43.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (cbrt (* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))) (cbrt (* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))
17.4b	(cbrt (* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))
17.4b	(cbrt (* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))
17.4b	(cbrt (* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))

rewrite206.0ms

Algorithm

rewrite-expression-head

Rules

33×	`cbrt-div`
22×	`sin-cos-mult` `sin-mult`
20×	`frac-times`
14×	`associate-r/` `associate-l/`
11×	`pow1`
10×	`add-sqr-sqrt`
9×	`pow1/3`
8×	`add-cube-cbrt` `*-un-lft-identity`
7×	`cbrt-prod`
6×	`add-exp-log`
4×	`swap-sqr` `associate-r` `associate-l` `add-cbrt-cube` `add-log-exp`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 82

Calls

4 calls:

109.0ms	(* (cbrt (* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))) (cbrt (* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))
30.0ms	(cbrt (* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))
33.0ms	(cbrt (* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))
30.0ms	(cbrt (* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))

series968.0ms

Counts

4 → 12

Calls

4 calls:

273.0ms	(* (cbrt (* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))) (cbrt (* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))
233.0ms	(cbrt (* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))
231.0ms	(cbrt (* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))
231.0ms	(cbrt (* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))

simplify45.0ms

Counts

94 → 94

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	304	1411
1	1196	1254
2	5001	1189
done	5001	1189

prune574.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

regimes400.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	48
1	39	48
done	39	48

end0.0ms

sample8.4s

Algorithm

intervals

Results

5.9s	4615×	body	1280	valid
1.5s	2033×	body	640	valid
453.0ms	514×	body	320	valid
98.0ms	643×	body	80	valid
61.0ms	195×	body	160	valid