Details

sample789.0ms

Algorithm

intervals

Results

590.0ms	148×	body	1280	valid
141.0ms	64×	body	640	valid
23.0ms	17×	body	320	valid
10.0ms	23×	body	80	valid
4.0ms	4×	body	160	valid

simplify38.0ms

Counts

1 → 1

Iterations

Iter	Nodes
5	73
4	73
3	69
2	45
1	27
0	17

prune26.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.0b

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)))
5.1b	(cos (- lambda1 lambda2))
5.2b	(sin (- lambda1 lambda2))

rewrite98.0ms

Algorithm

rewrite-expression-head

Rules

11×	`pow1` `add-cbrt-cube` `add-exp-log`
9×	`add-sqr-sqrt`
7×	`*-un-lft-identity` `add-cube-cbrt`
6×	`associate-r`
4×	`associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `insert-posit16` `add-log-exp`
3×	`cos-diff`
2×	`cos-sum` `sub-neg` `sin-sum` `*-commutative` `sin-cos-mult`
1×	`distribute-rgt-in` `distribute-lft-in` `associate-*l/` `sin-diff` `unswap-sqr`

Counts

4 → 64

Calls

4 calls:

24.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
41.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
16.0ms	(cos (- lambda1 lambda2))
16.0ms	(sin (- lambda1 lambda2))

series330.0ms

Counts

4 → 12

Calls

4 calls:

108.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
161.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
26.0ms	(cos (- lambda1 lambda2))
35.0ms	(sin (- lambda1 lambda2))

simplify1.6s

Counts

76 → 76

Iterations

Iter	Nodes
3	2671
2	792
1	274
0	120

prune642.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 6.9b

localize128.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
0.2b	(* (cos lambda1) (sin lambda2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
5.1b	(cos (- lambda1 lambda2))

rewrite159.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt` `pow1` `add-cbrt-cube` `add-exp-log`
9×	`-un-lft-identity` `associate-r*` `add-cube-cbrt`
7×	`associate-l`
5×	`pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`insert-posit16` `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 → 73

Calls

4 calls:

67.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
11.0ms	(* (cos lambda1) (sin lambda2))
62.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
17.0ms	(cos (- lambda1 lambda2))

series416.0ms

Counts

4 → 12

Calls

4 calls:

200.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
56.0ms	(* (cos lambda1) (sin lambda2))
130.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
30.0ms	(cos (- lambda1 lambda2))

simplify3.5s

Counts

85 → 85

Iterations

Iter	Nodes
3	4417
2	1174
1	367
0	149

prune622.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize72.0ms

Local error

Found 4 expressions with local error:

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

rewrite144.0ms

Algorithm

rewrite-expression-head

Rules

32×	`pow1` `add-cbrt-cube` `add-exp-log`
18×	`pow-prod-down` `prod-exp` `cbrt-unprod`
12×	`add-sqr-sqrt`
8×	`-un-lft-identity` `associate-r` `associate-l*` `add-cube-cbrt`
4×	`*-commutative` `insert-posit16` `sin-cos-mult` `add-log-exp`
3×	`sin-mult`
2×	`frac-times` `associate-l/` `associate-r/` `cos-mult` `unswap-sqr`

Counts

4 → 91

Calls

4 calls:

44.0ms	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))
18.0ms	(* (sin lambda1) (sin lambda2))
18.0ms	(* (cos lambda1) (sin lambda2))
63.0ms	(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))

series401.0ms

Counts

4 → 12

Calls

4 calls:

152.0ms	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))
81.0ms	(* (sin lambda1) (sin lambda2))
50.0ms	(* (cos lambda1) (sin lambda2))
118.0ms	(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))

simplify3.2s

Counts

103 → 103

Iterations

Iter	Nodes
3	6952
2	1498
1	414
0	157

prune926.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize81.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin lambda1) (sin lambda2))
0.2b	(* (cos lambda1) (sin lambda2))
0.3b	(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
2.9b	(log (exp (* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))

rewrite89.0ms

Algorithm

rewrite-expression-head

Rules

21×	`pow1`
20×	`add-cbrt-cube` `add-exp-log`
13×	`add-sqr-sqrt`
10×	`pow-prod-down` `prod-exp` `cbrt-unprod`
9×	`*-un-lft-identity` `add-cube-cbrt`
7×	`associate-r` `associate-l`
5×	`add-log-exp`
4×	`insert-posit16`
3×	`log-prod` `log-pow` `*-commutative` `sin-mult`
2×	`sin-cos-mult` `unswap-sqr`
1×	`frac-times` `exp-prod` `exp-to-pow` `rem-log-exp` `associate-l/` `associate-r/`

Counts

4 → 80

Calls

4 calls:

20.0ms	(* (sin lambda1) (sin lambda2))
16.0ms	(* (cos lambda1) (sin lambda2))
42.0ms	(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
9.0ms	(log (exp (* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))

series411.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(* (sin lambda1) (sin lambda2))
63.0ms	(* (cos lambda1) (sin lambda2))
138.0ms	(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
149.0ms	(log (exp (* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))

simplify1.4s

Counts

92 → 92

Iterations

Iter	Nodes
3	4022
2	951
1	322
0	141

prune865.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

regimes650.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify11.0ms

Iterations

Iter	Nodes
2	37
1	37
0	27

end0.0ms

sample24.6s

Algorithm

intervals

Results

18.0s	4509×	body	1280	valid
5.0s	2043×	body	640	valid
719.0ms	555×	body	320	valid
293.0ms	664×	body	80	valid
226.0ms	229×	body	160	valid