Details

sample918.0ms

Algorithm

intervals

Results

395.0ms	10×	body	160	valid
390.0ms	143×	body	1280	valid
82.0ms	62×	body	640	valid
20.0ms	24×	body	320	valid
5.0ms	17×	body	80	valid

simplify58.0ms

Counts

1 → 1

Iterations

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

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.5b

localize81.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin (- lambda1 lambda2)) (cos phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
3.2b	(sin (- lambda1 lambda2))
3.3b	(cos (- lambda1 lambda2))

rewrite132.0ms

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:

52.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
43.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
14.0ms	(sin (- lambda1 lambda2))
21.0ms	(cos (- lambda1 lambda2))

series255.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
125.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
28.0ms	(sin (- lambda1 lambda2))
26.0ms	(cos (- lambda1 lambda2))

simplify2.4s

Counts

76 → 76

Iterations

Iter	Nodes
done	5000
3	2963
2	793
1	276
0	120

prune766.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 5.4b

localize71.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (sin phi1) (cos phi2))
0.2b	(* (cos lambda1) (sin lambda2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
3.3b	(cos (- lambda1 lambda2))

rewrite107.0ms

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` `*-commutative`
2×	`cos-sum` `sin-cos-mult` `unswap-sqr`
1×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `associate-*l/`

Counts

4 → 72

Calls

4 calls:

12.0ms	(* (sin phi1) (cos phi2))
19.0ms	(* (cos lambda1) (sin lambda2))
37.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
34.0ms	(cos (- lambda1 lambda2))

series292.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(* (sin phi1) (cos phi2))
63.0ms	(* (cos lambda1) (sin lambda2))
144.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
20.0ms	(cos (- lambda1 lambda2))

simplify2.7s

Counts

84 → 84

Iterations

Iter	Nodes
done	5001
3	3379
2	913
1	324
0	136

prune936.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize91.0ms

Local error

Found 4 expressions with local error:

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

rewrite177.0ms

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:

23.0ms	(* (cos lambda1) (sin lambda2))
71.0ms	(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
16.0ms	(* (sin lambda1) (sin lambda2))
62.0ms	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))

series479.0ms

Counts

4 → 12

Calls

4 calls:

74.0ms	(* (cos lambda1) (sin lambda2))
150.0ms	(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
78.0ms	(* (sin lambda1) (sin lambda2))
177.0ms	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))

simplify1.8s

Counts

103 → 103

Iterations

Iter	Nodes
done	5001
2	1511
1	415
0	157

prune974.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.0b

localize135.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (sin lambda2)) (cbrt (sin lambda2)))
0.6b	(cbrt (sin lambda2))
0.6b	(cbrt (sin lambda2))
0.6b	(cbrt (sin lambda2))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`*-un-lft-identity` `add-cube-cbrt`
11×	`pow1`
9×	`pow1/3`
6×	`swap-sqr` `associate-r` `associate-l` `add-exp-log`
4×	`add-cbrt-cube` `insert-posit16` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 77

Calls

4 calls:

27.0ms	(* (cbrt (sin lambda2)) (cbrt (sin lambda2)))
3.0ms	(cbrt (sin lambda2))
2.0ms	(cbrt (sin lambda2))
3.0ms	(cbrt (sin lambda2))

series622.0ms

Counts

4 → 12

Calls

4 calls:

156.0ms	(* (cbrt (sin lambda2)) (cbrt (sin lambda2)))
159.0ms	(cbrt (sin lambda2))
176.0ms	(cbrt (sin lambda2))
130.0ms	(cbrt (sin lambda2))

simplify1.8s

Counts

89 → 89

Iterations

Iter	Nodes
done	5001
3	1403
2	456
1	176
0	77

prune889.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.0b

regimes1.0s

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify8.0ms

Iterations

Iter	Nodes
done	44
1	44
0	31

end0.0ms

sample19.1s

Algorithm

intervals

Results

13.7s	4582×	body	1280	valid
3.7s	1943×	body	640	valid
608.0ms	583×	body	320	valid
551.0ms	688×	body	80	valid
163.0ms	204×	body	160	valid