Details

sample1.0s

Algorithm

intervals

Results

550.0ms	63×	body	640	valid
383.0ms	145×	body	1280	valid
18.0ms	18×	body	320	valid
6.0ms	21×	body	80	valid
6.0ms	9×	body	160	valid

simplify45.0ms

Counts

1 → 1

Iterations

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

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.1b

localize85.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (sin (- lambda1 lambda2)) (cos phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
2.0b	(cos (- lambda1 lambda2))
2.1b	(sin (- lambda1 lambda2))

rewrite90.0ms

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` `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 → 60

Calls

4 calls:

25.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
31.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
16.0ms	(cos (- lambda1 lambda2))
16.0ms	(sin (- lambda1 lambda2))

series289.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
152.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
20.0ms	(cos (- lambda1 lambda2))
34.0ms	(sin (- lambda1 lambda2))

simplify2.6s

Counts

72 → 72

Iterations

Iter	Nodes
done	5003
3	2867
2	793
1	272
0	116

prune730.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 6.7b

localize93.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos lambda1) (sin lambda2))
0.1b	(* (sin lambda1) (cos lambda2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
2.0b	(cos (- lambda1 lambda2))

rewrite108.0ms

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×	`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:

18.0ms	(* (cos lambda1) (sin lambda2))
24.0ms	(* (sin lambda1) (cos lambda2))
47.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
16.0ms	(cos (- lambda1 lambda2))

series303.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(* (cos lambda1) (sin lambda2))
77.0ms	(* (sin lambda1) (cos lambda2))
119.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
28.0ms	(cos (- lambda1 lambda2))

simplify3.1s

Counts

80 → 80

Iterations

Iter	Nodes
done	5000
3	3695
2	1042
1	357
0	148

prune968.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize90.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (sin lambda1) (cos lambda2))
0.2b	(* (* (sin lambda1) (sin lambda2)) (* (sin phi1) (cos phi2)))
0.2b	(* (* (cos lambda1) (cos lambda2)) (* (sin phi1) (cos phi2)))
0.3b	(* (sin lambda1) (sin lambda2))

rewrite147.0ms

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`
5×	`sin-cos-mult`
4×	`*-commutative` `add-log-exp`
3×	`sin-mult`
2×	`frac-times` `associate-l/` `associate-r/` `cos-mult` `unswap-sqr`

Counts

4 → 88

Calls

4 calls:

9.0ms	(* (sin lambda1) (cos lambda2))
47.0ms	(* (* (sin lambda1) (sin lambda2)) (* (sin phi1) (cos phi2)))
65.0ms	(* (* (cos lambda1) (cos lambda2)) (* (sin phi1) (cos phi2)))
24.0ms	(* (sin lambda1) (sin lambda2))

series523.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(* (sin lambda1) (cos lambda2))
172.0ms	(* (* (sin lambda1) (sin lambda2)) (* (sin phi1) (cos phi2)))
201.0ms	(* (* (cos lambda1) (cos lambda2)) (* (sin phi1) (cos phi2)))
68.0ms	(* (sin lambda1) (sin lambda2))

simplify1.7s

Counts

100 → 100

Iterations

Iter	Nodes
done	5001
2	1508
1	432
0	157

prune981.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize112.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (cbrt (cos lambda2)) (cbrt (cos lambda2)))
0.3b	(cbrt (cos lambda2))
0.3b	(cbrt (cos lambda2))
0.3b	(cbrt (cos lambda2))

rewrite32.0ms

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` `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 → 73

Calls

4 calls:

24.0ms	(* (cbrt (cos lambda2)) (cbrt (cos lambda2)))
2.0ms	(cbrt (cos lambda2))
2.0ms	(cbrt (cos lambda2))
2.0ms	(cbrt (cos lambda2))

series651.0ms

Counts

4 → 12

Calls

4 calls:

233.0ms	(* (cbrt (cos lambda2)) (cbrt (cos lambda2)))
137.0ms	(cbrt (cos lambda2))
142.0ms	(cbrt (cos lambda2))
139.0ms	(cbrt (cos lambda2))

simplify1.9s

Counts

85 → 85

Iterations

Iter	Nodes
done	5000
3	1140
2	366
1	144
0	64

prune833.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.0b

regimes939.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify6.0ms

Iterations

Iter	Nodes
done	39
1	39
0	28

end0.0ms

sample18.7s

Algorithm

intervals

Results

13.5s	4593×	body	1280	valid
3.6s	1988×	body	640	valid
446.0ms	549×	body	320	valid
264.0ms	647×	body	80	valid
213.0ms	223×	body	160	valid