Details

sample558.0ms

Algorithm

intervals

Results

359.0ms	154×	body	1280	valid
144.0ms	62×	body	640	valid
16.0ms	15×	body	320	valid
6.0ms	19×	body	80	valid
3.0ms	6×	body	160	valid

simplify492.0ms

Counts

1 → 1

Iterations

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

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.2b

localize83.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin (- lambda1 lambda2)) (cos phi2))
0.3b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
2.0b	(sin (- lambda1 lambda2))
2.0b	(cos (- lambda1 lambda2))

rewrite82.0ms

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))
39.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
8.0ms	(sin (- lambda1 lambda2))
9.0ms	(cos (- lambda1 lambda2))

series310.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
147.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
33.0ms	(sin (- lambda1 lambda2))
29.0ms	(cos (- lambda1 lambda2))

simplify2.6s

Counts

76 → 76

Iterations

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

prune800.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 6.7b

localize124.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (* (cos phi1) (sin phi2)) (* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2))))
0.2b	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
0.3b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
2.0b	(cos (- lambda1 lambda2))

rewrite139.0ms

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` `add-log-exp`
5×	`cos-diff`
4×	`associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `insert-posit16`
3×	`associate-*l/`
2×	`distribute-rgt-in` `cos-sum` `sub-neg` `distribute-lft-in` `flip3--` `*-commutative` `flip--` `associate--r+`
1×	`diff-log` `sin-cos-mult` `unswap-sqr`

Counts

4 → 69

Calls

4 calls:

12.0ms	(- (* (cos phi1) (sin phi2)) (* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2))))
66.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
52.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
8.0ms	(cos (- lambda1 lambda2))

series585.0ms

Counts

4 → 12

Calls

4 calls:

187.0ms	(- (* (cos phi1) (sin phi2)) (* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2))))
223.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
150.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
25.0ms	(cos (- lambda1 lambda2))

simplify1.6s

Counts

81 → 81

Iterations

Iter	Nodes
done	5002
2	1347
1	379
0	144

prune1.0s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize103.0ms

Local error

Found 4 expressions with local error:

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

rewrite171.0ms

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×	`associate-l/` `-commutative` `insert-posit16` `sin-cos-mult` `add-log-exp`
3×	`sin-mult`
2×	`frac-times` `associate-*r/` `cos-mult` `unswap-sqr`
1×	`flip3--` `flip--`

Counts

4 → 93

Calls

4 calls:

61.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
12.0ms	(* (sin lambda1) (sin lambda2))
41.0ms	(* (* (sin lambda1) (sin lambda2)) (* (sin phi1) (cos phi2)))
55.0ms	(* (* (cos lambda1) (cos lambda2)) (* (sin phi1) (cos phi2)))

series626.0ms

Counts

4 → 12

Calls

4 calls:

192.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
77.0ms	(* (sin lambda1) (sin lambda2))
147.0ms	(* (* (sin lambda1) (sin lambda2)) (* (sin phi1) (cos phi2)))
210.0ms	(* (* (cos lambda1) (cos lambda2)) (* (sin phi1) (cos phi2)))

simplify1.6s

Counts

105 → 105

Iterations

Iter	Nodes
done	5001
2	1723
1	454
0	169

prune1.2s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize122.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (* (sin lambda1) (sin lambda2))) (cbrt (* (sin lambda1) (sin lambda2))))
8.2b	(cbrt (* (sin lambda1) (sin lambda2)))
8.2b	(cbrt (* (sin lambda1) (sin lambda2)))
8.2b	(cbrt (* (sin lambda1) (sin lambda2)))

rewrite86.0ms

Algorithm

rewrite-expression-head

Rules

11×	`pow1`
10×	`add-sqr-sqrt`
9×	`pow1/3`
8×	`*-un-lft-identity` `add-cube-cbrt`
7×	`cbrt-prod` `cbrt-div` `sin-mult`
6×	`add-exp-log`
4×	`add-cbrt-cube` `swap-sqr` `associate-r` `associate-l` `insert-posit16` `add-log-exp`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `frac-times` `pow-plus` `associate-l/` `prod-exp` `associate-r/` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 68

Calls

4 calls:

53.0ms	(* (cbrt (* (sin lambda1) (sin lambda2))) (cbrt (* (sin lambda1) (sin lambda2))))
10.0ms	(cbrt (* (sin lambda1) (sin lambda2)))
10.0ms	(cbrt (* (sin lambda1) (sin lambda2)))
11.0ms	(cbrt (* (sin lambda1) (sin lambda2)))

series546.0ms

Counts

4 → 12

Calls

4 calls:

157.0ms	(* (cbrt (* (sin lambda1) (sin lambda2))) (cbrt (* (sin lambda1) (sin lambda2))))
118.0ms	(cbrt (* (sin lambda1) (sin lambda2)))
138.0ms	(cbrt (* (sin lambda1) (sin lambda2)))
134.0ms	(cbrt (* (sin lambda1) (sin lambda2)))

simplify2.1s

Counts

80 → 80

Iterations

Iter	Nodes
done	5000
3	2061
2	651
1	231
0	91

prune884.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

regimes618.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify7.0ms

Iterations

Iter	Nodes
done	39
1	39
0	28

end0.0ms

sample19.9s

Algorithm

intervals

Results

14.9s	4666×	body	1280	valid
3.6s	1945×	body	640	valid
623.0ms	564×	body	320	valid
213.0ms	641×	body	80	valid
100.0ms	184×	body	160	valid