Details

sample534.0ms

Algorithm

intervals

Results

365.0ms	142×	body	1280	valid
61.0ms	54×	body	640	valid
21.0ms	23×	body	320	valid
8.0ms	14×	body	160	valid
6.0ms	23×	body	80	valid

simplify195.0ms

Counts

1 → 1

Iterations

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

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.6b

localize193.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin (- lambda1 lambda2)) (cos phi2))
0.3b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
3.3b	(sin (- lambda1 lambda2))
3.4b	(cos (- lambda1 lambda2))

rewrite236.0ms

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:

80.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
99.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
27.0ms	(sin (- lambda1 lambda2))
25.0ms	(cos (- lambda1 lambda2))

series451.0ms

Counts

4 → 12

Calls

4 calls:

160.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
219.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
46.0ms	(sin (- lambda1 lambda2))
26.0ms	(cos (- lambda1 lambda2))

simplify7.1s

Counts

76 → 76

Iterations

Iter	Nodes
done	5001
3	2978
2	792
1	274
0	120

prune1.5s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 7.0b

localize252.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos phi1) (sin phi2))
0.2b	(* (cos lambda1) (sin lambda2))
0.3b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
3.4b	(cos (- lambda1 lambda2))

rewrite237.0ms

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

Counts

4 → 71

Calls

4 calls:

55.0ms	(* (cos phi1) (sin phi2))
54.0ms	(* (cos lambda1) (sin lambda2))
81.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
40.0ms	(cos (- lambda1 lambda2))

series455.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(* (cos phi1) (sin phi2))
126.0ms	(* (cos lambda1) (sin lambda2))
203.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
45.0ms	(cos (- lambda1 lambda2))

simplify7.8s

Counts

83 → 83

Iterations

Iter	Nodes
done	5001
3	3804
2	994
1	356
0	150

prune1.3s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

localize402.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos lambda1) (sin lambda2))
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)))

rewrite358.0ms

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:

33.0ms	(* (cos lambda1) (sin lambda2))
32.0ms	(* (sin lambda1) (sin lambda2))
130.0ms	(* (* (sin lambda1) (sin lambda2)) (* (sin phi1) (cos phi2)))
157.0ms	(* (* (cos lambda1) (cos lambda2)) (* (sin phi1) (cos phi2)))

series718.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(* (cos lambda1) (sin lambda2))
81.0ms	(* (sin lambda1) (sin lambda2))
228.0ms	(* (* (sin lambda1) (sin lambda2)) (* (sin phi1) (cos phi2)))
315.0ms	(* (* (cos lambda1) (cos lambda2)) (* (sin phi1) (cos phi2)))

simplify3.3s

Counts

103 → 103

Iterations

Iter	Nodes
done	5000
2	1567
1	426
0	159

prune2.0s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.0b

localize429.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (sin lambda1)) (cbrt (sin lambda1)))
0.6b	(cbrt (sin lambda1))
0.6b	(cbrt (sin lambda1))
0.6b	(cbrt (sin lambda1))

rewrite90.0ms

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:

60.0ms	(* (cbrt (sin lambda1)) (cbrt (sin lambda1)))
7.0ms	(cbrt (sin lambda1))
7.0ms	(cbrt (sin lambda1))
9.0ms	(cbrt (sin lambda1))

series849.0ms

Counts

4 → 12

Calls

4 calls:

243.0ms	(* (cbrt (sin lambda1)) (cbrt (sin lambda1)))
222.0ms	(cbrt (sin lambda1))
181.0ms	(cbrt (sin lambda1))
202.0ms	(cbrt (sin lambda1))

simplify10.3s

Counts

89 → 89

Iterations

Iter	Nodes
done	5025
4	4899
3	1333
2	443
1	176
0	77

prune1.5s

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 0.0b

regimes2.6s

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify15.0ms

Iterations

Iter	Nodes
done	39
1	39
0	28

end0.0ms

sample20.2s

Algorithm

intervals

Results

15.0s	4601×	body	1280	valid
3.6s	1955×	body	640	valid
716.0ms	546×	body	320	valid
187.0ms	675×	body	80	valid
159.0ms	223×	body	160	valid