Details

sample798.0ms

Algorithm

intervals

Results

518.0ms	142×	body	1280	valid
192.0ms	54×	body	640	valid
35.0ms	23×	body	320	valid
15.0ms	14×	body	160	valid
9.0ms	23×	body	80	valid

simplify67.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	79
4	79
3	71
2	46
1	27
0	17

prune30.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.6b

localize58.0ms

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))

rewrite87.0ms

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:

21.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
39.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
11.0ms	(sin (- lambda1 lambda2))
16.0ms	(cos (- lambda1 lambda2))

series322.0ms

Counts

4 → 12

Calls

4 calls:

100.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
159.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
34.0ms	(sin (- lambda1 lambda2))
29.0ms	(cos (- lambda1 lambda2))

simplify1.0s

Counts

76 → 76

Iterations

Iter	Nodes
done	5000
2	1309
1	276
0	120

prune712.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 7.0b

localize71.0ms

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))

rewrite80.0ms

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:

19.0ms	(* (cos phi1) (sin phi2))
10.0ms	(* (cos lambda1) (sin lambda2))
33.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
16.0ms	(cos (- lambda1 lambda2))

series331.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(* (cos phi1) (sin phi2))
82.0ms	(* (cos lambda1) (sin lambda2))
151.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
33.0ms	(cos (- lambda1 lambda2))

simplify1.3s

Counts

83 → 83

Iterations

Iter	Nodes
done	5001
2	1698
1	356
0	150

prune852.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

localize99.0ms

Local error

Found 4 expressions with local error:

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

rewrite129.0ms

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:

10.0ms	(* (cos lambda1) (sin lambda2))
14.0ms	(* (sin lambda1) (sin lambda2))
55.0ms	(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
49.0ms	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))

series485.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(* (cos lambda1) (sin lambda2))
75.0ms	(* (sin lambda1) (sin lambda2))
137.0ms	(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
199.0ms	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))

simplify1.5s

Counts

103 → 103

Iterations

Iter	Nodes
done	5000
2	2047
1	412
0	157

prune1.0s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.0b

localize111.0ms

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))

rewrite19.0ms

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:

11.0ms	(* (cbrt (sin lambda1)) (cbrt (sin lambda1)))
1.0ms	(cbrt (sin lambda1))
3.0ms	(cbrt (sin lambda1))
3.0ms	(cbrt (sin lambda1))

series519.0ms

Counts

4 → 12

Calls

4 calls:

128.0ms	(* (cbrt (sin lambda1)) (cbrt (sin lambda1)))
109.0ms	(cbrt (sin lambda1))
123.0ms	(cbrt (sin lambda1))
158.0ms	(cbrt (sin lambda1))

simplify1.6s

Counts

89 → 89

Iterations

Iter	Nodes
done	5000
2	743
1	179
0	77

prune841.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 0.0b

regimes1.1s

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

sample23.1s

Algorithm

intervals

Results

17.5s	4601×	body	1280	valid
3.9s	1955×	body	640	valid
770.0ms	546×	body	320	valid
284.0ms	675×	body	80	valid
190.0ms	223×	body	160	valid