Details

sample675.0ms

Algorithm

intervals

Results

481.0ms	140×	body	1280	valid
139.0ms	71×	body	640	valid
19.0ms	17×	body	320	valid
10.0ms	23×	body	80	valid
3.0ms	5×	body	160	valid

simplify70.0ms

Counts

1 → 1

Iterations

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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.8b

localize83.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos phi1) (sin phi2))
0.3b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
2.4b	(cos (- lambda1 lambda2))
2.6b	(sin (- lambda1 lambda2))

rewrite160.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-sqr-sqrt`
18×	`associate-l`
11×	`pow1` `add-cbrt-cube` `add-exp-log`
10×	`*-un-lft-identity` `add-cube-cbrt`
9×	`associate-r`
5×	`unswap-sqr`
4×	`pow-prod-down` `prod-exp` `cbrt-unprod` `insert-posit16` `add-log-exp`
3×	`cos-diff` `*-commutative`
2×	`cos-sum` `sub-neg` `sin-sum`
1×	`distribute-rgt-in` `distribute-lft-in` `associate-*l/` `sin-diff` `sin-cos-mult`

Counts

4 → 76

Calls

4 calls:

14.0ms	(* (cos phi1) (sin phi2))
90.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
30.0ms	(cos (- lambda1 lambda2))
23.0ms	(sin (- lambda1 lambda2))

series264.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(* (cos phi1) (sin phi2))
151.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
24.0ms	(cos (- lambda1 lambda2))
24.0ms	(sin (- lambda1 lambda2))

simplify2.8s

Counts

88 → 88

Iterations

Iter	Nodes
done	5001
3	3370
2	902
1	338
0	151

prune801.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 5.2b

localize72.0ms

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)))
2.4b	(cos (- lambda1 lambda2))

rewrite124.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
21×	`associate-l`
13×	`pow1` `add-cbrt-cube` `add-exp-log`
12×	`-un-lft-identity` `associate-r*` `add-cube-cbrt`
6×	`unswap-sqr`
5×	`pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`*-commutative` `insert-posit16` `add-log-exp`
3×	`cos-diff`
2×	`cos-sum`
1×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `associate-*l/` `sin-cos-mult`

Counts

4 → 84

Calls

4 calls:

12.0ms	(* (cos phi1) (sin phi2))
18.0ms	(* (cos lambda1) (sin lambda2))
72.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
20.0ms	(cos (- lambda1 lambda2))

series287.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(* (cos phi1) (sin phi2))
61.0ms	(* (cos lambda1) (sin lambda2))
151.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
24.0ms	(cos (- lambda1 lambda2))

simplify2.8s

Counts

96 → 96

Iterations

Iter	Nodes
done	5001
3	3714
2	1064
1	392
0	169

prune999.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

localize130.0ms

Local error

Found 4 expressions with local error:

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

rewrite369.0ms

Algorithm

rewrite-expression-head

Rules

28×	`associate-l`
27×	`add-sqr-sqrt`
22×	`*-un-lft-identity`
19×	`associate-r`
15×	`pow1` `add-cbrt-cube` `add-exp-log`
14×	`add-cube-cbrt`
7×	`unswap-sqr`
6×	`pow-prod-down` `prod-exp` `cbrt-unprod`
5×	`*-commutative`
4×	`insert-posit16` `sin-cos-mult` `distribute-lft-out` `add-log-exp`
3×	`frac-times` `associate-*r/` `sin-mult`
2×	`distribute-rgt-in` `+-commutative` `distribute-lft-in` `flip3-+` `frac-add` `cos-mult` `flip-+`
1×	`associate-*l/`

Counts

4 → 105

Calls

4 calls:

26.0ms	(* (cos phi1) (sin phi2))
25.0ms	(* (cos lambda1) (sin lambda2))
17.0ms	(* (sin lambda1) (sin lambda2))
296.0ms	(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))

series446.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(* (cos phi1) (sin phi2))
67.0ms	(* (cos lambda1) (sin lambda2))
64.0ms	(* (sin lambda1) (sin lambda2))
250.0ms	(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))

simplify2.5s

Counts

117 → 117

Iterations

Iter	Nodes
done	5000
2	2328
1	630
0	212

prune1.2s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize93.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* (sin phi1) (* (cbrt (cos phi2)) (cbrt (cos phi2)))) (* (cbrt (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))
0.3b	(cbrt (cos phi2))
0.3b	(cbrt (cos phi2))
0.3b	(cbrt (cos phi2))

rewrite1.1s

Algorithm

rewrite-expression-head

Rules

175×	`add-sqr-sqrt`
108×	`unswap-sqr`
63×	`cbrt-prod` `associate-l`
61×	`add-cbrt-cube`
60×	`associate-r`
57×	`cbrt-unprod`
30×	`*-un-lft-identity`
25×	`pow1` `add-exp-log`
22×	`add-cube-cbrt`
15×	`pow-prod-down` `prod-exp`
14×	`swap-sqr`
8×	`distribute-rgt-in` `distribute-lft-in` `*-commutative`
6×	`associate-*r/`
4×	`+-commutative` `insert-posit16` `distribute-lft-out` `add-log-exp`
3×	`pow1/3`
1×	`flip3-+` `frac-add` `cos-mult` `flip-+` `sin-mult`

Counts

4 → 180

Calls

4 calls:

1.1s	(* (* (sin phi1) (* (cbrt (cos phi2)) (cbrt (cos phi2)))) (* (cbrt (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))
1.0ms	(cbrt (cos phi2))
1.0ms	(cbrt (cos phi2))
1.0ms	(cbrt (cos phi2))

series706.0ms

Counts

4 → 12

Calls

4 calls:

284.0ms	(* (* (sin phi1) (* (cbrt (cos phi2)) (cbrt (cos phi2)))) (* (cbrt (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))
132.0ms	(cbrt (cos phi2))
143.0ms	(cbrt (cos phi2))
146.0ms	(cbrt (cos phi2))

simplify3.6s

Counts

192 → 192

Iterations

Iter	Nodes
done	5002
2	4461
1	891
0	238

prune1.7s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.0b

regimes954.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify10.0ms

Iterations

Iter	Nodes
done	37
1	37
0	27

end0.0ms

sample25.8s

Algorithm

intervals

Results

18.7s	4534×	body	1280	valid
5.1s	1950×	body	640	valid
997.0ms	618×	body	320	valid
330.0ms	682×	body	80	valid
256.0ms	216×	body	160	valid