Details

sample462.0ms

Algorithm

intervals

Results

328.0ms	141×	body	1280	valid
80.0ms	68×	body	640	valid
11.0ms	16×	body	320	valid
5.0ms	26×	body	80	valid
2.0ms	5×	body	160	valid

simplify130.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	95
4	95
3	78
2	47
1	28
0	17

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.4b

localize84.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin (- lambda1 lambda2)) (cos phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
3.6b	(sin (- lambda1 lambda2))
3.8b	(cos (- lambda1 lambda2))

rewrite113.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt`
19×	`*-un-lft-identity` `add-cube-cbrt`
18×	`prod-diff`
11×	`pow1` `cos-sum` `add-cbrt-cube` `sin-sum` `add-exp-log`
6×	`associate-r`
4×	`expm1-log1p-u` `associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
3×	`cos-diff`
2×	`sub-neg` `*-commutative` `sin-cos-mult`
1×	`distribute-rgt-in` `distribute-lft-in` `associate-*l/` `sin-diff` `unswap-sqr`

Counts

4 → 86

Calls

4 calls:

33.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
50.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
13.0ms	(sin (- lambda1 lambda2))
11.0ms	(cos (- lambda1 lambda2))

series285.0ms

Counts

4 → 12

Calls

4 calls:

99.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
136.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
23.0ms	(sin (- lambda1 lambda2))
26.0ms	(cos (- lambda1 lambda2))

simplify1.2s

Counts

98 → 98

Iterations

Iter	Nodes
done	5000
2	1802
1	434
0	210

prune1.2s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 5.7b

localize86.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin phi1) (cos phi2))
0.2b	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
3.8b	(cos (- lambda1 lambda2))

rewrite149.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-sqr-sqrt`
15×	`*-un-lft-identity` `add-cube-cbrt`
13×	`pow1` `add-cbrt-cube` `add-exp-log`
11×	`cos-sum`
9×	`associate-r` `prod-diff`
7×	`associate-l`
5×	`pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`cos-diff` `associate-l/` `-commutative`
2×	`sin-cos-mult` `unswap-sqr`
1×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `flip3--` `flip--`

Counts

4 → 87

Calls

4 calls:

10.0ms	(* (sin phi1) (cos phi2))
67.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
52.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
18.0ms	(cos (- lambda1 lambda2))

series421.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(* (sin phi1) (cos phi2))
199.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
142.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
20.0ms	(cos (- lambda1 lambda2))

simplify1.7s

Counts

99 → 99

Iterations

Iter	Nodes
done	5000
2	2064
1	469
0	209

prune1.3s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize80.0ms

Local error

Found 4 expressions with local error:

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

rewrite129.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt`
15×	`pow1` `add-cbrt-cube` `add-exp-log`
12×	`associate-r`
11×	`*-un-lft-identity` `add-cube-cbrt`
10×	`associate-l`
6×	`pow-prod-down` `prod-exp` `cbrt-unprod`
5×	`sin-cos-mult`
4×	`expm1-log1p-u` `*-commutative` `log1p-expm1-u` `add-log-exp`
3×	`frac-times` `associate-l/` `associate-r/` `sin-mult` `unswap-sqr`
2×	`flip3-+` `frac-add` `cos-mult` `flip-+`
1×	`distribute-rgt-in` `distribute-lft-in` `flip3--` `flip--`

Counts

4 → 93

Calls

4 calls:

9.0ms	(* (sin phi1) (cos phi2))
50.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
9.0ms	(* (sin lambda1) (sin lambda2))
59.0ms	(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))

series719.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(* (sin phi1) (cos phi2))
249.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
83.0ms	(* (sin lambda1) (sin lambda2))
330.0ms	(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))

simplify2.6s

Counts

105 → 105

Iterations

Iter	Nodes
done	5000
2	3450
1	554
0	189

prune1.4s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize138.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (sin phi1) (cos phi2)) (- (* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2))) (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2)))))
0.2b	(/ (* (* (sin phi1) (cos phi2)) (- (* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2))) (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2))))) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
0.3b	(* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2)))
0.4b	(* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2)))

rewrite1.2s

Algorithm

rewrite-expression-head

Rules

87×	`pow1`
78×	`cos-mult` `sin-mult`
74×	`associate-*r/`
66×	`frac-times`
44×	`associate-*l/`
42×	`add-cbrt-cube` `add-exp-log`
37×	`pow-prod-down` `frac-sub`
34×	`sin-cos-mult`
33×	`associate-/l/`
22×	`prod-exp` `cbrt-unprod`
21×	`sub-div`
8×	`pow-sqr` `pow-prod-up`
7×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
6×	`associate-r`
5×	`flip3--` `flip--`
4×	`expm1-log1p-u` `pow-plus` `associate-/r/` `log1p-expm1-u` `add-log-exp`
3×	`distribute-rgt-in` `cbrt-undiv` `associate-/r` `distribute-lft-in` `times-frac` `div-exp` `associate-l` `-commutative`
2×	`pow2` `sub-neg` `swap-sqr` `prod-diff`
1×	`clear-num` `frac-2neg` `div-inv` `associate-/l*` `difference-of-squares`

Counts

4 → 200

Calls

4 calls:

374.0ms	(* (* (sin phi1) (cos phi2)) (- (* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2))) (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2)))))
314.0ms	(/ (* (* (sin phi1) (cos phi2)) (- (* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2))) (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2))))) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
434.0ms	(* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2)))
32.0ms	(* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2)))

series1.3s

Counts

4 → 12

Calls

4 calls:

269.0ms	(* (* (sin phi1) (cos phi2)) (- (* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2))) (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2)))))
852.0ms	(/ (* (* (sin phi1) (cos phi2)) (- (* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2))) (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2))))) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
78.0ms	(* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2)))
82.0ms	(* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2)))

simplify1.4s

Counts

212 → 212

Iterations

Iter	Nodes
done	5001
1	1055
0	322

prune2.3s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

regimes810.0ms

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	36
1	36
0	27

end0.0ms

sample17.7s

Algorithm

intervals

Results

12.6s	4601×	body	1280	valid
3.2s	2007×	body	640	valid
989.0ms	542×	body	320	valid
196.0ms	650×	body	80	valid
136.0ms	200×	body	160	valid