Details

sample854.0ms

Algorithm

intervals

Results

633.0ms	153×	body	1280	valid
142.0ms	69×	body	640	valid
20.0ms	17×	body	320	valid
5.0ms	7×	body	160	valid
3.0ms	10×	body	80	valid

simplify182.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	74
4	74
3	69
2	45
1	27
0	17

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.9b

localize124.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin (- lambda1 lambda2)) (cos phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
3.4b	(cos (- lambda1 lambda2))
3.6b	(sin (- lambda1 lambda2))

rewrite197.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 60

Calls

4 calls:

57.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
82.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
21.0ms	(cos (- lambda1 lambda2))
31.0ms	(sin (- lambda1 lambda2))

series388.0ms

Counts

4 → 12

Calls

4 calls:

119.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
186.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
33.0ms	(cos (- lambda1 lambda2))
50.0ms	(sin (- lambda1 lambda2))

simplify4.7s

Counts

72 → 72

Iterations

Iter	Nodes
done	5003
3	3013
2	794
1	272
0	116

prune1.1s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 8.1b

localize156.0ms

Local error

Found 4 expressions with local error:

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

rewrite233.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 69

Calls

4 calls:

26.0ms	(* (cos lambda1) (sin lambda2))
114.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
69.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
21.0ms	(cos (- lambda1 lambda2))

series587.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(* (cos lambda1) (sin lambda2))
271.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
188.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
35.0ms	(cos (- lambda1 lambda2))

simplify6.0s

Counts

81 → 81

Iterations

Iter	Nodes
done	5006
3	4915
2	1171
1	359
0	143

prune1.4s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize144.0ms

Local error

Found 4 expressions with local error:

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

rewrite304.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 84

Calls

4 calls:

23.0ms	(* (cos lambda1) (sin lambda2))
25.0ms	(* (sin lambda1) (sin lambda2))
123.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
127.0ms	(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))

series775.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(* (cos lambda1) (sin lambda2))
80.0ms	(* (sin lambda1) (sin lambda2))
246.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
355.0ms	(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))

simplify4.2s

Counts

96 → 96

Iterations

Iter	Nodes
done	5000
2	2102
1	530
0	183

prune1.8s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize208.0ms

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 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))))
0.4b	(* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2)))

rewrite1.3s

Algorithm

rewrite-expression-head

Rules

87×	`pow1`
78×	`cos-mult` `sin-mult`
74×	`associate-*r/`
66×	`frac-times`
44×	`associate-*l/`
42×	`add-exp-log` `add-cbrt-cube`
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` `add-cube-cbrt` `*-un-lft-identity`
6×	`associate-r`
5×	`flip3--` `flip--`
4×	`pow-plus` `associate-/r/` `add-log-exp`
3×	`cbrt-undiv` `times-frac` `div-exp` `associate-l` `associate-/r` `-commutative`
2×	`pow2` `distribute-rgt-in` `sub-neg` `distribute-lft-in` `swap-sqr`
1×	`frac-2neg` `clear-num` `div-inv` `associate-/l*` `difference-of-squares`

Counts

4 → 190

Calls

4 calls:

598.0ms	(* (* (sin phi1) (cos phi2)) (- (* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2))) (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2)))))
93.0ms	(* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2)))
524.0ms	(/ (* (* (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))))
91.0ms	(* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2)))

series1.7s

Counts

4 → 12

Calls

4 calls:

486.0ms	(* (* (sin phi1) (cos phi2)) (- (* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2))) (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2)))))
105.0ms	(* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2)))
1.0s	(/ (* (* (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))))
107.0ms	(* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2)))

simplify5.2s

Counts

202 → 202

Iterations

Iter	Nodes
done	5001
2	4369
1	958
0	300

prune3.4s

Pruning

11 alts after pruning (10 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

simplify13.0ms

Iterations

Iter	Nodes
done	36
1	36
0	28

end0.0ms

sample28.3s

Algorithm

intervals

Results

21.3s	4600×	body	1280	valid
4.4s	1990×	body	640	valid
1.2s	544×	body	320	valid
444.0ms	659×	body	80	valid
147.0ms	207×	body	160	valid