Details

sample844.0ms

Algorithm

intervals

Results

491.0ms	156×	body	1280	valid
185.0ms	63×	body	640	valid
26.0ms	25×	body	320	valid
5.0ms	7×	body	160	valid
2.0ms	5×	body	80	valid

simplify56.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	34
3	34
2	33
1	26
0	17

prune50.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.8b

localize100.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin phi1) (sin phi2))
0.2b	(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
0.3b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
3.9b	(cos (- lambda1 lambda2))

rewrite133.0ms

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

Counts

4 → 58

Calls

4 calls:

25.0ms	(* (sin phi1) (sin phi2))
73.0ms	(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
4.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
26.0ms	(cos (- lambda1 lambda2))

series382.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(* (sin phi1) (sin phi2))
218.0ms	(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
24.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
45.0ms	(cos (- lambda1 lambda2))

simplify5.0s

Counts

70 → 70

Iterations

Iter	Nodes
done	5000
3	2897
2	757
1	281
0	125

prune1.0s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 2.6b

localize151.0ms

Local error

Found 4 expressions with local error:

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

rewrite214.0ms

Algorithm

rewrite-expression-head

Rules

30×	`pow1` `add-exp-log` `add-cbrt-cube`
17×	`pow-prod-down` `prod-exp` `cbrt-unprod`
8×	`add-sqr-sqrt`
6×	`add-cube-cbrt` `*-un-lft-identity` `cos-mult`
5×	`associate-r` `associate-l`
4×	`add-log-exp`
3×	`*-commutative`
2×	`frac-times` `associate-r/` `associate-l/` `sin-mult`
1×	`acos-asin` `unswap-sqr`

Counts

4 → 76

Calls

4 calls:

14.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2))) (* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2)))))) R)
89.0ms	(* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2)))
101.0ms	(* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2)))
4.0ms	(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2))) (* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2))))))

series639.0ms

Counts

4 → 12

Calls

4 calls:

146.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2))) (* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2)))))) R)
248.0ms	(* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2)))
203.0ms	(* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2)))
42.0ms	(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2))) (* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2))))))

simplify3.3s

Counts

88 → 88

Iterations

Iter	Nodes
done	5001
2	1540
1	428
0	167

prune1.4s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 2.4b

localize162.0ms

Local error

Found 4 expressions with local error:

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

rewrite134.0ms

Algorithm

rewrite-expression-head

Rules

20×	`pow1` `add-exp-log` `add-cbrt-cube`
12×	`add-sqr-sqrt`
10×	`pow-prod-down` `prod-exp` `cbrt-unprod`
8×	`add-cube-cbrt` `*-un-lft-identity`
7×	`associate-r` `associate-l`
4×	`add-log-exp`
3×	`*-commutative` `sin-mult`
2×	`cos-mult` `unswap-sqr`
1×	`acos-asin` `frac-times` `associate-r/` `associate-l/`

Counts

4 → 70

Calls

4 calls:

23.0ms	(* (sin phi1) (sin phi2))
13.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (+ (* (cos lambda1) (* (cos lambda2) (* (cos phi1) (cos phi2)))) (* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2)))))) R)
90.0ms	(* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2)))
4.0ms	(acos (+ (* (sin phi1) (sin phi2)) (+ (* (cos lambda1) (* (cos lambda2) (* (cos phi1) (cos phi2)))) (* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2))))))

series563.0ms

Counts

4 → 12

Calls

4 calls:

168.0ms	(* (sin phi1) (sin phi2))
151.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (+ (* (cos lambda1) (* (cos lambda2) (* (cos phi1) (cos phi2)))) (* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2)))))) R)
204.0ms	(* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2)))
37.0ms	(acos (+ (* (sin phi1) (sin phi2)) (+ (* (cos lambda1) (* (cos lambda2) (* (cos phi1) (cos phi2)))) (* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2))))))

simplify6.2s

Counts

82 → 82

Iterations

Iter	Nodes
done	5001
3	3834
2	1084
1	356
0	156

prune1.4s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 2.4b

localize166.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (acos (+ (* (sin phi1) (sin phi2)) (+ (* (cos lambda1) (* (cos lambda2) (* (cos phi1) (cos phi2)))) (log (exp (* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2)))))))) R)
0.3b	(* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2)))
0.3b	(acos (+ (* (sin phi1) (sin phi2)) (+ (* (cos lambda1) (* (cos lambda2) (* (cos phi1) (cos phi2)))) (log (exp (* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2))))))))
3.3b	(log (exp (* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2)))))

rewrite131.0ms

Algorithm

rewrite-expression-head

Rules

19×	`pow1`
18×	`add-exp-log` `add-cbrt-cube`
9×	`add-sqr-sqrt` `pow-prod-down` `prod-exp` `cbrt-unprod`
7×	`add-cube-cbrt` `*-un-lft-identity`
5×	`add-log-exp`
4×	`associate-r` `associate-l`
3×	`log-prod` `log-pow`
2×	`cos-mult` `*-commutative` `sin-mult`
1×	`acos-asin` `frac-times` `exp-prod` `exp-to-pow` `associate-r/` `rem-log-exp` `associate-l/` `unswap-sqr`

Counts

4 → 65

Calls

4 calls:

14.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (+ (* (cos lambda1) (* (cos lambda2) (* (cos phi1) (cos phi2)))) (log (exp (* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2)))))))) R)
94.0ms	(* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2)))
4.0ms	(acos (+ (* (sin phi1) (sin phi2)) (+ (* (cos lambda1) (* (cos lambda2) (* (cos phi1) (cos phi2)))) (log (exp (* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2))))))))
15.0ms	(log (exp (* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2)))))

series609.0ms

Counts

4 → 12

Calls

4 calls:

155.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (+ (* (cos lambda1) (* (cos lambda2) (* (cos phi1) (cos phi2)))) (log (exp (* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2)))))))) R)
207.0ms	(* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2)))
44.0ms	(acos (+ (* (sin phi1) (sin phi2)) (+ (* (cos lambda1) (* (cos lambda2) (* (cos phi1) (cos phi2)))) (log (exp (* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2))))))))
203.0ms	(log (exp (* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2)))))

simplify6.2s

Counts

77 → 77

Iterations

Iter	Nodes
done	5001
3	4067
2	986
1	318
0	145

prune1.3s

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 2.4b

regimes2.1s

Accuracy

0% (0.3b remaining)

Error of 4.0b against oracle of 3.7b and baseline of 4.0b

bsearch0.0ms

simplify23.0ms

Iterations

Iter	Nodes
done	34
1	34
0	25

end4.0ms

sample26.4s

Algorithm

intervals

Results

19.6s	4768×	body	1280	valid
4.7s	2067×	body	640	valid
903.0ms	735×	body	320	valid
260.0ms	285×	body	160	valid
59.0ms	8×	body	2560	valid
48.0ms	138×	body	80	valid