Details

sample1.7s

Algorithm

intervals

Results

1.3s	147×	body	1280	valid
245.0ms	71×	body	640	valid
27.0ms	26×	body	320	valid
6.0ms	9×	body	160	valid
1.0ms	3×	body	80	valid

simplify50.0ms

Counts

1 → 1

Iterations

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

prune52.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.5b

localize95.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin phi1) (sin phi2))
0.3b	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
1.3b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
2.2b	(cos (- lambda1 lambda2))

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
8×	`pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
6×	`associate-r` `associate-l`
4×	`insert-posit16` `add-log-exp`
2×	`cos-sum` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`acos-asin` `cos-diff` `sub-neg` `sin-mult`

Counts

4 → 59

Calls

4 calls:

25.0ms	(* (sin phi1) (sin phi2))
13.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
4.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
26.0ms	(cos (- lambda1 lambda2))

series202.0ms

Counts

4 → 12

Calls

4 calls:

75.0ms	(* (sin phi1) (sin phi2))
74.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
10.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
42.0ms	(cos (- lambda1 lambda2))

simplify2.8s

Counts

71 → 71

Iterations

Iter	Nodes
done	5008
4	2710
3	1060
2	432
1	211
0	115

prune724.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 3.7b

localize112.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin lambda1) (sin lambda2))
0.2b	(* (sin phi1) (sin phi2))
0.3b	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
1.3b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
10×	`pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
9×	`associate-r` `associate-l`
4×	`insert-posit16` `add-log-exp`
3×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
2×	`sin-mult`
1×	`acos-asin`

Counts

4 → 68

Calls

4 calls:

24.0ms	(* (sin lambda1) (sin lambda2))
25.0ms	(* (sin phi1) (sin phi2))
14.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
4.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

series279.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(* (sin lambda1) (sin lambda2))
75.0ms	(* (sin phi1) (sin phi2))
102.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
32.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

simplify2.8s

Counts

80 → 80

Iterations

Iter	Nodes
done	5000
4	2975
3	1449
2	628
1	281
0	138

prune1.1s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 3.6b

localize67.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin phi1) (sin phi2))
0.3b	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2)))))))) R)
1.3b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2))))))))
3.1b	(log (exp (* (sin lambda1) (sin lambda2))))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt`
9×	`pow1` `*-un-lft-identity` `add-cube-cbrt`
8×	`add-cbrt-cube` `add-exp-log`
6×	`associate-r` `associate-l`
5×	`add-log-exp`
4×	`insert-posit16`
3×	`log-prod` `log-pow`
2×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`acos-asin` `exp-prod` `exp-to-pow` `rem-log-exp` `sin-mult`

Counts

4 → 63

Calls

4 calls:

18.0ms	(* (sin phi1) (sin phi2))
7.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2)))))))) R)
2.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2))))))))
5.0ms	(log (exp (* (sin lambda1) (sin lambda2))))

series207.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(* (sin phi1) (sin phi2))
64.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2)))))))) R)
15.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2))))))))
50.0ms	(log (exp (* (sin lambda1) (sin lambda2))))

simplify3.6s

Counts

75 → 75

Iterations

Iter	Nodes
done	5001
5	4205
4	2144
3	1105
2	535
1	237
0	125

prune1.1s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 3.6b

localize97.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (log (exp (acos (+ (* (sin phi2) (sin phi1)) (* (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda2) (sin lambda1))) (* (cos phi2) (cos phi1))))))) R)
0.4b	(exp (acos (+ (* (sin phi2) (sin phi1)) (* (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda2) (sin lambda1))) (* (cos phi2) (cos phi1))))))
1.0b	(log (exp (acos (+ (* (sin phi2) (sin phi1)) (* (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda2) (sin lambda1))) (* (cos phi2) (cos phi1)))))))
1.3b	(acos (+ (* (sin phi2) (sin phi1)) (* (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda2) (sin lambda1))) (* (cos phi2) (cos phi1)))))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
10×	`*-un-lft-identity` `add-cube-cbrt`
9×	`exp-prod`
8×	`pow1` `log-pow`
7×	`associate-l`
6×	`add-cbrt-cube` `add-exp-log`
5×	`add-log-exp`
4×	`insert-posit16`
3×	`acos-asin` `log-prod` `associate-r`
2×	`exp-diff`
1×	`log-div` `rem-log-exp` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr` `rem-exp-log`

Counts

4 → 62

Calls

4 calls:

18.0ms	(* (log (exp (acos (+ (* (sin phi2) (sin phi1)) (* (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda2) (sin lambda1))) (* (cos phi2) (cos phi1))))))) R)
3.0ms	(exp (acos (+ (* (sin phi2) (sin phi1)) (* (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda2) (sin lambda1))) (* (cos phi2) (cos phi1))))))
6.0ms	(log (exp (acos (+ (* (sin phi2) (sin phi1)) (* (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda2) (sin lambda1))) (* (cos phi2) (cos phi1)))))))
2.0ms	(acos (+ (* (sin phi2) (sin phi1)) (* (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda2) (sin lambda1))) (* (cos phi2) (cos phi1)))))

series211.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(* (log (exp (acos (+ (* (sin phi2) (sin phi1)) (* (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda2) (sin lambda1))) (* (cos phi2) (cos phi1))))))) R)
61.0ms	(exp (acos (+ (* (sin phi2) (sin phi1)) (* (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda2) (sin lambda1))) (* (cos phi2) (cos phi1))))))
31.0ms	(log (exp (acos (+ (* (sin phi2) (sin phi1)) (* (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda2) (sin lambda1))) (* (cos phi2) (cos phi1)))))))
28.0ms	(acos (+ (* (sin phi2) (sin phi1)) (* (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda2) (sin lambda1))) (* (cos phi2) (cos phi1)))))

simplify5.3s

Counts

74 → 74

Iterations

Iter	Nodes
done	5000
6	4748
5	1532
4	942
3	649
2	349
1	186
0	108

prune736.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 3.5b

regimes1.7s

Accuracy

0% (0.4b remaining)

Error of 3.9b against oracle of 3.4b and baseline of 3.9b

bsearch0.0ms

simplify6.0ms

Iterations

Iter	Nodes
done	32
1	32
0	24

end0.0ms

sample17.3s

Algorithm

intervals

Results

11.8s	4691×	body	1280	valid
4.3s	2154×	body	640	valid
600.0ms	756×	body	320	valid
137.0ms	265×	body	160	valid
92.0ms	20×	body	2560	valid
74.0ms	117×	body	80	valid