Details

sample702.0ms

Algorithm

intervals

Results

335.0ms	148×	body	1280	valid
121.0ms	65×	body	640	valid
21.0ms	29×	body	320	valid
4.0ms	7×	body	160	valid
2.0ms	7×	body	80	valid

simplify59.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	46
4	46
3	44
2	38
1	27
0	17

prune40.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 18.3b

localize75.0ms

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)
0.5b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
4.2b	(cos (- lambda1 lambda2))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
14×	`*-un-lft-identity` `add-cube-cbrt`
11×	`cos-sum`
9×	`prod-diff`
8×	`pow1` `add-cbrt-cube` `add-exp-log`
6×	`associate-r` `associate-l`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`acos-asin` `cos-diff` `sub-neg` `sin-mult`

Counts

4 → 72

Calls

4 calls:

14.0ms	(* (sin phi1) (sin phi2))
5.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
1.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
13.0ms	(cos (- lambda1 lambda2))

series223.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(* (sin phi1) (sin phi2))
89.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
23.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
54.0ms	(cos (- lambda1 lambda2))

simplify655.0ms

Counts

84 → 84

Iterations

Iter	Nodes
done	5000
2	932
1	335
0	187

prune894.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 2.9b

localize117.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin lambda1) (- (sin lambda2)))
0.2b	(* (sin phi1) (sin phi2))
0.2b	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (- (sin lambda2))))))) R)
0.5b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (- (sin lambda2)))))))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
16×	`associate-r`
12×	`*-un-lft-identity` `add-cube-cbrt`
10×	`pow1` `add-cbrt-cube` `add-exp-log`
9×	`associate-l`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`distribute-lft-neg-in` `distribute-rgt-neg-in` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`acos-asin` `neg-mul-1` `distribute-rgt-neg-out` `sin-mult`

Counts

4 → 79

Calls

4 calls:

17.0ms	(* (sin lambda1) (- (sin lambda2)))
9.0ms	(* (sin phi1) (sin phi2))
5.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (- (sin lambda2))))))) R)
2.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (- (sin lambda2)))))))

series288.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(* (sin lambda1) (- (sin lambda2)))
55.0ms	(* (sin phi1) (sin phi2))
126.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (- (sin lambda2))))))) R)
40.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (- (sin lambda2)))))))

simplify885.0ms

Counts

91 → 91

Iterations

Iter	Nodes
done	5000
2	1365
1	339
0	155

prune1.3s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 2.8b

localize100.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (cbrt (- (pow (* (sin lambda1) (sin lambda2)) 3))))))) R)
0.3b	(pow (* (sin lambda1) (sin lambda2)) 3)
0.5b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (cbrt (- (pow (* (sin lambda1) (sin lambda2)) 3)))))))
26.9b	(cbrt (- (pow (* (sin lambda1) (sin lambda2)) 3)))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

20×	`cbrt-prod`
12×	`add-sqr-sqrt`
10×	`*-un-lft-identity` `add-cube-cbrt`
9×	`pow1` `add-cbrt-cube` `add-exp-log`
8×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`cube-mult` `pow-unpow` `unpow-prod-down` `unpow3` `cube-prod` `associate-r` `associate-l` `sqr-pow`
2×	`cube-div` `pow-pow` `pow-prod-down` `pow-exp` `prod-exp` `cbrt-unprod` `sin-mult` `rem-cube-cbrt`
1×	`acos-asin` `pow-to-exp` `cbrt-div` `neg-mul-1` `pow1/3` `*-commutative` `distribute-neg-frac` `unswap-sqr`

Counts

4 → 86

Calls

4 calls:

6.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (cbrt (- (pow (* (sin lambda1) (sin lambda2)) 3))))))) R)
7.0ms	(pow (* (sin lambda1) (sin lambda2)) 3)
1.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (cbrt (- (pow (* (sin lambda1) (sin lambda2)) 3)))))))
5.0ms	(cbrt (- (pow (* (sin lambda1) (sin lambda2)) 3)))

series490.0ms

Counts

4 → 12

Calls

4 calls:

186.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (cbrt (- (pow (* (sin lambda1) (sin lambda2)) 3))))))) R)
113.0ms	(pow (* (sin lambda1) (sin lambda2)) 3)
52.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (cbrt (- (pow (* (sin lambda1) (sin lambda2)) 3)))))))
139.0ms	(cbrt (- (pow (* (sin lambda1) (sin lambda2)) 3)))

simplify848.0ms

Counts

98 → 98

Iterations

Iter	Nodes
done	5001
2	1578
1	399
0	176

prune1.5s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 2.8b

localize134.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos phi2) (* (cos lambda1) (cos lambda2)))
0.2b	(* (acos (fma (sin phi2) (sin phi1) (* (cos phi1) (- (* (cos phi2) (* (cos lambda1) (cos lambda2))) (* (cbrt -1) (* (sin lambda2) (* (sin lambda1) (cos phi2)))))))) R)
0.3b	(* (sin lambda2) (* (sin lambda1) (cos phi2)))
0.5b	(acos (fma (sin phi2) (sin phi1) (* (cos phi1) (- (* (cos phi2) (* (cos lambda1) (cos lambda2))) (* (cbrt -1) (* (sin lambda2) (* (sin lambda1) (cos phi2))))))))

rewrite83.0ms

Algorithm

rewrite-expression-head

Rules

16×	`pow1` `add-cbrt-cube` `add-exp-log`
10×	`add-sqr-sqrt`
9×	`associate-l`
8×	`*-un-lft-identity` `add-cube-cbrt`
7×	`pow-prod-down` `prod-exp` `cbrt-unprod`
5×	`associate-r`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`*-commutative`
2×	`associate-*r/`
1×	`acos-asin` `cos-mult` `sin-cos-mult` `unswap-sqr`

Counts

4 → 72

Calls

4 calls:

28.0ms	(* (cos phi2) (* (cos lambda1) (cos lambda2)))
11.0ms	(* (acos (fma (sin phi2) (sin phi1) (* (cos phi1) (- (* (cos phi2) (* (cos lambda1) (cos lambda2))) (* (cbrt -1) (* (sin lambda2) (* (sin lambda1) (cos phi2)))))))) R)
41.0ms	(* (sin lambda2) (* (sin lambda1) (cos phi2)))
1.0ms	(acos (fma (sin phi2) (sin phi1) (* (cos phi1) (- (* (cos phi2) (* (cos lambda1) (cos lambda2))) (* (cbrt -1) (* (sin lambda2) (* (sin lambda1) (cos phi2))))))))

series415.0ms

Counts

4 → 12

Calls

4 calls:

126.0ms	(* (cos phi2) (* (cos lambda1) (cos lambda2)))
152.0ms	(* (acos (fma (sin phi2) (sin phi1) (* (cos phi1) (- (* (cos phi2) (* (cos lambda1) (cos lambda2))) (* (cbrt -1) (* (sin lambda2) (* (sin lambda1) (cos phi2)))))))) R)
104.0ms	(* (sin lambda2) (* (sin lambda1) (cos phi2)))
33.0ms	(acos (fma (sin phi2) (sin phi1) (* (cos phi1) (- (* (cos phi2) (* (cos lambda1) (cos lambda2))) (* (cbrt -1) (* (sin lambda2) (* (sin lambda1) (cos phi2))))))))

simplify1.1s

Counts

84 → 84

Iterations

Iter	Nodes
done	5000
2	1326
1	365
0	162

prune912.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 2.8b

regimes1.6s

Accuracy

0% (0.4b remaining)

Error of 3.9b against oracle of 3.5b and baseline of 3.9b

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
done	35
1	35
0	28

end0.0ms

sample19.3s

Algorithm

intervals

Results

14.3s	4762×	body	1280	valid
3.3s	2104×	body	640	valid
532.0ms	672×	body	320	valid
266.0ms	302×	body	160	valid
68.0ms	14×	body	2560	valid
39.0ms	147×	body	80	valid