Details

sample420.0ms

Algorithm

intervals

Results

273.0ms	115×	body	1280	valid
75.0ms	61×	body	640	valid
27.0ms	35×	body	320	valid
7.0ms	15×	body	160	valid
7.0ms	30×	body	80	valid

simplify7.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	20
1	20	20
2	21	20
done	21	20

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.1b

localize63.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos phi2) (sin (- lambda1 lambda2)))
0.7b	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
3.7b	(sin (- lambda1 lambda2))
3.7b	(cos (- lambda1 lambda2))

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 55

Calls

4 calls:

35.0ms	(* (cos phi2) (sin (- lambda1 lambda2)))
11.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
9.0ms	(sin (- lambda1 lambda2))
10.0ms	(cos (- lambda1 lambda2))

series306.0ms

Counts

4 → 12

Calls

4 calls:

108.0ms	(* (cos phi2) (sin (- lambda1 lambda2)))
136.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
31.0ms	(sin (- lambda1 lambda2))
30.0ms	(cos (- lambda1 lambda2))

simplify720.0ms

Counts

67 → 67

Iterations

Useful iterations: done (717.0ms)

Iter	Nodes	Cost
0	112	733
1	265	711
2	998	649
done	5000	645

prune605.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.9b

localize51.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin lambda1) (sin (- lambda2)))
0.2b	(* (cos phi2) (sin (- lambda1 lambda2)))
0.6b	(+ (cos phi1) (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))
3.7b	(sin (- lambda1 lambda2))

rewrite84.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
8×	`pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
6×	`sin-sum` `associate-r` `associate-l` `add-log-exp`
5×	`sub-neg`
4×	`distribute-rgt-in` `associate-+r+` `distribute-lft-in`
2×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`+-commutative` `sum-log` `flip3-+` `sin-neg` `sin-diff` `distribute-rgt-neg-out` `flip-+` `sin-mult`

Counts

4 → 67

Calls

4 calls:

31.0ms	(* (sin lambda1) (sin (- lambda2)))
31.0ms	(* (cos phi2) (sin (- lambda1 lambda2)))
8.0ms	(+ (cos phi1) (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))
9.0ms	(sin (- lambda1 lambda2))

series559.0ms

Counts

4 → 12

Calls

4 calls:

97.0ms	(* (sin lambda1) (sin (- lambda2)))
96.0ms	(* (cos phi2) (sin (- lambda1 lambda2)))
335.0ms	(+ (cos phi1) (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))
32.0ms	(sin (- lambda1 lambda2))

simplify790.0ms

Counts

79 → 79

Iterations

Useful iterations: done (786.0ms)

Iter	Nodes	Cost
0	138	1016
1	332	981
2	1375	880
done	5000	861

prune842.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize104.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))
0.2b	(* (* (cos lambda1) (sin (- lambda2))) (cos phi2))
0.2b	(* (sin lambda1) (sin (- lambda2)))
0.6b	(+ (cos phi1) (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))

rewrite189.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 80

Calls

4 calls:

97.0ms	(* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))
48.0ms	(* (* (cos lambda1) (sin (- lambda2))) (cos phi2))
24.0ms	(* (sin lambda1) (sin (- lambda2)))
15.0ms	(+ (cos phi1) (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))

series772.0ms

Counts

4 → 12

Calls

4 calls:

199.0ms	(* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))
97.0ms	(* (* (cos lambda1) (sin (- lambda2))) (cos phi2))
88.0ms	(* (sin lambda1) (sin (- lambda2)))
387.0ms	(+ (cos phi1) (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))

simplify1.4s

Counts

92 → 92

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	176	1492
1	469	1409
2	2346	1222
done	5001	1202

prune1.4s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize101.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin lambda1) (sin lambda2))
0.6b	(cbrt (pow (+ (* (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (cos phi2)) (cos phi1)) 3))
0.6b	(+ (* (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (cos phi2)) (cos phi1))
0.6b	(pow (+ (* (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (cos phi2)) (cos phi1)) 3)

rewrite145.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
12×	`cbrt-prod` `*-un-lft-identity` `add-cube-cbrt`
7×	`pow1` `add-cbrt-cube` `add-exp-log`
6×	`unpow-prod-down` `cube-prod` `add-log-exp`
4×	`cube-div`
3×	`pow-unpow` `flip3-+` `associate-r` `associate-l` `flip-+`
2×	`cube-mult` `cbrt-div` `unpow3` `sqr-pow`
1×	`pow-to-exp` `+-commutative` `sum-log` `pow-pow` `pow1/3` `pow-prod-down` `pow-exp` `prod-exp` `*-commutative` `rem-cbrt-cube` `cbrt-unprod` `sin-mult` `rem-cube-cbrt` `unswap-sqr`

Counts

4 → 78

Calls

4 calls:

10.0ms	(* (sin lambda1) (sin lambda2))
37.0ms	(cbrt (pow (+ (* (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (cos phi2)) (cos phi1)) 3))
42.0ms	(+ (* (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (cos phi2)) (cos phi1))
54.0ms	(pow (+ (* (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (cos phi2)) (cos phi1)) 3)

series1.2s

Counts

4 → 12

Calls

4 calls:

67.0ms	(* (sin lambda1) (sin lambda2))
345.0ms	(cbrt (pow (+ (* (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (cos phi2)) (cos phi1)) 3))
296.0ms	(+ (* (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (cos phi2)) (cos phi1))
475.0ms	(pow (+ (* (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (cos phi2)) (cos phi1)) 3)

simplify1.8s

Counts

90 → 90

Iterations

Useful iterations: 2 (322.0ms)

Iter	Nodes	Cost
0	137	2320
1	398	2067
2	2208	1837
done	5002	1837

prune826.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

regimes975.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify7.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	27	75
1	39	75
done	39	75

end0.0ms

sample13.1s

Algorithm

intervals

Results

7.1s	3510×	body	1280	valid
3.8s	2346×	body	640	valid
717.0ms	959×	body	320	valid
697.0ms	475×	body	160	valid
241.0ms	710×	body	80	valid