Details

sample374.0ms

Algorithm

intervals

Results

221.0ms	108×	body	1280	valid
79.0ms	79×	body	640	valid
30.0ms	41×	body	320	valid
5.0ms	10×	body	160	valid
4.0ms	18×	body	80	valid

simplify9.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.8b

localize77.0ms

Local error

Found 4 expressions with local error:

0.2b	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
0.5b	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
5.5b	(sin (- lambda1 lambda2))
6.0b	(cos (- lambda1 lambda2))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 40

Calls

4 calls:

0.0ms	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
10.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
11.0ms	(sin (- lambda1 lambda2))
19.0ms	(cos (- lambda1 lambda2))

series299.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
192.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
53.0ms	(sin (- lambda1 lambda2))
32.0ms	(cos (- lambda1 lambda2))

simplify3.4s

Counts

52 → 52

Iterations

Useful iterations: 2 (409.0ms)

Iter	Nodes	Cost
0	97	702
1	309	687
2	1583	613
done	5000	613

prune348.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.6b

localize73.0ms

Local error

Found 4 expressions with local error:

0.2b	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (+ (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2)))) (* (* (sin lambda1) (sin lambda2)) (cos phi2))))
0.2b	(* (sin lambda1) (sin lambda2))
0.4b	(+ (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2))))
5.5b	(sin (- lambda1 lambda2))

rewrite80.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 47

Calls

4 calls:

0.0ms	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (+ (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2)))) (* (* (sin lambda1) (sin lambda2)) (cos phi2))))
36.0ms	(* (sin lambda1) (sin lambda2))
20.0ms	(+ (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2))))
21.0ms	(sin (- lambda1 lambda2))

series382.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (+ (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2)))) (* (* (sin lambda1) (sin lambda2)) (cos phi2))))
83.0ms	(* (sin lambda1) (sin lambda2))
226.0ms	(+ (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2))))
41.0ms	(sin (- lambda1 lambda2))

simplify5.6s

Counts

59 → 59

Iterations

Useful iterations: 2 (2.6s)

Iter	Nodes	Cost
0	119	889
1	436	872
2	4794	733
done	5000	733

prune458.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize45.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin lambda1) (cos lambda2))
0.2b	(* (sin lambda1) (sin lambda2))
0.2b	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (+ (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2)))) (* (* (sin lambda1) (sin lambda2)) (cos phi2))))
0.4b	(+ (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2))))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
8×	`pow1` `add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
6×	`associate-r` `associate-l` `add-log-exp`
2×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`+-commutative` `flip3-+` `sum-log` `sin-cos-mult` `flip-+` `sin-mult`

Counts

4 → 56

Calls

4 calls:

24.0ms	(* (sin lambda1) (cos lambda2))
21.0ms	(* (sin lambda1) (sin lambda2))
0.0ms	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (+ (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2)))) (* (* (sin lambda1) (sin lambda2)) (cos phi2))))
11.0ms	(+ (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2))))

series366.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(* (sin lambda1) (cos lambda2))
65.0ms	(* (sin lambda1) (sin lambda2))
38.0ms	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (+ (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2)))) (* (* (sin lambda1) (sin lambda2)) (cos phi2))))
203.0ms	(+ (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2))))

simplify1.2s

Counts

68 → 68

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	132	1053
1	531	1035
done	5000	870

prune548.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize88.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (+ (pow (cos phi1) 3) (pow (* (cos phi2) (* (cos lambda1) (cos lambda2))) 3)) (+ (* (cos phi1) (cos phi1)) (* (- (* (cos phi2) (* (cos lambda1) (cos lambda2))) (cos phi1)) (* (cos phi2) (* (cos lambda1) (cos lambda2))))))
0.4b	(pow (cos phi1) 3)
0.6b	(pow (* (cos phi2) (* (cos lambda1) (cos lambda2))) 3)
1.2b	(- (* (cos phi2) (* (cos lambda1) (cos lambda2))) (cos phi1))

rewrite269.0ms

Algorithm

rewrite-expression-head

Rules

26×	`*-un-lft-identity`
18×	`add-sqr-sqrt` `add-cube-cbrt`
15×	`times-frac`
13×	`add-exp-log` `add-cbrt-cube`
11×	`pow1`
9×	`cos-mult`
7×	`associate-/r/`
6×	`pow-unpow` `add-log-exp`
5×	`associate-r/` `frac-add` `associate-/l`
4×	`unpow-prod-down` `pow-pow` `cube-prod` `pow-exp` `sum-cubes` `distribute-lft-out` `rem-cube-cbrt`
3×	`flip3--` `pow-prod-down` `prod-exp` `associate-/r*` `flip--` `cbrt-unprod`
2×	`cube-mult` `frac-times` `pow-to-exp` `flip3-+` `unpow3` `associate-*l/` `flip-+` `associate-/l/` `sqr-pow`
1×	`cbrt-undiv` `cube-div` `sub-neg` `frac-2neg` `diff-log` `div-exp` `clear-num` `div-inv`

Counts

4 → 105

Calls

4 calls:

206.0ms	(/ (+ (pow (cos phi1) 3) (pow (* (cos phi2) (* (cos lambda1) (cos lambda2))) 3)) (+ (* (cos phi1) (cos phi1)) (* (- (* (cos phi2) (* (cos lambda1) (cos lambda2))) (cos phi1)) (* (cos phi2) (* (cos lambda1) (cos lambda2))))))
4.0ms	(pow (cos phi1) 3)
24.0ms	(pow (* (cos phi2) (* (cos lambda1) (cos lambda2))) 3)
29.0ms	(- (* (cos phi2) (* (cos lambda1) (cos lambda2))) (cos phi1))

series1.6s

Counts

4 → 12

Calls

4 calls:

1.1s	(/ (+ (pow (cos phi1) 3) (pow (* (cos phi2) (* (cos lambda1) (cos lambda2))) 3)) (+ (* (cos phi1) (cos phi1)) (* (- (* (cos phi2) (* (cos lambda1) (cos lambda2))) (cos phi1)) (* (cos phi2) (* (cos lambda1) (cos lambda2))))))
49.0ms	(pow (cos phi1) 3)
175.0ms	(pow (* (cos phi2) (* (cos lambda1) (cos lambda2))) 3)
252.0ms	(- (* (cos phi2) (* (cos lambda1) (cos lambda2))) (cos phi1))

simplify4.2s

Counts

117 → 117

Iterations

Useful iterations: done (4.2s)

Iter	Nodes	Cost
0	243	3895
1	2812	3631
done	5002	3403

prune1.2s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

regimes954.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	32	70
1	45	70
done	45	70

end0.0ms

sample14.2s

Algorithm

intervals

Results

8.9s	3560×	body	1280	valid
3.4s	2369×	body	640	valid
788.0ms	980×	body	320	valid
225.0ms	407×	body	160	valid
146.0ms	684×	body	80	valid