Details

sample174.0ms

Algorithm

intervals

Results

100.0ms	110×	body	1280	valid
42.0ms	81×	body	640	valid
11.0ms	33×	body	320	valid
4.0ms	19×	body	160	valid
2.0ms	13×	body	80	valid

simplify7.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.0b

localize21.0ms

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))))
4.9b	(cos (- lambda1 lambda2))
5.0b	(sin (- lambda1 lambda2))

rewrite14.0ms

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)))))
4.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
5.0ms	(cos (- lambda1 lambda2))
5.0ms	(sin (- lambda1 lambda2))

series158.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
103.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
17.0ms	(cos (- lambda1 lambda2))
28.0ms	(sin (- lambda1 lambda2))

simplify1.3s

Counts

52 → 52

Iterations

Useful iterations: 3 (150.0ms)

Iter	Nodes	Cost
0	97	702
1	204	687
2	447	615
3	1007	613
4	2284	613
done	5001	613

prune242.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.8b

localize36.0ms

Local error

Found 4 expressions with local error:

0.2b	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2))) (* (* (sin lambda1) (sin lambda2)) (cos phi2))))
0.2b	(* (sin lambda1) (sin lambda2))
0.4b	(+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))
5.0b	(sin (- lambda1 lambda2))

rewrite13.0ms

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 lambda1) (cos lambda2)) (cos phi2))) (* (* (sin lambda1) (sin lambda2)) (cos phi2))))
5.0ms	(* (sin lambda1) (sin lambda2))
3.0ms	(+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))
5.0ms	(sin (- lambda1 lambda2))

series211.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2))) (* (* (sin lambda1) (sin lambda2)) (cos phi2))))
49.0ms	(* (sin lambda1) (sin lambda2))
125.0ms	(+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))
21.0ms	(sin (- lambda1 lambda2))

simplify2.0s

Counts

59 → 59

Iterations

Useful iterations: 2 (73.0ms)

Iter	Nodes	Cost
0	119	889
1	255	872
2	728	733
3	2280	733
done	5000	733

prune329.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize37.0ms

Local error

Found 4 expressions with local error:

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

rewrite13.0ms

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:

4.0ms	(* (sin lambda1) (cos lambda2))
0.0ms	(atan2 (* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))) (+ (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2))) (* (* (sin lambda1) (sin lambda2)) (cos phi2))))
4.0ms	(* (sin lambda1) (sin lambda2))
3.0ms	(+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))

series239.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(* (sin lambda1) (cos lambda2))
19.0ms	(atan2 (* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))) (+ (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2))) (* (* (sin lambda1) (sin lambda2)) (cos phi2))))
48.0ms	(* (sin lambda1) (sin lambda2))
127.0ms	(+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))

simplify1.7s

Counts

68 → 68

Iterations

Useful iterations: 3 (532.0ms)

Iter	Nodes	Cost
0	140	1067
1	321	1048
2	900	881
3	2701	870
done	5000	870

prune379.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize48.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (+ (pow (cos phi1) 3) (pow (* (* (cos lambda1) (cos lambda2)) (cos phi2)) 3)) (+ (* (cos phi1) (cos phi1)) (* (* (cos lambda1) (* (cos phi2) (cos lambda2))) (- (* (cos lambda1) (* (cos phi2) (cos lambda2))) (cos phi1)))))
0.4b	(pow (cos phi1) 3)
0.6b	(pow (* (* (cos lambda1) (cos lambda2)) (cos phi2)) 3)
1.9b	(- (* (cos lambda1) (* (cos phi2) (cos lambda2))) (cos phi1))

rewrite81.0ms

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:

59.0ms	(/ (+ (pow (cos phi1) 3) (pow (* (* (cos lambda1) (cos lambda2)) (cos phi2)) 3)) (+ (* (cos phi1) (cos phi1)) (* (* (cos lambda1) (* (cos phi2) (cos lambda2))) (- (* (cos lambda1) (* (cos phi2) (cos lambda2))) (cos phi1)))))
2.0ms	(pow (cos phi1) 3)
8.0ms	(pow (* (* (cos lambda1) (cos lambda2)) (cos phi2)) 3)
9.0ms	(- (* (cos lambda1) (* (cos phi2) (cos lambda2))) (cos phi1))

series970.0ms

Counts

4 → 12

Calls

4 calls:

692.0ms	(/ (+ (pow (cos phi1) 3) (pow (* (* (cos lambda1) (cos lambda2)) (cos phi2)) 3)) (+ (* (cos phi1) (cos phi1)) (* (* (cos lambda1) (* (cos phi2) (cos lambda2))) (- (* (cos lambda1) (* (cos phi2) (cos lambda2))) (cos phi1)))))
30.0ms	(pow (cos phi1) 3)
114.0ms	(pow (* (* (cos lambda1) (cos lambda2)) (cos phi2)) 3)
133.0ms	(- (* (cos lambda1) (* (cos phi2) (cos lambda2))) (cos phi1))

simplify1.2s

Counts

117 → 117

Iterations

Useful iterations: 2 (369.0ms)

Iter	Nodes	Cost
0	250	3895
1	658	3646
2	2972	3353
done	5000	3353

prune763.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

regimes449.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	33	118
1	47	118
done	47	118

end0.0ms

sample5.2s

Algorithm

intervals

Results

3.2s	3554×	body	1280	valid
1.2s	2379×	body	640	valid
327.0ms	925×	body	320	valid
95.0ms	439×	body	160	valid
69.0ms	702×	body	80	valid
3.0ms	1×	body	2560	valid