Details

sample414.0ms

Algorithm

intervals

Results

205.0ms	108×	body	1280	valid
133.0ms	79×	body	640	valid
33.0ms	41×	body	320	valid
6.0ms	10×	body	160	valid
4.0ms	18×	body	80	valid

simplify15.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

prune43.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.8b

localize48.0ms

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))

rewrite43.0ms

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)))))
15.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
15.0ms	(sin (- lambda1 lambda2))
11.0ms	(cos (- lambda1 lambda2))

series232.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
144.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
31.0ms	(sin (- lambda1 lambda2))
36.0ms	(cos (- lambda1 lambda2))

simplify4.8s

Counts

52 → 52

Iterations

Useful iterations: 3 (391.0ms)

Iter	Nodes	Cost
0	97	702
1	204	687
2	458	615
3	967	613
4	2013	613
5	4634	613
done	5000	613

prune446.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.6b

localize48.0ms

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))

rewrite50.0ms

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:

1.0ms	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (+ (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2)))) (* (* (sin lambda1) (sin lambda2)) (cos phi2))))
14.0ms	(* (sin lambda1) (sin lambda2))
21.0ms	(+ (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2))))
12.0ms	(sin (- lambda1 lambda2))

series310.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (+ (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2)))) (* (* (sin lambda1) (sin lambda2)) (cos phi2))))
78.0ms	(* (sin lambda1) (sin lambda2))
181.0ms	(+ (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2))))
33.0ms	(sin (- lambda1 lambda2))

simplify2.4s

Counts

59 → 59

Iterations

Useful iterations: 2 (191.0ms)

Iter	Nodes	Cost
0	119	889
1	260	872
2	688	733
3	1962	733
done	5001	733

prune509.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize64.0ms

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))))

rewrite40.0ms

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:

12.0ms	(* (sin lambda1) (cos lambda2))
15.0ms	(* (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))))

series399.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(* (sin lambda1) (cos lambda2))
89.0ms	(* (sin lambda1) (sin lambda2))
36.0ms	(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))))
201.0ms	(+ (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2))))

simplify3.0s

Counts

68 → 68

Iterations

Useful iterations: 3 (1.4s)

Iter	Nodes	Cost
0	140	1067
1	320	1048
2	854	881
3	2316	870
done	5000	870

prune555.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize81.0ms

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 phi2) (* (cos lambda1) (cos lambda2))) (cos phi1)))))
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))

rewrite337.0ms

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` `associate-*r/` `add-log-exp`
5×	`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` `flip-+` `associate-/l/` `sqr-pow`
1×	`cbrt-undiv` `cube-div` `sub-neg` `frac-2neg` `diff-log` `div-exp` `associate-*l/` `clear-num` `div-inv`

Counts

4 → 105

Calls

4 calls:

232.0ms	(/ (+ (pow (cos phi1) 3) (pow (* (cos phi2) (* (cos lambda1) (cos lambda2))) 3)) (+ (* (cos phi1) (cos phi1)) (* (* (cos phi2) (* (cos lambda1) (cos lambda2))) (- (* (cos phi2) (* (cos lambda1) (cos lambda2))) (cos phi1)))))
7.0ms	(pow (cos phi1) 3)
37.0ms	(pow (* (cos phi2) (* (cos lambda1) (cos lambda2))) 3)
56.0ms	(- (* (cos phi2) (* (cos lambda1) (cos lambda2))) (cos phi1))

series1.5s

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 phi2) (* (cos lambda1) (cos lambda2))) (cos phi1)))))
55.0ms	(pow (cos phi1) 3)
137.0ms	(pow (* (cos phi2) (* (cos lambda1) (cos lambda2))) 3)
168.0ms	(- (* (cos phi2) (* (cos lambda1) (cos lambda2))) (cos phi1))

simplify2.1s

Counts

117 → 117

Iterations

Useful iterations: 2 (697.0ms)

Iter	Nodes	Cost
0	243	3895
1	637	3646
2	2804	3353
done	5000	3353

prune1.1s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

regimes770.0ms

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	34	71
1	48	71
done	48	71

end0.0ms

sample11.6s

Algorithm

intervals

Results

6.1s	3560×	body	1280	valid
3.3s	2369×	body	640	valid
1.4s	980×	body	320	valid
187.0ms	407×	body	160	valid
165.0ms	684×	body	80	valid