Details

Time bar (total: 2.3m)

sample1.6s

Algorithm
intervals
Results
1.3s103×body1280valid
116.0ms68×body640valid
40.0ms39×body320valid
29.0ms16×body160valid
15.0ms30×body80valid

simplify72.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01420
12020
22120
done2120

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.0b

localize167.0ms

Local error

Found 4 expressions with local error:

0.2b
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
0.7b
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
2.6b
(sin (- lambda1 lambda2))
2.8b
(cos (- lambda1 lambda2))

rewrite462.0ms

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:
1.0ms
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
64.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
321.0ms
(sin (- lambda1 lambda2))
51.0ms
(cos (- lambda1 lambda2))

series909.0ms

Counts
4 → 12
Calls
4 calls:
151.0ms
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
557.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
93.0ms
(sin (- lambda1 lambda2))
102.0ms
(cos (- lambda1 lambda2))

simplify4.2s

Counts
52 → 52
Iterations

Useful iterations: 3 (877.0ms)

IterNodesCost
097702
1207687
2532615
31518613
done5000613

prune1.3s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.8b

localize329.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (cos lambda1) (sin lambda2))
0.2b
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
0.7b
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
2.8b
(cos (- lambda1 lambda2))

rewrite96.0ms

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×cos-diff associate-*r* associate-*l*
2×cos-sum associate-+r+
1×+-commutative distribute-rgt-in sub-neg distribute-lft-in flip3-+ pow-prod-down prod-exp sum-log *-commutative cbrt-unprod flip-+ unswap-sqr
Counts
4 → 48
Calls
4 calls:
35.0ms
(* (cos lambda1) (sin lambda2))
0.0ms
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
22.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
35.0ms
(cos (- lambda1 lambda2))

series821.0ms

Counts
4 → 12
Calls
4 calls:
98.0ms
(* (cos lambda1) (sin lambda2))
27.0ms
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
538.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
152.0ms
(cos (- lambda1 lambda2))

simplify9.6s

Counts
60 → 60
Iterations

Useful iterations: 3 (3.5s)

IterNodesCost
0115857
1262841
2815743
34052741
done5000741

prune1.6s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize167.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (cos lambda1) (sin lambda2))
0.2b
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (+ (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2)))) (* (cos phi2) (* (sin lambda1) (sin lambda2)))))
0.2b
(* (sin lambda1) (sin lambda2))
0.7b
(+ (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2))))

rewrite390.0ms

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 flip-+ sin-mult
Counts
4 → 55
Calls
4 calls:
284.0ms
(* (cos lambda1) (sin lambda2))
1.0ms
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (+ (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2)))) (* (cos phi2) (* (sin lambda1) (sin lambda2)))))
69.0ms
(* (sin lambda1) (sin lambda2))
22.0ms
(+ (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2))))

series988.0ms

Counts
4 → 12
Calls
4 calls:
115.0ms
(* (cos lambda1) (sin lambda2))
50.0ms
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (+ (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2)))) (* (cos phi2) (* (sin lambda1) (sin lambda2)))))
292.0ms
(* (sin lambda1) (sin lambda2))
530.0ms
(+ (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2))))

simplify2.9s

Counts
67 → 67
Iterations

Useful iterations: done (2.9s)

IterNodesCost
01291044
13141026
21161865
done5000861

prune2.0s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize188.0ms

Local error

Found 4 expressions with local error:

0.3b
(cbrt (cos lambda1))
0.3b
(cbrt (cos lambda1))
0.3b
(cbrt (cos lambda1))
0.7b
(+ (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2))))

rewrite343.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod
7×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
6×add-log-exp
4×pow1 add-exp-log add-cbrt-cube
3×pow1/3
1×+-commutative flip3-+ sum-log flip-+
Counts
4 → 44
Calls
4 calls:
2.0ms
(cbrt (cos lambda1))
2.0ms
(cbrt (cos lambda1))
27.0ms
(cbrt (cos lambda1))
20.0ms
(+ (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2))))

series7.1s

Counts
4 → 12
Calls
4 calls:
5.2s
(cbrt (cos lambda1))
533.0ms
(cbrt (cos lambda1))
526.0ms
(cbrt (cos lambda1))
823.0ms
(+ (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2))))

simplify5.6s

Counts
56 → 56
Iterations

Useful iterations: 3 (1.9s)

IterNodesCost
067510
1167489
2567440
32652431
done5000431

prune1.7s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.1b

regimes1.9s

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 0.2b

bsearch0.0ms

simplify8.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02546
13646
done3646

end0.0ms

sample1.6m

Algorithm
intervals
Results
53.2s3614×body1280valid
22.6s2337×body640valid
14.4s949×body320valid
1.1s701×body80valid
499.0ms399×body160valid