Details

Time bar (total: 14.2s)

sample175.0ms

Algorithm
intervals
Results
103.0ms111×body1280valid
44.0ms86×body640valid
9.0ms27×body320valid
2.0ms23×body80valid
2.0ms9×body160valid

simplify7.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01420
12020
22120
done2120

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.7b

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)))))
0.4b
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
3.3b
(sin (- lambda1 lambda2))
3.3b
(cos (- lambda1 lambda2))

rewrite19.0ms

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)))))
3.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
9.0ms
(sin (- lambda1 lambda2))
5.0ms
(cos (- lambda1 lambda2))

series145.0ms

Counts
4 → 12
Calls
4 calls:
10.0ms
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
97.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
20.0ms
(sin (- lambda1 lambda2))
18.0ms
(cos (- lambda1 lambda2))

simplify1.6s

Counts
52 → 52
Iterations

Useful iterations: 3 (143.0ms)

IterNodesCost
097702
1204687
2446635
31084633
42994633
done5000633

prune236.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.5b

localize29.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (cos phi2) (cos (- lambda1 lambda2)))
0.2b
(atan2 (* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
0.4b
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
3.3b
(cos (- lambda1 lambda2))

rewrite14.0ms

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
5×cos-diff
3×associate-*r* associate-*l*
2×distribute-rgt-in cos-sum associate-+r+ distribute-lft-in
1×+-commutative sub-neg flip3-+ pow-prod-down prod-exp sum-log cos-mult *-commutative cbrt-unprod flip-+ unswap-sqr
Counts
4 → 51
Calls
4 calls:
5.0ms
(* (cos phi2) (cos (- lambda1 lambda2)))
0.0ms
(atan2 (* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
3.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
5.0ms
(cos (- lambda1 lambda2))

series185.0ms

Counts
4 → 12
Calls
4 calls:
56.0ms
(* (cos phi2) (cos (- lambda1 lambda2)))
12.0ms
(atan2 (* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
97.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
19.0ms
(cos (- lambda1 lambda2))

simplify914.0ms

Counts
63 → 63
Iterations

Useful iterations: 3 (298.0ms)

IterNodesCost
0116964
1261931
2632889
31939874
done5001874

prune331.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize32.0ms

Local error

Found 4 expressions with local error:

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

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
11×pow1 add-exp-log add-cbrt-cube
9×add-sqr-sqrt
7×add-cube-cbrt *-un-lft-identity
6×associate-*r* add-log-exp
4×associate-*l* pow-prod-down prod-exp cbrt-unprod
2×*-commutative sin-mult
1×+-commutative flip3-+ associate-*l/ sum-log flip-+ unswap-sqr
Counts
4 → 56
Calls
4 calls:
9.0ms
(* (* (sin lambda1) (sin lambda2)) (cos phi2))
4.0ms
(* (sin lambda1) (sin 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))))
3.0ms
(+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))

series260.0ms

Counts
4 → 12
Calls
4 calls:
73.0ms
(* (* (sin lambda1) (sin lambda2)) (cos phi2))
47.0ms
(* (sin lambda1) (sin lambda2))
18.0ms
(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))))
121.0ms
(+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))

simplify2.1s

Counts
68 → 68
Iterations

Useful iterations: 3 (855.0ms)

IterNodesCost
01311137
13051116
21026921
34124910
done5000910

prune374.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize40.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin lambda1) (sin lambda2))
0.2b
(exp (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2))))
0.4b
(+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))
0.5b
(log (exp (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))))

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt
9×add-cube-cbrt *-un-lft-identity add-log-exp
7×pow1
6×add-exp-log exp-prod add-cbrt-cube
4×log-prod log-pow
3×associate-*r* associate-*l*
2×exp-sum sum-log rem-exp-log
1×+-commutative flip3-+ rem-log-exp pow-prod-down prod-exp *-commutative cbrt-unprod flip-+ sin-mult unswap-sqr
Counts
4 → 59
Calls
4 calls:
4.0ms
(* (sin lambda1) (sin lambda2))
6.0ms
(exp (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2))))
3.0ms
(+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))
7.0ms
(log (exp (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))))

series452.0ms

Counts
4 → 12
Calls
4 calls:
44.0ms
(* (sin lambda1) (sin lambda2))
160.0ms
(exp (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2))))
124.0ms
(+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))
123.0ms
(log (exp (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))))

simplify1.1s

Counts
71 → 71
Iterations

Useful iterations: 2 (69.0ms)

IterNodesCost
0113972
1246914
2765812
32783812
done5001812

prune389.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

regimes425.0ms

Accuracy

0% (0.1b 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)

IterNodesCost
03469
14969
done4969

end0.0ms

sample5.3s

Algorithm
intervals
Results
3.2s3551×body1280valid
1.3s2449×body640valid
339.0ms943×body320valid
82.0ms372×body160valid
74.0ms685×body80valid