Details

Time bar (total: 28.2s)

sample351.0ms

Algorithm
intervals
Results
178.0ms110×body1280valid
118.0ms79×body640valid
19.0ms29×body320valid
7.0ms16×body160valid
4.0ms22×body80valid

simplify8.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01420
12020
22120
done2120

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.5b

localize51.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (cos phi2) (sin (- lambda1 lambda2)))
0.6b
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
3.2b
(sin (- lambda1 lambda2))
3.4b
(cos (- lambda1 lambda2))

rewrite108.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt
6×pow1 add-exp-log add-cube-cbrt *-un-lft-identity sin-sum add-cbrt-cube add-log-exp
4×sub-neg
3×distribute-rgt-in cos-diff distribute-lft-in associate-*r* associate-*l*
2×cos-sum associate-+r+
1×+-commutative flip3-+ pow-prod-down prod-exp sum-log sin-diff *-commutative cbrt-unprod flip-+ unswap-sqr
Counts
4 → 55
Calls
4 calls:
55.0ms
(* (cos phi2) (sin (- lambda1 lambda2)))
20.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
18.0ms
(sin (- lambda1 lambda2))
14.0ms
(cos (- lambda1 lambda2))

series309.0ms

Counts
4 → 12
Calls
4 calls:
105.0ms
(* (cos phi2) (sin (- lambda1 lambda2)))
145.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
37.0ms
(sin (- lambda1 lambda2))
21.0ms
(cos (- lambda1 lambda2))

simplify3.6s

Counts
67 → 67
Iterations

Useful iterations: 3 (508.0ms)

IterNodesCost
0112733
1247711
2658647
31474645
43013645
done5000645

prune493.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 1.2b

localize72.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin lambda1) (cos lambda2))
0.2b
(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
0.6b
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
3.4b
(cos (- lambda1 lambda2))

rewrite619.0ms

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
3×distribute-rgt-in cos-diff sub-neg distribute-lft-in
2×cos-sum associate-+r+ associate-*r/ pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×+-commutative flip3-- flip3-+ sum-log sin-cos-mult flip-- flip-+
Counts
4 → 66
Calls
4 calls:
24.0ms
(* (sin lambda1) (cos lambda2))
543.0ms
(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
15.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
33.0ms
(cos (- lambda1 lambda2))

series480.0ms

Counts
4 → 12
Calls
4 calls:
62.0ms
(* (sin lambda1) (cos lambda2))
217.0ms
(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
169.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
32.0ms
(cos (- lambda1 lambda2))

simplify2.4s

Counts
78 → 78
Iterations

Useful iterations: 3 (1.0s)

IterNodesCost
01491021
1352992
21045898
33121896
done5000896

prune610.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize77.0ms

Local error

Found 4 expressions with local error:

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

rewrite153.0ms

Algorithm
rewrite-expression-head
Rules
16×add-sqr-sqrt
10×pow1 add-exp-log add-cube-cbrt *-un-lft-identity add-cbrt-cube
9×associate-*r* associate-*l*
6×add-log-exp
3×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
2×distribute-rgt-in sub-neg distribute-lft-in associate-*r/
1×+-commutative flip3-- flip3-+ sum-log sin-cos-mult flip-- flip-+ sin-mult
Counts
4 → 73
Calls
4 calls:
17.0ms
(* (sin lambda1) (cos lambda2))
98.0ms
(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
16.0ms
(* (sin lambda1) (sin lambda2))
21.0ms
(+ (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2))))

series506.0ms

Counts
4 → 12
Calls
4 calls:
53.0ms
(* (sin lambda1) (cos lambda2))
219.0ms
(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
66.0ms
(* (sin lambda1) (sin lambda2))
168.0ms
(+ (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2))))

simplify3.4s

Counts
85 → 85
Iterations

Useful iterations: 2 (198.0ms)

IterNodesCost
01521078
13721047
21179939
34042939
done5000939

prune654.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize108.0ms

Local error

Found 4 expressions with local error:

0.4b
(+ (pow (cos phi1) 3) (pow (* (cos phi2) (* (cos lambda1) (cos lambda2))) 3))
0.4b
(pow (cos phi1) 3)
0.7b
(pow (* (cos phi2) (* (cos lambda1) (cos lambda2))) 3)
1.9b
(- (* (cos phi2) (* (cos lambda1) (cos lambda2))) (cos phi1))

rewrite127.0ms

Algorithm
rewrite-expression-head
Rules
11×pow1 add-exp-log add-cbrt-cube
10×*-un-lft-identity
8×add-sqr-sqrt add-cube-cbrt add-log-exp
6×pow-unpow
4×unpow-prod-down pow-pow cube-prod pow-exp rem-cube-cbrt
3×pow-prod-down prod-exp cbrt-unprod
2×cube-mult pow-to-exp unpow3 sqr-pow
1×+-commutative cube-div sub-neg flip3-- flip3-+ diff-log associate-*r/ sum-log cos-mult sum-cubes flip-- flip-+ distribute-lft-out
Counts
4 → 74
Calls
4 calls:
33.0ms
(+ (pow (cos phi1) 3) (pow (* (cos phi2) (* (cos lambda1) (cos lambda2))) 3))
7.0ms
(pow (cos phi1) 3)
40.0ms
(pow (* (cos phi2) (* (cos lambda1) (cos lambda2))) 3)
44.0ms
(- (* (cos phi2) (* (cos lambda1) (cos lambda2))) (cos phi1))

series710.0ms

Counts
4 → 12
Calls
4 calls:
287.0ms
(+ (pow (cos phi1) 3) (pow (* (cos phi2) (* (cos lambda1) (cos lambda2))) 3))
35.0ms
(pow (cos phi1) 3)
175.0ms
(pow (* (cos phi2) (* (cos lambda1) (cos lambda2))) 3)
213.0ms
(- (* (cos phi2) (* (cos lambda1) (cos lambda2))) (cos phi1))

simplify1.3s

Counts
86 → 86
Iterations

Useful iterations: done (1.3s)

IterNodesCost
01461188
13801047
21404935
done5001934

prune675.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

regimes611.0ms

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)

IterNodesCost
03584
14884
done4884

end0.0ms

sample10.7s

Algorithm
intervals
Results
5.8s3516×body1280valid
2.8s2346×body640valid
899.0ms988×body320valid
454.0ms740×body80valid
144.0ms410×body160valid