Details

Time bar (total: 22.4s)

sample431.0ms

Algorithm
intervals
Results
228.0ms114×body1280valid
137.0ms79×body640valid
27.0ms33×body320valid
6.0ms25×body80valid
3.0ms5×body160valid

simplify9.0ms

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: 1.0b

localize107.0ms

Local error

Found 4 expressions with local error:

0.2b
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
0.6b
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
2.5b
(sin (- lambda1 lambda2))
2.6b
(cos (- lambda1 lambda2))

rewrite44.0ms

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)))))
14.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
11.0ms
(sin (- lambda1 lambda2))
16.0ms
(cos (- lambda1 lambda2))

series255.0ms

Counts
4 → 12
Calls
4 calls:
14.0ms
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
173.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
35.0ms
(sin (- lambda1 lambda2))
33.0ms
(cos (- lambda1 lambda2))

simplify1.3s

Counts
52 → 52
Iterations

Useful iterations: 3 (466.0ms)

IterNodesCost
097702
1207687
2532615
31518613
done5000613

prune462.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.8b

localize47.0ms

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))
0.5b
(+ (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2))))
2.5b
(sin (- lambda1 lambda2))

rewrite53.0ms

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 phi2) (* (cos lambda1) (cos lambda2)))) (* (* (sin lambda1) (sin lambda2)) (cos phi2))))
13.0ms
(* (sin lambda1) (sin lambda2))
11.0ms
(+ (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2))))
27.0ms
(sin (- lambda1 lambda2))

series318.0ms

Counts
4 → 12
Calls
4 calls:
23.0ms
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (+ (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2)))) (* (* (sin lambda1) (sin lambda2)) (cos phi2))))
68.0ms
(* (sin lambda1) (sin lambda2))
203.0ms
(+ (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2))))
24.0ms
(sin (- lambda1 lambda2))

simplify779.0ms

Counts
59 → 59
Iterations

Useful iterations: 2 (184.0ms)

IterNodesCost
0119889
1266872
2869733
done5000733

prune595.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize72.0ms

Local error

Found 4 expressions with local error:

0.2b
(+ (+ (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2)))) (* (* (sin lambda1) (sin lambda2)) (cos phi2)))
0.2b
(atan2 (* (cos phi2) (- (* (cos lambda2) (sin lambda1)) (* (cos lambda1) (sin lambda2)))) (+ (+ (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2)))) (* (* (sin lambda1) (sin lambda2)) (cos phi2))))
0.2b
(* (sin lambda1) (sin lambda2))
0.5b
(+ (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2))))

rewrite88.0ms

Algorithm
rewrite-expression-head
Rules
11×add-log-exp
8×add-sqr-sqrt
6×pow1 add-exp-log add-cube-cbrt *-un-lft-identity add-cbrt-cube
4×sum-log
3×flip3-+ associate-*r* associate-*l* flip-+ sin-mult
2×+-commutative associate-*l/ frac-add
1×associate-+l+ pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
Counts
4 → 52
Calls
4 calls:
57.0ms
(+ (+ (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2)))) (* (* (sin lambda1) (sin lambda2)) (cos phi2)))
1.0ms
(atan2 (* (cos phi2) (- (* (cos lambda2) (sin lambda1)) (* (cos lambda1) (sin lambda2)))) (+ (+ (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2)))) (* (* (sin lambda1) (sin lambda2)) (cos phi2))))
16.0ms
(* (sin lambda1) (sin lambda2))
11.0ms
(+ (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2))))

series554.0ms

Counts
4 → 12
Calls
4 calls:
276.0ms
(+ (+ (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2)))) (* (* (sin lambda1) (sin lambda2)) (cos phi2)))
27.0ms
(atan2 (* (cos phi2) (- (* (cos lambda2) (sin lambda1)) (* (cos lambda1) (sin lambda2)))) (+ (+ (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2)))) (* (* (sin lambda1) (sin lambda2)) (cos phi2))))
70.0ms
(* (sin lambda1) (sin lambda2))
181.0ms
(+ (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2))))

simplify1.1s

Counts
64 → 64
Iterations

Useful iterations: 2 (229.0ms)

IterNodesCost
01331517
13351448
215281237
done50001237

prune600.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize126.0ms

Local error

Found 4 expressions with local error:

0.5b
(+ (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2))))
0.5b
(+ (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2))))
0.5b
(+ (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2))))
0.7b
(pow (+ (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2)))) 3)

rewrite63.0ms

Algorithm
rewrite-expression-head
Rules
10×add-log-exp
7×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
5×pow1 add-exp-log add-cbrt-cube
4×flip3-+ flip-+
3×+-commutative unpow-prod-down pow-unpow cube-prod sum-log
2×cube-div
1×cube-mult pow-to-exp pow-pow unpow3 pow-exp rem-cube-cbrt sqr-pow
Counts
4 → 58
Calls
4 calls:
20.0ms
(+ (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2))))
11.0ms
(+ (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2))))
12.0ms
(+ (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2))))
18.0ms
(pow (+ (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2)))) 3)

series938.0ms

Counts
4 → 12
Calls
4 calls:
223.0ms
(+ (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2))))
215.0ms
(+ (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2))))
194.0ms
(+ (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2))))
306.0ms
(pow (+ (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2)))) 3)

simplify1.2s

Counts
70 → 70
Iterations

Useful iterations: 2 (268.0ms)

IterNodesCost
0771348
12771186
213581124
done50001124

prune607.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

regimes1.0s

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03068
14268
done4268

end0.0ms

sample11.6s

Algorithm
intervals
Results
6.5s3557×body1280valid
3.7s2375×body640valid
604.0ms899×body320valid
163.0ms427×body160valid
121.0ms742×body80valid