Details

Time bar (total: 40.7s)

sample560.0ms

Algorithm
intervals
Results
279.0ms130×body1280valid
228.0ms75×body640valid
14.0ms16×body320valid
8.0ms28×body80valid
4.0ms7×body160valid

simplify90.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01724
12724
24624
37124
47224
done7224

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.4b

localize78.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (sin (- lambda1 lambda2)) (cos phi2))
0.2b
(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
2.6b
(sin (- lambda1 lambda2))
2.8b
(cos (- lambda1 lambda2))

rewrite163.0ms

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*
4×associate-*l* pow-prod-down prod-exp cbrt-unprod add-log-exp
3×cos-diff
2×sub-neg cos-sum sin-sum *-commutative sin-cos-mult
1×distribute-rgt-in distribute-lft-in associate-*l/ sin-diff unswap-sqr
Counts
4 → 60
Calls
4 calls:
46.0ms
(* (sin (- lambda1 lambda2)) (cos phi2))
71.0ms
(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
22.0ms
(sin (- lambda1 lambda2))
22.0ms
(cos (- lambda1 lambda2))

series310.0ms

Counts
4 → 12
Calls
4 calls:
111.0ms
(* (sin (- lambda1 lambda2)) (cos phi2))
147.0ms
(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
32.0ms
(sin (- lambda1 lambda2))
20.0ms
(cos (- lambda1 lambda2))

simplify7.2s

Counts
72 → 72
Iterations

Useful iterations: 3 (1.1s)

IterNodesCost
0116760
1258748
2816644
32177642
43715642
done5000642

prune548.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 7.5b

localize70.0ms

Local error

Found 4 expressions with local error:

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

rewrite152.0ms

Algorithm
rewrite-expression-head
Rules
13×pow1 add-exp-log add-sqr-sqrt add-cbrt-cube
9×add-cube-cbrt *-un-lft-identity associate-*r*
7×associate-*l*
5×pow-prod-down prod-exp cbrt-unprod
4×add-log-exp
3×cos-diff associate-*l/ *-commutative
2×cos-sum sin-cos-mult unswap-sqr
1×distribute-rgt-in sub-neg flip3-- distribute-lft-in flip--
Counts
4 → 70
Calls
4 calls:
66.0ms
(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
18.0ms
(* (sin lambda1) (cos lambda2))
46.0ms
(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
19.0ms
(cos (- lambda1 lambda2))

series387.0ms

Counts
4 → 12
Calls
4 calls:
157.0ms
(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
65.0ms
(* (sin lambda1) (cos lambda2))
131.0ms
(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
34.0ms
(cos (- lambda1 lambda2))

simplify3.2s

Counts
82 → 82
Iterations

Useful iterations: 3 (1.5s)

IterNodesCost
01481039
13471016
21158888
33747880
done5001880

prune642.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize51.0ms

Local error

Found 4 expressions with local error:

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

rewrite240.0ms

Algorithm
rewrite-expression-head
Rules
32×pow1 add-exp-log add-cbrt-cube
18×pow-prod-down prod-exp cbrt-unprod
12×add-sqr-sqrt
8×add-cube-cbrt *-un-lft-identity associate-*r* associate-*l*
5×sin-cos-mult
4×*-commutative add-log-exp
3×sin-mult
2×frac-times associate-*r/ associate-*l/ cos-mult unswap-sqr
Counts
4 → 88
Calls
4 calls:
24.0ms
(* (sin lambda1) (cos lambda2))
25.0ms
(* (sin lambda1) (sin lambda2))
96.0ms
(* (* (sin lambda1) (sin lambda2)) (* (sin phi1) (cos phi2)))
88.0ms
(* (* (cos lambda1) (cos lambda2)) (* (sin phi1) (cos phi2)))

series526.0ms

Counts
4 → 12
Calls
4 calls:
86.0ms
(* (sin lambda1) (cos lambda2))
66.0ms
(* (sin lambda1) (sin lambda2))
191.0ms
(* (* (sin lambda1) (sin lambda2)) (* (sin phi1) (cos phi2)))
184.0ms
(* (* (cos lambda1) (cos lambda2)) (* (sin phi1) (cos phi2)))

simplify1.5s

Counts
100 → 100
Iterations

Useful iterations: 2 (320.0ms)

IterNodesCost
01611238
14171212
21686952
done5000952

prune826.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize84.0ms

Local error

Found 4 expressions with local error:

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

rewrite196.0ms

Algorithm
rewrite-expression-head
Rules
29×pow1 add-exp-log add-cbrt-cube
16×pow-prod-down prod-exp cbrt-unprod
13×add-sqr-sqrt
10×associate-*l*
9×add-cube-cbrt *-un-lft-identity
8×associate-*r*
4×*-commutative add-log-exp
3×associate-*r/ sin-cos-mult sin-mult
2×unswap-sqr
1×frac-times associate-*l/ cos-mult
Counts
4 → 85
Calls
4 calls:
25.0ms
(* (sin lambda1) (cos lambda2))
18.0ms
(* (sin lambda1) (sin lambda2))
52.0ms
(* (* (sin lambda1) (sin lambda2)) (* (sin phi1) (cos phi2)))
95.0ms
(* (sin phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2))))

series514.0ms

Counts
4 → 12
Calls
4 calls:
87.0ms
(* (sin lambda1) (cos lambda2))
64.0ms
(* (sin lambda1) (sin lambda2))
191.0ms
(* (* (sin lambda1) (sin lambda2)) (* (sin phi1) (cos phi2)))
170.0ms
(* (sin phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2))))

simplify1.6s

Counts
97 → 97
Iterations

Useful iterations: 2 (308.0ms)

IterNodesCost
01661165
14221143
21659905
done5000905

prune631.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

regimes519.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify5.0ms

Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
03155
14553
done4553

end0.0ms

sample20.6s

Algorithm
intervals
Results
14.7s4655×body1280valid
4.3s1872×body640valid
678.0ms552×body320valid
201.0ms716×body80valid
108.0ms205×body160valid