Details

Time bar (total: 20.7s)

sample267.0ms

Algorithm
intervals
Results
187.0ms147×body1280valid
51.0ms66×body640valid
9.0ms21×body320valid
2.0ms9×body160valid
2.0ms13×body80valid

simplify38.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01724
12724
24524
37024
47224
done7224

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.1b

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin (- lambda1 lambda2)) (cos phi2))
0.3b
(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
4.9b
(cos (- lambda1 lambda2))
5.0b
(sin (- lambda1 lambda2))

rewrite34.0ms

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:
13.0ms
(* (sin (- lambda1 lambda2)) (cos phi2))
10.0ms
(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
5.0ms
(cos (- lambda1 lambda2))
5.0ms
(sin (- lambda1 lambda2))

series188.0ms

Counts
4 → 12
Calls
4 calls:
63.0ms
(* (sin (- lambda1 lambda2)) (cos phi2))
88.0ms
(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
16.0ms
(cos (- lambda1 lambda2))
21.0ms
(sin (- lambda1 lambda2))

simplify4.4s

Counts
72 → 72
Iterations

Useful iterations: 3 (701.0ms)

IterNodesCost
0116760
1260748
2848644
32510642
44629642
done5000642

prune332.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 6.2b

localize34.0ms

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))
0.3b
(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
4.9b
(cos (- lambda1 lambda2))

rewrite37.0ms

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:
16.0ms
(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
4.0ms
(* (sin lambda1) (cos lambda2))
10.0ms
(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
5.0ms
(cos (- lambda1 lambda2))

series279.0ms

Counts
4 → 12
Calls
4 calls:
128.0ms
(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
45.0ms
(* (sin lambda1) (cos lambda2))
88.0ms
(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
18.0ms
(cos (- lambda1 lambda2))

simplify2.1s

Counts
82 → 82
Iterations

Useful iterations: 3 (1.0s)

IterNodesCost
01481039
13481016
21204882
34170880
done5001880

prune424.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize35.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin lambda1) (cos lambda2))
0.2b
(* (sin lambda1) (sin lambda2))
0.2b
(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))
0.3b
(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))

rewrite41.0ms

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:
4.0ms
(* (sin lambda1) (cos lambda2))
4.0ms
(* (sin lambda1) (sin lambda2))
13.0ms
(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))
17.0ms
(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))

series301.0ms

Counts
4 → 12
Calls
4 calls:
43.0ms
(* (sin lambda1) (cos lambda2))
48.0ms
(* (sin lambda1) (sin lambda2))
111.0ms
(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))
99.0ms
(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))

simplify901.0ms

Counts
100 → 100
Iterations

Useful iterations: 2 (145.0ms)

IterNodesCost
01571238
14081212
21452952
done5001952

prune521.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize36.0ms

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 lambda1) (sin lambda2))
0.3b
(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))

rewrite43.0ms

Algorithm
rewrite-expression-head
Rules
22×pow1 add-exp-log add-cbrt-cube
16×add-sqr-sqrt
11×pow-prod-down prod-exp cbrt-unprod
10×add-cube-cbrt *-un-lft-identity associate-*r* associate-*l*
4×*-commutative add-log-exp
3×associate-*l/ sin-cos-mult sin-mult unswap-sqr
1×frac-times flip3-- associate-*r/ flip--
Counts
4 → 83
Calls
4 calls:
19.0ms
(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
4.0ms
(* (sin lambda1) (cos lambda2))
4.0ms
(* (sin lambda1) (sin lambda2))
14.0ms
(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))

series324.0ms

Counts
4 → 12
Calls
4 calls:
130.0ms
(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
46.0ms
(* (sin lambda1) (cos lambda2))
46.0ms
(* (sin lambda1) (sin lambda2))
100.0ms
(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))

simplify935.0ms

Counts
95 → 95
Iterations

Useful iterations: 2 (132.0ms)

IterNodesCost
01591209
13791180
21289984
done5000984

prune438.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

regimes389.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02853
13953
done3953

end0.0ms

sample8.7s

Algorithm
intervals
Results
6.4s4627×body1280valid
1.5s1948×body640valid
280.0ms557×body320valid
90.0ms652×body80valid
66.0ms216×body160valid