Details

Time bar (total: 22.4s)

sample539.0ms

Algorithm
intervals
Results
380.0ms136×body1280valid
97.0ms75×body640valid
24.0ms23×body320valid
4.0ms18×body80valid
2.0ms4×body160valid

simplify103.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01724
12824
24724
37824
48824
done8824

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.2b

localize64.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin (- lambda1 lambda2)) (cos phi2))
0.2b
(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
5.5b
(sin (- lambda1 lambda2))
6.0b
(cos (- lambda1 lambda2))

rewrite176.0ms

Algorithm
rewrite-expression-head
Rules
21×add-sqr-sqrt
19×add-cube-cbrt *-un-lft-identity
18×prod-diff
11×pow1 add-exp-log cos-sum sin-sum add-cbrt-cube
6×associate-*r*
4×expm1-log1p-u associate-*l* pow-prod-down prod-exp cbrt-unprod log1p-expm1-u add-log-exp
3×cos-diff
2×sub-neg *-commutative sin-cos-mult
1×distribute-rgt-in distribute-lft-in associate-*l/ sin-diff unswap-sqr
Counts
4 → 86
Calls
4 calls:
39.0ms
(* (sin (- lambda1 lambda2)) (cos phi2))
61.0ms
(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
43.0ms
(sin (- lambda1 lambda2))
30.0ms
(cos (- lambda1 lambda2))

series297.0ms

Counts
4 → 12
Calls
4 calls:
117.0ms
(* (sin (- lambda1 lambda2)) (cos phi2))
134.0ms
(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
23.0ms
(sin (- lambda1 lambda2))
21.0ms
(cos (- lambda1 lambda2))

simplify8.0s

Counts
98 → 98
Iterations

Useful iterations: done (8.0s)

IterNodesCost
02101766
14031430
29951144
324661059
44346878
done5001787

prune598.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 6.5b

localize47.0ms

Local error

Found 4 expressions with local error:

0.2b
(- (* (cos phi1) (sin phi2)) (* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2))))
0.2b
(* (sin lambda1) (cos lambda2))
0.2b
(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
6.0b
(cos (- lambda1 lambda2))

rewrite106.0ms

Algorithm
rewrite-expression-head
Rules
15×add-sqr-sqrt
13×add-cube-cbrt *-un-lft-identity
11×pow1 add-exp-log cos-sum add-cbrt-cube
10×prod-diff
6×associate-*r* add-log-exp
5×cos-diff
4×expm1-log1p-u associate-*l* pow-prod-down prod-exp cbrt-unprod log1p-expm1-u
2×distribute-rgt-in sub-neg distribute-lft-in *-commutative sin-cos-mult associate--r+
1×flip3-- fma-neg diff-log associate-*l/ flip-- unswap-sqr
Counts
4 → 83
Calls
4 calls:
15.0ms
(- (* (cos phi1) (sin phi2)) (* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2))))
15.0ms
(* (sin lambda1) (cos lambda2))
46.0ms
(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
26.0ms
(cos (- lambda1 lambda2))

series481.0ms

Counts
4 → 12
Calls
4 calls:
242.0ms
(- (* (cos phi1) (sin phi2)) (* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2))))
67.0ms
(* (sin lambda1) (cos lambda2))
133.0ms
(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
39.0ms
(cos (- lambda1 lambda2))

simplify3.7s

Counts
95 → 95
Iterations

Useful iterations: 3 (1.9s)

IterNodesCost
02221615
14701406
213621210
344081163
done50001163

prune971.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize53.0ms

Local error

Found 4 expressions with local error:

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

rewrite270.0ms

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×expm1-log1p-u *-commutative log1p-expm1-u add-log-exp
3×sin-mult
2×frac-times associate-*r/ associate-*l/ cos-mult unswap-sqr
Counts
4 → 96
Calls
4 calls:
26.0ms
(* (sin lambda1) (cos lambda2))
27.0ms
(* (sin lambda1) (sin lambda2))
102.0ms
(* (* (sin lambda1) (sin lambda2)) (* (sin phi1) (cos phi2)))
110.0ms
(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))

series896.0ms

Counts
4 → 12
Calls
4 calls:
88.0ms
(* (sin lambda1) (cos lambda2))
437.0ms
(* (sin lambda1) (sin lambda2))
160.0ms
(* (* (sin lambda1) (sin lambda2)) (* (sin phi1) (cos phi2)))
211.0ms
(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))

simplify1.8s

Counts
108 → 108
Iterations

Useful iterations: 2 (374.0ms)

IterNodesCost
01651310
14151283
216441023
done50001023

prune953.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

localize85.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin lambda1) (sin lambda2))
0.2b
(log1p (* (sin lambda1) (cos lambda2)))
0.3b
(* (* (sin lambda1) (sin lambda2)) (* (sin phi1) (cos phi2)))
0.3b
(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))

rewrite229.0ms

Algorithm
rewrite-expression-head
Rules
30×pow1 add-exp-log add-cbrt-cube
17×pow-prod-down prod-exp cbrt-unprod
8×add-sqr-sqrt
6×add-cube-cbrt *-un-lft-identity
5×expm1-log1p-u associate-*r* associate-*l*
4×sin-cos-mult log1p-expm1-u add-log-exp
3×*-commutative sin-mult
2×frac-times associate-*r/ associate-*l/ cos-mult
1×log1p-udef log1p-expm1 unswap-sqr
Counts
4 → 86
Calls
4 calls:
18.0ms
(* (sin lambda1) (sin lambda2))
1.0ms
(log1p (* (sin lambda1) (cos lambda2)))
103.0ms
(* (* (sin lambda1) (sin lambda2)) (* (sin phi1) (cos phi2)))
104.0ms
(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))

series493.0ms

Counts
4 → 12
Calls
4 calls:
91.0ms
(* (sin lambda1) (sin lambda2))
106.0ms
(log1p (* (sin lambda1) (cos lambda2)))
142.0ms
(* (* (sin lambda1) (sin lambda2)) (* (sin phi1) (cos phi2)))
155.0ms
(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))

simplify1.8s

Counts
98 → 98
Iterations

Useful iterations: done (1.8s)

IterNodesCost
01551244
13791216
21543961
done5000959

prune879.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 0.0b

regimes22.0ms