Details

Time bar (total: 21.6s)

sample701.0ms

Algorithm
intervals
Results
509.0ms136×body1280valid
122.0ms75×body640valid
27.0ms23×body320valid
6.0ms18×body80valid
3.0ms4×body160valid

simplify63.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01724
12724
24624
37124
47224
done7224

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.2b

localize77.0ms

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))

rewrite119.0ms

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:
29.0ms
(* (sin (- lambda1 lambda2)) (cos phi2))
45.0ms
(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
21.0ms
(sin (- lambda1 lambda2))
22.0ms
(cos (- lambda1 lambda2))

series346.0ms

Counts
4 → 12
Calls
4 calls:
103.0ms
(* (sin (- lambda1 lambda2)) (cos phi2))
181.0ms
(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
42.0ms
(sin (- lambda1 lambda2))
20.0ms
(cos (- lambda1 lambda2))

simplify7.6s

Counts
72 → 72
Iterations

Useful iterations: 3 (1.6s)

IterNodesCost
0116760
1258748
2816644
32177642
43715642
done5000642

prune530.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 6.5b

localize44.0ms

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))

rewrite114.0ms

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* add-log-exp
5×cos-diff
4×associate-*l* pow-prod-down prod-exp cbrt-unprod
2×distribute-rgt-in sub-neg cos-sum distribute-lft-in *-commutative sin-cos-mult associate--r+
1×flip3-- diff-log associate-*l/ flip-- unswap-sqr
Counts
4 → 64
Calls
4 calls:
14.0ms
(- (* (cos phi1) (sin phi2)) (* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2))))
20.0ms
(* (sin lambda1) (cos lambda2))
55.0ms
(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
23.0ms
(cos (- lambda1 lambda2))

series435.0ms

Counts
4 → 12
Calls
4 calls:
215.0ms
(- (* (cos phi1) (sin phi2)) (* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2))))
61.0ms
(* (sin lambda1) (cos lambda2))
134.0ms
(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
24.0ms
(cos (- lambda1 lambda2))

simplify4.0s

Counts
76 → 76
Iterations

Useful iterations: 3 (1.7s)

IterNodesCost
01411015
1337973
21122873
33753871
done5000871

prune681.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize86.0ms

Local error

Found 4 expressions with local error:

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

rewrite171.0ms

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:
23.0ms
(* (sin lambda1) (cos lambda2))
15.0ms
(* (sin lambda1) (sin lambda2))
66.0ms
(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
61.0ms
(* (* (cos lambda1) (cos lambda2)) (* (sin phi1) (cos phi2)))

series553.0ms

Counts
4 → 12
Calls
4 calls:
88.0ms
(* (sin lambda1) (cos lambda2))
88.0ms
(* (sin lambda1) (sin lambda2))
166.0ms
(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
212.0ms
(* (* (cos lambda1) (cos lambda2)) (* (sin phi1) (cos phi2)))

simplify1.8s

Counts
100 → 100
Iterations

Useful iterations: 2 (362.0ms)

IterNodesCost
01611238
14081212
21624952
done5000952

prune876.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.1b

localize79.0ms

Local error

Found 4 expressions with local error:

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

rewrite268.0ms

Algorithm
rewrite-expression-head
Rules
32×pow1 add-exp-log add-cbrt-cube
18×pow-prod-down prod-exp cbrt-unprod
10×add-sqr-sqrt associate-*l*
8×add-cube-cbrt *-un-lft-identity
6×associate-*r*
4×associate-*r/ *-commutative sin-cos-mult add-log-exp
3×sin-mult
1×frac-times associate-*l/ unswap-sqr
Counts
4 → 85
Calls
4 calls:
55.0ms
(* (cos lambda2) (* (sin phi1) (cos phi2)))
78.0ms
(* (cos lambda1) (* (cos lambda2) (* (sin phi1) (cos phi2))))
31.0ms
(* (sin lambda1) (sin lambda2))
97.0ms
(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))

series618.0ms

Counts
4 → 12
Calls
4 calls:
147.0ms
(* (cos lambda2) (* (sin phi1) (cos phi2)))
209.0ms
(* (cos lambda1) (* (cos lambda2) (* (sin phi1) (cos phi2))))
94.0ms
(* (sin lambda1) (sin lambda2))
167.0ms
(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))

simplify1.8s

Counts
97 → 97
Iterations

Useful iterations: 2 (294.0ms)

IterNodesCost
01391230
13401208
21451942
done5000942

prune740.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

regimes17.0ms