Details

Time bar (total: 52.8s)

sample482.0ms

Algorithm
intervals
Results
275.0ms115×body1280valid
136.0ms74×body640valid
34.0ms34×body320valid
9.0ms12×body160valid
6.0ms21×body80valid

simplify18.0ms

Counts
1 → 1
Iterations
IterNodes
321
221
120
014

prune19.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.3b

localize69.0ms

Local error

Found 4 expressions with local error:

0.2b
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
0.5b
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
3.1b
(cos (- lambda1 lambda2))
3.2b
(sin (- lambda1 lambda2))

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
6×add-log-exp
4×add-sqr-sqrt pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt insert-posit16
3×cos-diff
2×cos-sum associate-+r+ sub-neg sin-sum
1×distribute-rgt-in +-commutative sum-log distribute-lft-in flip3-+ sin-diff flip-+
Counts
4 → 44
Calls
4 calls:
0.0ms
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
16.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
14.0ms
(cos (- lambda1 lambda2))
9.0ms
(sin (- lambda1 lambda2))

series245.0ms

Counts
4 → 12
Calls
4 calls:
10.0ms
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
171.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
39.0ms
(cos (- lambda1 lambda2))
25.0ms
(sin (- lambda1 lambda2))

simplify920.0ms

Counts
56 → 56
Iterations
IterNodes
42207
31046
2467
1209
0101

prune1.0s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 1.1b

localize69.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin lambda1) (cos lambda2))
0.2b
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
0.5b
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
3.1b
(cos (- lambda1 lambda2))

rewrite66.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt
6×pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt add-log-exp
4×insert-posit16
3×cos-diff associate-*r* associate-*l*
2×cos-sum associate-+r+
1×distribute-rgt-in +-commutative sum-log sub-neg distribute-lft-in flip3-+ pow-prod-down prod-exp *-commutative cbrt-unprod flip-+ sin-cos-mult unswap-sqr
Counts
4 → 53
Calls
4 calls:
28.0ms
(* (sin lambda1) (cos lambda2))
0.0ms
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
17.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
19.0ms
(cos (- lambda1 lambda2))

series245.0ms

Counts
4 → 12
Calls
4 calls:
58.0ms
(* (sin lambda1) (cos lambda2))
22.0ms
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
145.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
19.0ms
(cos (- lambda1 lambda2))

simplify1.8s

Counts
65 → 65
Iterations
IterNodes
43814
31659
2671
1282
0127

prune1.5s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize82.0ms

Local error

Found 4 expressions with local error:

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

rewrite57.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
8×pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt
6×associate-*r* associate-*l* add-log-exp
4×insert-posit16
2×associate-+r+ pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×distribute-rgt-in +-commutative sum-log distribute-lft-in flip3-+ flip-+ sin-cos-mult sin-mult
Counts
4 → 62
Calls
4 calls:
21.0ms
(* (sin lambda1) (cos lambda2))
0.0ms
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
24.0ms
(* (sin lambda1) (sin lambda2))
11.0ms
(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

series490.0ms

Counts
4 → 12
Calls
4 calls:
75.0ms
(* (sin lambda1) (cos lambda2))
28.0ms
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
48.0ms
(* (sin lambda1) (sin lambda2))
340.0ms
(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

simplify1.7s

Counts
74 → 74
Iterations
IterNodes
34392
2963
1327
0140

prune1.7s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize145.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (- (* (cos phi2) (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2)))) (cos phi1)) (* (cos phi2) (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2)))))
0.4b
(/ (+ (* (* (* (cos phi2) (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2)))) (* (cos phi2) (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))))) (* (cos phi2) (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))))) (* (cos phi1) (* (cos phi1) (cos phi1)))) (+ (* (- (* (cos phi2) (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2)))) (cos phi1)) (* (cos phi2) (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))))) (* (cos phi1) (cos phi1))))
0.4b
(* (* (cos phi2) (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2)))) (* (cos phi2) (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2)))))
0.8b
(- (* (cos phi2) (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2)))) (cos phi1))

rewrite1.8s

Algorithm
rewrite-expression-head
Rules
273×associate-*r/
136×frac-add cos-mult
102×frac-times
65×associate-/l/
64×flip3-+ flip-+
62×sin-mult
48×pow1
34×associate-*l/
23×add-cbrt-cube add-exp-log
20×pow-prod-down
14×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
13×associate-/r/
12×times-frac
11×prod-exp cbrt-unprod
9×distribute-rgt-in distribute-lft-in flip3-- flip--
6×add-log-exp
4×cube-unmult associate-*l* pow3 pow-sqr sum-cubes pow-prod-up insert-posit16 associate-/l*
3×associate-/r*
2×pow-plus associate-*r* associate--l+ *-commutative
1×pow2 cbrt-undiv clear-num sub-neg frac-2neg diff-log swap-sqr div-exp div-inv
Counts
4 → 213
Calls
4 calls:
254.0ms
(* (- (* (cos phi2) (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2)))) (cos phi1)) (* (cos phi2) (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2)))))
1.2s
(/ (+ (* (* (* (cos phi2) (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2)))) (* (cos phi2) (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))))) (* (cos phi2) (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))))) (* (cos phi1) (* (cos phi1) (cos phi1)))) (+ (* (- (* (cos phi2) (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2)))) (cos phi1)) (* (cos phi2) (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))))) (* (cos phi1) (cos phi1))))
246.0ms
(* (* (cos phi2) (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2)))) (* (cos phi2) (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2)))))
51.0ms
(- (* (cos phi2) (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2)))) (cos phi1))

series5.1s

Counts
4 → 12
Calls
4 calls:
609.0ms
(* (- (* (cos phi2) (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2)))) (cos phi1)) (* (cos phi2) (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2)))))
4.0s
(/ (+ (* (* (* (cos phi2) (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2)))) (* (cos phi2) (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))))) (* (cos phi2) (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))))) (* (cos phi1) (* (cos phi1) (cos phi1)))) (+ (* (- (* (cos phi2) (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2)))) (cos phi1)) (* (cos phi2) (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))))) (* (cos phi1) (cos phi1))))
213.0ms
(* (* (cos phi2) (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2)))) (* (cos phi2) (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2)))))
247.0ms
(- (* (cos phi2) (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2)))) (cos phi1))

simplify9.3s

Counts
225 → 225
Iterations
IterNodes
28032
11567
0495

prune7.7s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

regimes1.3s

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify13.0ms

Iterations
IterNodes
245
145
031

end0.0ms

sample17.0s

Algorithm
intervals
Results
10.6s3598×body1280valid
4.3s2305×body640valid
1.1s939×body320valid
365.0ms448×body160valid
233.0ms710×body80valid