Details

Time bar (total: 43.5s)

sample503.0ms

Algorithm
intervals
Results
311.0ms115×body1280valid
117.0ms74×body640valid
36.0ms34×body320valid
10.0ms12×body160valid
6.0ms21×body80valid

simplify11.0ms

Counts
1 → 1
Iterations
IterNodes
done21
221
120
014

prune36.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.3b

localize60.0ms

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))

rewrite59.0ms

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)))))
17.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
16.0ms
(cos (- lambda1 lambda2))
16.0ms
(sin (- lambda1 lambda2))

series230.0ms

Counts
4 → 12
Calls
4 calls:
10.0ms
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
148.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
31.0ms
(cos (- lambda1 lambda2))
40.0ms
(sin (- lambda1 lambda2))

simplify1.2s

Counts
56 → 56
Iterations
IterNodes
done2001
42001
31179
2486
1211
0101

prune933.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 1.1b

localize63.0ms

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))

rewrite40.0ms

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:
16.0ms
(* (sin lambda1) (cos lambda2))
0.0ms
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
14.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
8.0ms
(cos (- lambda1 lambda2))

series314.0ms

Counts
4 → 12
Calls
4 calls:
66.0ms
(* (sin lambda1) (cos lambda2))
24.0ms
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
192.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
31.0ms
(cos (- lambda1 lambda2))

simplify1.4s

Counts
65 → 65
Iterations
IterNodes
done2000
42000
31893
2697
1284
0127

prune1.4s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize119.0ms

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)))))

rewrite39.0ms

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:
11.0ms
(* (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))))))
12.0ms
(* (sin lambda1) (sin lambda2))
15.0ms
(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

series525.0ms

Counts
4 → 12
Calls
4 calls:
58.0ms
(* (sin lambda1) (cos lambda2))
31.0ms
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
86.0ms
(* (sin lambda1) (sin lambda2))
349.0ms
(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

simplify1.1s

Counts
74 → 74
Iterations
IterNodes
done2011
32011
2999
1329
0140

prune1.6s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize158.0ms

Local error

Found 4 expressions with local error:

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

rewrite1.7s

Algorithm
rewrite-expression-head
Rules
283×associate-*r/
136×frac-add cos-mult
102×frac-times
65×associate-/l/
64×flip3-+ flip-+
62×sin-mult
48×pow1
24×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×distribute-rgt-in distribute-lft-in prod-exp cbrt-unprod
9×flip3-- flip--
8×cube-unmult
6×associate--l+ add-log-exp
4×associate-*r* pow-sqr sum-cubes pow-prod-up insert-posit16 associate-/l*
3×associate-/r* sub-neg
2×pow-plus associate-*l* *-commutative
1×pow2 cbrt-undiv clear-num frac-2neg diff-log swap-sqr div-exp div-inv
Counts
4 → 217
Calls
4 calls:
251.0ms
(* (* (cos phi2) (+ (* (sin lambda2) (sin lambda1)) (* (cos lambda1) (cos lambda2)))) (- (* (cos phi2) (+ (* (sin lambda2) (sin lambda1)) (* (cos lambda1) (cos lambda2)))) (cos phi1)))
1.2s
(/ (+ (* (* (cos phi2) (+ (* (sin lambda2) (sin lambda1)) (* (cos lambda1) (cos lambda2)))) (* (* (cos phi2) (+ (* (sin lambda2) (sin lambda1)) (* (cos lambda1) (cos lambda2)))) (* (cos phi2) (+ (* (sin lambda2) (sin lambda1)) (* (cos lambda1) (cos lambda2)))))) (* (cos phi1) (* (cos phi1) (cos phi1)))) (+ (* (* (cos phi2) (+ (* (sin lambda2) (sin lambda1)) (* (cos lambda1) (cos lambda2)))) (- (* (cos phi2) (+ (* (sin lambda2) (sin lambda1)) (* (cos lambda1) (cos lambda2)))) (cos phi1))) (* (cos phi1) (cos phi1))))
155.0ms
(* (* (cos phi2) (+ (* (sin lambda2) (sin lambda1)) (* (cos lambda1) (cos lambda2)))) (* (cos phi2) (+ (* (sin lambda2) (sin lambda1)) (* (cos lambda1) (cos lambda2)))))
65.0ms
(- (* (cos phi2) (+ (* (sin lambda2) (sin lambda1)) (* (cos lambda1) (cos lambda2)))) (cos phi1))

series5.1s

Counts
4 → 12
Calls
4 calls:
538.0ms
(* (* (cos phi2) (+ (* (sin lambda2) (sin lambda1)) (* (cos lambda1) (cos lambda2)))) (- (* (cos phi2) (+ (* (sin lambda2) (sin lambda1)) (* (cos lambda1) (cos lambda2)))) (cos phi1)))
4.0s
(/ (+ (* (* (cos phi2) (+ (* (sin lambda2) (sin lambda1)) (* (cos lambda1) (cos lambda2)))) (* (* (cos phi2) (+ (* (sin lambda2) (sin lambda1)) (* (cos lambda1) (cos lambda2)))) (* (cos phi2) (+ (* (sin lambda2) (sin lambda1)) (* (cos lambda1) (cos lambda2)))))) (* (cos phi1) (* (cos phi1) (cos phi1)))) (+ (* (* (cos phi2) (+ (* (sin lambda2) (sin lambda1)) (* (cos lambda1) (cos lambda2)))) (- (* (cos phi2) (+ (* (sin lambda2) (sin lambda1)) (* (cos lambda1) (cos lambda2)))) (cos phi1))) (* (cos phi1) (cos phi1))))
234.0ms
(* (* (cos phi2) (+ (* (sin lambda2) (sin lambda1)) (* (cos lambda1) (cos lambda2)))) (* (cos phi2) (+ (* (sin lambda2) (sin lambda1)) (* (cos lambda1) (cos lambda2)))))
319.0ms
(- (* (cos phi2) (+ (* (sin lambda2) (sin lambda1)) (* (cos lambda1) (cos lambda2)))) (cos phi1))

simplify1.8s

Counts
229 → 229
Iterations
IterNodes
done2002
22002
11747
0500

prune7.2s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

regimes1.0s

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify30.0ms

Iterations
IterNodes
done66
166
046

end0.0ms

sample16.8s

Algorithm
intervals
Results
10.1s3598×body1280valid
4.1s2305×body640valid
1.2s939×body320valid
692.0ms448×body160valid
229.0ms710×body80valid