Details

Time bar (total: 50.6s)

sample413.0ms

Algorithm
intervals
Results
229.0ms109×body1280valid
67.0ms61×body640valid
28.0ms39×body320valid
10.0ms18×body160valid
7.0ms29×body80valid

simplify53.0ms

Counts
1 → 1
Iterations
IterNodes
done21
221
120
014

prune27.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.5b

localize186.0ms

Local error

Found 4 expressions with local error:

0.2b
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
0.4b
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
3.3b
(sin (- lambda1 lambda2))
3.4b
(cos (- lambda1 lambda2))

rewrite113.0ms

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:
2.0ms
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
41.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
43.0ms
(sin (- lambda1 lambda2))
23.0ms
(cos (- lambda1 lambda2))

series415.0ms

Counts
4 → 12
Calls
4 calls:
76.0ms
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
247.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
49.0ms
(sin (- lambda1 lambda2))
43.0ms
(cos (- lambda1 lambda2))

simplify5.8s

Counts
56 → 56
Iterations
IterNodes
done5007
42653
31172
2478
1210
0101

prune1.2s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.3b

localize253.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (cos lambda1) (sin lambda2))
0.2b
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
0.4b
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
3.4b
(cos (- lambda1 lambda2))

rewrite154.0ms

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-+ unswap-sqr
Counts
4 → 52
Calls
4 calls:
55.0ms
(* (cos lambda1) (sin lambda2))
3.0ms
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
43.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
49.0ms
(cos (- lambda1 lambda2))

series469.0ms

Counts
4 → 12
Calls
4 calls:
103.0ms
(* (cos lambda1) (sin lambda2))
91.0ms
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
229.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
46.0ms
(cos (- lambda1 lambda2))

simplify4.9s

Counts
64 → 64
Iterations
IterNodes
done5001
32109
2668
1273
0122

prune1.4s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize326.0ms

Local error

Found 4 expressions with local error:

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
(* (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)))))

rewrite238.0ms

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
3×associate-*r/
2×distribute-rgt-in associate-+r+ distribute-lft-in flip3-+ pow-prod-down prod-exp *-commutative cbrt-unprod flip-+ sin-mult unswap-sqr
1×+-commutative sum-log frac-add cos-mult
Counts
4 → 66
Calls
4 calls:
3.0ms
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
159.0ms
(* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
29.0ms
(* (sin lambda1) (sin lambda2))
41.0ms
(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

series1.2s

Counts
4 → 12
Calls
4 calls:
132.0ms
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
339.0ms
(* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
101.0ms
(* (sin lambda1) (sin lambda2))
586.0ms
(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

simplify4.6s

Counts
78 → 78
Iterations
IterNodes
done5007
21561
1417
0154

prune1.7s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize372.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin lambda2) (sin lambda1))
0.2b
(exp (+ (cos phi1) (* (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda2) (sin lambda1))) (cos phi2))))
0.5b
(+ (cos phi1) (* (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda2) (sin lambda1))) (cos phi2)))
0.6b
(log (exp (+ (cos phi1) (* (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda2) (sin lambda1))) (cos phi2)))))

rewrite161.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt
9×*-un-lft-identity add-cube-cbrt add-log-exp
7×pow1
6×exp-prod add-cbrt-cube add-exp-log
4×log-prod log-pow insert-posit16
3×associate-*r* associate-*l*
2×sum-log exp-sum rem-exp-log
1×+-commutative flip3-+ rem-log-exp pow-prod-down prod-exp *-commutative cbrt-unprod flip-+ sin-mult unswap-sqr
Counts
4 → 63
Calls
4 calls:
41.0ms
(* (sin lambda2) (sin lambda1))
34.0ms
(exp (+ (cos phi1) (* (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda2) (sin lambda1))) (cos phi2))))
30.0ms
(+ (cos phi1) (* (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda2) (sin lambda1))) (cos phi2)))
52.0ms
(log (exp (+ (cos phi1) (* (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda2) (sin lambda1))) (cos phi2)))))

series2.2s

Counts
4 → 12
Calls
4 calls:
111.0ms
(* (sin lambda2) (sin lambda1))
900.0ms
(exp (+ (cos phi1) (* (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda2) (sin lambda1))) (cos phi2))))
580.0ms
(+ (cos phi1) (* (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda2) (sin lambda1))) (cos phi2)))
589.0ms
(log (exp (+ (cos phi1) (* (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda2) (sin lambda1))) (cos phi2)))))

simplify8.9s

Counts
75 → 75
Iterations
IterNodes
done5000
34451
2874
1296
0125

prune1.6s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

regimes2.2s

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify29.0ms

Iterations
IterNodes
done34
134
024

end0.0ms

sample11.8s

Algorithm
intervals
Results
7.1s3530×body1280valid
3.0s2364×body640valid
832.0ms939×body320valid
256.0ms727×body80valid
214.0ms440×body160valid