Details

Time bar (total: 32.3s)

sample525.0ms

Algorithm
intervals
Results
317.0ms115×body1280valid
147.0ms85×body640valid
22.0ms21×body320valid
8.0ms9×body160valid
8.0ms26×body80valid

simplify12.0ms

Counts
1 → 1
Iterations
IterNodes
done21
221
120
014

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.2b

localize92.0ms

Local error

Found 4 expressions with local error:

0.2b
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
0.6b
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
2.4b
(cos (- lambda1 lambda2))
2.6b
(sin (- lambda1 lambda2))

rewrite53.0ms

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)))))
18.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
17.0ms
(cos (- lambda1 lambda2))
17.0ms
(sin (- lambda1 lambda2))

series252.0ms

Counts
4 → 12
Calls
4 calls:
18.0ms
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
166.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
32.0ms
(cos (- lambda1 lambda2))
36.0ms
(sin (- lambda1 lambda2))

simplify2.5s

Counts
56 → 56
Iterations
IterNodes
done5001
42616
31179
2486
1211
0101

prune537.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.9b

localize93.0ms

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)))))
0.6b
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
2.4b
(cos (- lambda1 lambda2))

rewrite37.0ms

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:
11.0ms
(* (cos lambda1) (sin lambda2))
0.0ms
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
16.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
9.0ms
(cos (- lambda1 lambda2))

series234.0ms

Counts
4 → 12
Calls
4 calls:
53.0ms
(* (cos lambda1) (sin lambda2))
12.0ms
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
146.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
24.0ms
(cos (- lambda1 lambda2))

simplify2.0s

Counts
64 → 64
Iterations
IterNodes
done5005
32585
2726
1276
0122

prune732.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.1b

localize64.0ms

Local error

Found 4 expressions with local error:

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

rewrite48.0ms

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-mult
Counts
4 → 61
Calls
4 calls:
13.0ms
(* (cos lambda1) (sin lambda2))
24.0ms
(* (sin lambda1) (sin 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))))))
10.0ms
(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

series514.0ms

Counts
4 → 12
Calls
4 calls:
64.0ms
(* (cos lambda1) (sin lambda2))
61.0ms
(* (sin lambda1) (sin lambda2))
25.0ms
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
364.0ms
(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

simplify3.0s

Counts
73 → 73
Iterations
IterNodes
done5001
34115
2946
1331
0137

prune1.2s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

localize80.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin lambda2) (sin lambda1))
0.2b
(exp (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda2) (sin lambda1))))))
0.6b
(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda2) (sin lambda1)))))
0.7b
(log (exp (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda2) (sin lambda1)))))))

rewrite78.0ms

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×associate-+r+ sum-log exp-sum rem-exp-log
1×distribute-rgt-in +-commutative distribute-lft-in flip3-+ rem-log-exp pow-prod-down prod-exp *-commutative cbrt-unprod flip-+ sin-mult unswap-sqr
Counts
4 → 65
Calls
4 calls:
12.0ms
(* (sin lambda2) (sin lambda1))
19.0ms
(exp (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda2) (sin lambda1))))))
20.0ms
(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda2) (sin lambda1)))))
26.0ms
(log (exp (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda2) (sin lambda1)))))))

series1.1s

Counts
4 → 12
Calls
4 calls:
65.0ms
(* (sin lambda2) (sin lambda1))
405.0ms
(exp (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda2) (sin lambda1))))))
328.0ms
(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda2) (sin lambda1)))))
283.0ms
(log (exp (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda2) (sin lambda1)))))))

simplify3.2s

Counts
77 → 77
Iterations
IterNodes
done5000
34505
2856
1307
0129

prune671.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.1b

regimes824.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify7.0ms

Iterations
IterNodes
done34
134
024

end0.0ms

sample14.4s

Algorithm
intervals
Results
8.4s3541×body1280valid
3.9s2316×body640valid
1.3s985×body320valid
253.0ms416×body160valid
245.0ms742×body80valid