Details

Time bar (total: 27.2s)

sample391.0ms

Algorithm
intervals
Results
276.0ms135×body1280valid
56.0ms54×body640valid
19.0ms29×body320valid
5.0ms12×body160valid
5.0ms26×body80valid

simplify18.0ms

Counts
1 → 1
Iterations
IterNodes
done21
221
120
014

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.0b

localize85.0ms

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))))
3.6b
(sin (- lambda1 lambda2))
3.7b
(cos (- lambda1 lambda2))

rewrite50.0ms

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
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 → 40
Calls
4 calls:
0.0ms
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
13.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
16.0ms
(sin (- lambda1 lambda2))
20.0ms
(cos (- lambda1 lambda2))

series218.0ms

Counts
4 → 12
Calls
4 calls:
23.0ms
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
139.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
35.0ms
(sin (- lambda1 lambda2))
21.0ms
(cos (- lambda1 lambda2))

simplify2.6s

Counts
52 → 52
Iterations
IterNodes
done5002
42583
31176
2476
1207
097

prune511.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.8b

localize102.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (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))))
3.7b
(cos (- lambda1 lambda2))

rewrite59.0ms

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
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 → 48
Calls
4 calls:
17.0ms
(* (cos lambda1) (sin lambda2))
0.0ms
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
14.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
25.0ms
(cos (- lambda1 lambda2))

series280.0ms

Counts
4 → 12
Calls
4 calls:
75.0ms
(* (cos lambda1) (sin lambda2))
14.0ms
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
160.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
32.0ms
(cos (- lambda1 lambda2))

simplify2.2s

Counts
60 → 60
Iterations
IterNodes
done5000
32083
2662
1269
0118

prune803.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize94.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (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)))))

rewrite42.0ms

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
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 → 57
Calls
4 calls:
20.0ms
(* (cos lambda1) (sin lambda2))
13.0ms
(* (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))))))
7.0ms
(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

series500.0ms

Counts
4 → 12
Calls
4 calls:
60.0ms
(* (cos lambda1) (sin lambda2))
86.0ms
(* (sin lambda1) (sin lambda2))
39.0ms
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
315.0ms
(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

simplify2.9s

Counts
69 → 69
Iterations
IterNodes
done5001
34089
2967
1328
0133

prune782.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize110.0ms

Local error

Found 4 expressions with local error:

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

rewrite95.0ms

Algorithm
rewrite-expression-head
Rules
11×add-log-exp
8×add-sqr-sqrt
6×pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt
4×sum-log
3×flip3-+ associate-*r* associate-*l* flip-+ sin-mult
2×+-commutative frac-add associate-*r/
1×associate-+l+ pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
Counts
4 → 52
Calls
4 calls:
58.0ms
(+ (+ (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2)))) (* (cos phi2) (* (sin lambda1) (sin lambda2))))
19.0ms
(* (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)))) (* (cos phi2) (* (sin lambda1) (sin lambda2)))))
15.0ms
(+ (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2))))

series646.0ms

Counts
4 → 12
Calls
4 calls:
337.0ms
(+ (+ (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2)))) (* (cos phi2) (* (sin lambda1) (sin lambda2))))
84.0ms
(* (sin lambda1) (sin lambda2))
39.0ms
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (+ (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2)))) (* (cos phi2) (* (sin lambda1) (sin lambda2)))))
185.0ms
(+ (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2))))

simplify1.8s

Counts
64 → 64
Iterations
IterNodes
done5000
21174
1334
0130

prune723.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

regimes820.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify5.0ms

Iterations
IterNodes
done32
132
023

end0.0ms

sample11.4s

Algorithm
intervals
Results
5.9s3573×body1280valid
4.0s2327×body640valid
691.0ms944×body320valid
215.0ms446×body160valid
158.0ms710×body80valid