Details

Time bar (total: 37.3s)

sample523.0ms

Algorithm
intervals
Results
280.0ms114×body1280valid
162.0ms75×body640valid
36.0ms35×body320valid
11.0ms15×body160valid
5.0ms17×body80valid

simplify19.0ms

Counts
1 → 1
Iterations
IterNodes
321
221
120
014

prune20.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.8b

localize71.0ms

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))))
2.4b
(cos (- lambda1 lambda2))
2.7b
(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)))))
9.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
16.0ms
(cos (- lambda1 lambda2))
14.0ms
(sin (- lambda1 lambda2))

series252.0ms

Counts
4 → 12
Calls
4 calls:
19.0ms
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
174.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
30.0ms
(cos (- lambda1 lambda2))
29.0ms
(sin (- lambda1 lambda2))

simplify1.1s

Counts
56 → 56
Iterations
IterNodes
42207
31046
2467
1209
0101

prune1.0s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.6b

localize69.0ms

Local error

Found 4 expressions with local error:

0.2b
(atan2 (* (cos phi2) (sin (- lambda1 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)))))
2.7b
(sin (- lambda1 lambda2))

rewrite41.0ms

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×associate-*r* associate-*l*
2×associate-+r+ sin-sum
1×distribute-rgt-in +-commutative sum-log sub-neg distribute-lft-in flip3-+ pow-prod-down prod-exp sin-diff *-commutative cbrt-unprod flip-+ sin-mult unswap-sqr
Counts
4 → 53
Calls
4 calls:
0.0ms
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
22.0ms
(* (sin lambda1) (sin lambda2))
9.0ms
(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))
8.0ms
(sin (- lambda1 lambda2))

series431.0ms

Counts
4 → 12
Calls
4 calls:
14.0ms
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
53.0ms
(* (sin lambda1) (sin lambda2))
338.0ms
(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))
26.0ms
(sin (- lambda1 lambda2))

simplify1.3s

Counts
65 → 65
Iterations
IterNodes
33698
2783
1278
0124

prune1.2s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize72.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (sin lambda1) (cos lambda2))
0.1b
(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
0.2b
(* (sin lambda1) (sin lambda2))
0.5b
(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

rewrite150.0ms

Algorithm
rewrite-expression-head
Rules
16×add-sqr-sqrt
10×pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt
9×associate-*r* associate-*l*
6×add-log-exp
4×insert-posit16
3×distribute-rgt-in distribute-lft-in pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
2×associate-+r+ sub-neg associate-*r/
1×+-commutative sum-log flip3-+ flip3-- flip-+ sin-cos-mult flip-- sin-mult
Counts
4 → 79
Calls
4 calls:
23.0ms
(* (sin lambda1) (cos lambda2))
100.0ms
(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
11.0ms
(* (sin lambda1) (sin lambda2))
13.0ms
(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

series661.0ms

Counts
4 → 12
Calls
4 calls:
68.0ms
(* (sin lambda1) (cos lambda2))
193.0ms
(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
68.0ms
(* (sin lambda1) (sin lambda2))
332.0ms
(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

simplify6.1s

Counts
91 → 91
Iterations
IterNodes
37383
21405
1431
0168

prune1.8s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize60.0ms

Local error

Found 4 expressions with local error:

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

rewrite106.0ms

Algorithm
rewrite-expression-head
Rules
11×pow1 add-cbrt-cube add-exp-log
9×add-sqr-sqrt
8×add-log-exp
7×*-un-lft-identity add-cube-cbrt
6×associate-*l*
4×associate-*r* pow-prod-down prod-exp cbrt-unprod insert-posit16
2×+-commutative associate-+r+ sum-log flip3-+ *-commutative distribute-rgt-neg-out flip-+
1×distribute-rgt-in distribute-lft-in unsub-neg associate-*r/ sin-cos-mult sin-mult distribute-lft-out unswap-sqr
Counts
4 → 69
Calls
4 calls:
41.0ms
(+ (* (cos phi2) (* (sin lambda1) (cos lambda2))) (* (cos phi2) (- (* (cos lambda1) (sin lambda2)))))
32.0ms
(* (cos phi2) (* (sin lambda1) (cos lambda2)))
17.0ms
(* (sin lambda1) (sin lambda2))
15.0ms
(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

series749.0ms

Counts
4 → 12
Calls
4 calls:
239.0ms
(+ (* (cos phi2) (* (sin lambda1) (cos lambda2))) (* (cos phi2) (- (* (cos lambda1) (sin lambda2)))))
104.0ms
(* (cos phi2) (* (sin lambda1) (cos lambda2)))
81.0ms
(* (sin lambda1) (sin lambda2))
325.0ms
(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

simplify2.9s

Counts
81 → 81
Iterations
IterNodes
37862
21390
1410
0151

prune1.7s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

regimes785.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify12.0ms

Iterations
IterNodes
449
349
248
142
025

end0.0ms

sample16.3s

Algorithm
intervals
Results
9.5s3557×body1280valid
4.8s2398×body640valid
964.0ms925×body320valid
309.0ms720×body80valid
272.0ms400×body160valid