Details

Time bar (total: 30.2s)

sample459.0ms

Algorithm
intervals
Results
298.0ms120×body1280valid
103.0ms76×body640valid
29.0ms30×body320valid
7.0ms23×body80valid
5.0ms7×body160valid

simplify16.0ms

Counts
1 → 1
Iterations
IterNodes
done21
221
120
014

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.1b

localize103.0ms

Local error

Found 4 expressions with local error:

0.2b
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
0.7b
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
3.1b
(cos (- lambda1 lambda2))
3.4b
(sin (- lambda1 lambda2))

rewrite37.0ms

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)))))
8.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
12.0ms
(cos (- lambda1 lambda2))
16.0ms
(sin (- lambda1 lambda2))

series237.0ms

Counts
4 → 12
Calls
4 calls:
16.0ms
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
165.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
22.0ms
(cos (- lambda1 lambda2))
33.0ms
(sin (- lambda1 lambda2))

simplify1.2s

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

prune517.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.8b

localize71.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
0.2b
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
0.7b
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
3.1b
(cos (- lambda1 lambda2))

rewrite97.0ms

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×distribute-rgt-in cos-diff sub-neg distribute-lft-in associate-*r* associate-*l*
2×cos-sum associate-+r+ associate-*r/
1×+-commutative sum-log flip3-+ flip3-- pow-prod-down prod-exp *-commutative cbrt-unprod flip-+ flip-- unswap-sqr
Counts
4 → 58
Calls
4 calls:
76.0ms
(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
0.0ms
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
12.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
8.0ms
(cos (- lambda1 lambda2))

series358.0ms

Counts
4 → 12
Calls
4 calls:
179.0ms
(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
24.0ms
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
137.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
19.0ms
(cos (- lambda1 lambda2))

simplify1.4s

Counts
70 → 70
Iterations
IterNodes
done2013
32013
2917
1312
0128

prune721.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.1b

localize114.0ms

Local error

Found 4 expressions with local error:

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

rewrite138.0ms

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×distribute-rgt-in sub-neg distribute-lft-in pow-prod-down prod-exp associate-*r/ *-commutative cbrt-unprod unswap-sqr
1×+-commutative sum-log flip3-+ flip3-- flip-+ flip-- sin-mult
Counts
4 → 65
Calls
4 calls:
84.0ms
(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos 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)))))
22.0ms
(* (sin lambda1) (sin lambda2))
30.0ms
(+ (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2))))

series454.0ms

Counts
4 → 12
Calls
4 calls:
190.0ms
(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
17.0ms
(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)))))
57.0ms
(* (sin lambda1) (sin lambda2))
190.0ms
(+ (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2))))

simplify1.2s

Counts
77 → 77
Iterations
IterNodes
done2003
32003
21139
1367
0144

prune766.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

localize158.0ms

Local error

Found 4 expressions with local error:

0.4b
(+ (* (* (* (cos lambda1) (cos lambda2)) (cos phi2)) (* (* (* (cos lambda1) (cos lambda2)) (cos phi2)) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))) (* (cos phi1) (* (cos phi1) (cos phi1))))
0.4b
(* (* (* (cos lambda1) (cos lambda2)) (cos phi2)) (- (* (* (cos lambda1) (cos lambda2)) (cos phi2)) (cos phi1)))
0.4b
(* (* (* (cos lambda1) (cos lambda2)) (cos phi2)) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))
1.2b
(- (* (* (cos lambda1) (cos lambda2)) (cos phi2)) (cos phi1))

rewrite873.0ms

Algorithm
rewrite-expression-head
Rules
127×pow1
72×pow-prod-down
49×add-cbrt-cube add-exp-log
33×prod-exp cbrt-unprod
26×cos-mult
24×associate-*l/
15×associate-*r/
9×pow-sqr pow-prod-up
8×frac-times add-log-exp
7×frac-add
5×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
4×associate-*r* insert-posit16
3×distribute-rgt-in sub-neg distribute-lft-in pow-plus flip3-- flip--
2×sqr-cos associate-+r+ cube-unmult associate-*l* *-commutative
1×pow2 +-commutative sum-log flip3-+ diff-log swap-sqr sum-cubes flip-+
Counts
4 → 130
Calls
4 calls:
496.0ms
(+ (* (* (* (cos lambda1) (cos lambda2)) (cos phi2)) (* (* (* (cos lambda1) (cos lambda2)) (cos phi2)) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))) (* (cos phi1) (* (cos phi1) (cos phi1))))
159.0ms
(* (* (* (cos lambda1) (cos lambda2)) (cos phi2)) (- (* (* (cos lambda1) (cos lambda2)) (cos phi2)) (cos phi1)))
163.0ms
(* (* (* (cos lambda1) (cos lambda2)) (cos phi2)) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))
52.0ms
(- (* (* (cos lambda1) (cos lambda2)) (cos phi2)) (cos phi1))

series902.0ms

Counts
4 → 12
Calls
4 calls:
261.0ms
(+ (* (* (* (cos lambda1) (cos lambda2)) (cos phi2)) (* (* (* (cos lambda1) (cos lambda2)) (cos phi2)) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))) (* (cos phi1) (* (cos phi1) (cos phi1))))
324.0ms
(* (* (* (cos lambda1) (cos lambda2)) (cos phi2)) (- (* (* (cos lambda1) (cos lambda2)) (cos phi2)) (cos phi1)))
122.0ms
(* (* (* (cos lambda1) (cos lambda2)) (cos phi2)) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))
195.0ms
(- (* (* (cos lambda1) (cos lambda2)) (cos phi2)) (cos phi1))

simplify1.3s

Counts
142 → 142
Iterations
IterNodes
done2003
22003
1725
0220

prune1.4s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

regimes883.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify9.0ms

Iterations
IterNodes
done46
146
032

end0.0ms

sample16.7s

Algorithm
intervals
Results
10.6s3593×body1280valid
3.8s2366×body640valid
986.0ms913×body320valid
658.0ms713×body80valid
315.0ms415×body160valid