Details

Time bar (total: 8.9s)

sample175.0ms

Algorithm
intervals
Results
104.0ms121×body1280valid
35.0ms72×body640valid
16.0ms32×body320valid
3.0ms27×body80valid
1.0ms4×body160valid

simplify5.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
02012
12112
22112
done2112

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.9b

localize20.0ms

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))))
2.5b
(sin (- lambda1 lambda2))
2.8b
(cos (- lambda1 lambda2))

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
6×add-log-exp
4×pow1 add-exp-log add-sqr-sqrt add-cube-cbrt *-un-lft-identity add-cbrt-cube
3×cos-diff
2×sub-neg cos-sum associate-+r+ sin-sum
1×+-commutative distribute-rgt-in distribute-lft-in flip3-+ sum-log sin-diff flip-+
Counts
4 → 40
Calls
4 calls:
0.0ms
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
10.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
10.0ms
(sin (- lambda1 lambda2))
10.0ms
(cos (- lambda1 lambda2))

series160.0ms

Counts
4 → 12
Calls
4 calls:
11.0ms
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
106.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
22.0ms
(sin (- lambda1 lambda2))
22.0ms
(cos (- lambda1 lambda2))

simplify117.0ms

Counts
52 → 52
Iterations

Useful iterations: 2 (13.0ms)

IterNodesCost
0205421
1508375
21327374
33684374
45001374
done5001374

prune222.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.7b

localize29.0ms

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 lambda2)))))
0.2b
(* (cos lambda1) (sin (- lambda2)))
0.6b
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
2.8b
(cos (- lambda1 lambda2))

rewrite37.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt
6×pow1 add-exp-log add-cube-cbrt *-un-lft-identity add-cbrt-cube add-log-exp
3×cos-diff associate-*r* associate-*l*
2×cos-sum associate-+r+
1×+-commutative distribute-rgt-in sub-neg distribute-lft-in flip3-+ pow-prod-down prod-exp sin-neg sum-log *-commutative distribute-rgt-neg-out cbrt-unprod flip-+ unswap-sqr
Counts
4 → 49
Calls
4 calls:
0.0ms
(atan2 (* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
14.0ms
(* (cos lambda1) (sin (- lambda2)))
9.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
12.0ms
(cos (- lambda1 lambda2))

series196.0ms

Counts
4 → 12
Calls
4 calls:
14.0ms
(atan2 (* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
57.0ms
(* (cos lambda1) (sin (- lambda2)))
107.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
18.0ms
(cos (- lambda1 lambda2))

simplify64.0ms

Counts
61 → 61
Iterations

Useful iterations: 2 (21.0ms)

IterNodesCost
0276573
1822502
22610501
35001501
done5001501

prune334.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize32.0ms

Local error

Found 4 expressions with local error:

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

rewrite39.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
8×pow1 add-exp-log add-cube-cbrt *-un-lft-identity add-cbrt-cube
6×associate-*r* associate-*l* add-log-exp
2×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×+-commutative flip3-+ sin-neg sum-log distribute-rgt-neg-out flip-+ sin-mult
Counts
4 → 56
Calls
4 calls:
0.0ms
(atan2 (* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))) (+ (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2))) (* (* (sin lambda1) (sin lambda2)) (cos phi2))))
17.0ms
(* (cos lambda1) (sin (- lambda2)))
11.0ms
(* (sin lambda1) (sin lambda2))
9.0ms
(+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))

series253.0ms

Counts
4 → 12
Calls
4 calls:
19.0ms
(atan2 (* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))) (+ (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2))) (* (* (sin lambda1) (sin lambda2)) (cos phi2))))
51.0ms
(* (cos lambda1) (sin (- lambda2)))
51.0ms
(* (sin lambda1) (sin lambda2))
131.0ms
(+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))

simplify39.0ms

Counts
68 → 68
Iterations

Useful iterations: 2 (33.0ms)

IterNodesCost
0328713
11194617
25002616
done5002616

prune392.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize38.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin lambda1) (sin lambda2))
0.2b
(exp (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2))))
0.4b
(+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))
0.6b
(log (exp (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))))

rewrite58.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt
9×add-cube-cbrt *-un-lft-identity add-log-exp
7×pow1
6×add-exp-log exp-prod add-cbrt-cube
4×log-prod log-pow
3×associate-*r* associate-*l*
2×exp-sum sum-log rem-exp-log
1×+-commutative flip3-+ rem-log-exp pow-prod-down prod-exp *-commutative cbrt-unprod flip-+ sin-mult unswap-sqr
Counts
4 → 59
Calls
4 calls:
12.0ms
(* (sin lambda1) (sin lambda2))
15.0ms
(exp (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2))))
9.0ms
(+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))
21.0ms
(log (exp (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))))

series495.0ms

Counts
4 → 12
Calls
4 calls:
46.0ms
(* (sin lambda1) (sin lambda2))
177.0ms
(exp (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2))))
133.0ms
(+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))
138.0ms
(log (exp (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))))

simplify101.0ms

Counts
71 → 71
Iterations

Useful iterations: 2 (24.0ms)

IterNodesCost
0248604
1925534
23624532
35001532
done5001532

prune360.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

regimes447.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 0.2b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04545
14545
done4545

end0.0ms

sample5.2s

Algorithm
intervals
Results
3.2s3552×body1280valid
1.2s2458×body640valid
305.0ms925×body320valid
80.0ms377×body160valid
66.0ms688×body80valid