Details

Time bar (total: 28.7s)

sample412.0ms

Algorithm
intervals
Results
253.0ms118×body1280valid
66.0ms71×body640valid
54.0ms37×body320valid
5.0ms12×body160valid
4.0ms18×body80valid

simplify17.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01420
12020
22120
done2120

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.9b

localize34.0ms

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))))
3.7b
(sin (- lambda1 lambda2))
3.8b
(cos (- lambda1 lambda2))

rewrite61.0ms

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)))))
33.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
13.0ms
(sin (- lambda1 lambda2))
11.0ms
(cos (- lambda1 lambda2))

series197.0ms

Counts
4 → 12
Calls
4 calls:
13.0ms
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
132.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
24.0ms
(sin (- lambda1 lambda2))
28.0ms
(cos (- lambda1 lambda2))

simplify4.7s

Counts
52 → 52
Iterations

Useful iterations: 3 (318.0ms)

IterNodesCost
097702
1204687
2458615
3967613
42013613
54634613
done5000613

prune429.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.7b

localize43.0ms

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 phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
0.6b
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
3.8b
(cos (- lambda1 lambda2))

rewrite154.0ms

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×distribute-rgt-in cos-diff sub-neg distribute-lft-in associate-*r* associate-*l*
2×cos-sum associate-+r+ associate-*r/
1×+-commutative flip3-- flip3-+ pow-prod-down prod-exp sum-log *-commutative flip-- cbrt-unprod flip-+ unswap-sqr
Counts
4 → 54
Calls
4 calls:
1.0ms
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
106.0ms
(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
21.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
23.0ms
(cos (- lambda1 lambda2))

series399.0ms

Counts
4 → 12
Calls
4 calls:
15.0ms
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
222.0ms
(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
140.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
22.0ms
(cos (- lambda1 lambda2))

simplify2.0s

Counts
66 → 66
Iterations

Useful iterations: 3 (762.0ms)

IterNodesCost
01211182
12891166
28701032
327531030
done50001030

prune527.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize47.0ms

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

rewrite162.0ms

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
4×distribute-rgt-in sub-neg associate-+r+ distribute-lft-in
2×associate-*r/ pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×+-commutative flip3-- flip3-+ sin-neg sum-log distribute-rgt-neg-out flip-- flip-+ sin-mult
Counts
4 → 66
Calls
4 calls:
1.0ms
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (- (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin (- lambda2)))))))
96.0ms
(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
35.0ms
(* (sin lambda1) (sin (- lambda2)))
27.0ms
(+ (cos phi1) (* (cos phi2) (- (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin (- lambda2))))))

series700.0ms

Counts
4 → 12
Calls
4 calls:
23.0ms
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (- (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin (- lambda2)))))))
214.0ms
(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
67.0ms
(* (sin lambda1) (sin (- lambda2)))
395.0ms
(+ (cos phi1) (* (cos phi2) (- (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin (- lambda2))))))

simplify3.3s

Counts
78 → 78
Iterations

Useful iterations: 3 (1.5s)

IterNodesCost
01521579
13561549
211281366
338821323
done50011323

prune620.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize47.0ms

Local error

Found 4 expressions with local error:

0.2b
(exp (+ (* (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda2) (cos lambda1))) (cos phi2)) (cos phi1)))
0.2b
(* (sin lambda1) (sin lambda2))
0.6b
(+ (* (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda2) (cos lambda1))) (cos phi2)) (cos phi1))
0.8b
(log (exp (+ (* (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda2) (cos lambda1))) (cos phi2)) (cos phi1))))

rewrite214.0ms

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:
104.0ms
(exp (+ (* (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda2) (cos lambda1))) (cos phi2)) (cos phi1)))
18.0ms
(* (sin lambda1) (sin lambda2))
32.0ms
(+ (* (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda2) (cos lambda1))) (cos phi2)) (cos phi1))
57.0ms
(log (exp (+ (* (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda2) (cos lambda1))) (cos phi2)) (cos phi1))))

series1.0s

Counts
4 → 12
Calls
4 calls:
410.0ms
(exp (+ (* (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda2) (cos lambda1))) (cos phi2)) (cos phi1)))
55.0ms
(* (sin lambda1) (sin lambda2))
260.0ms
(+ (* (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda2) (cos lambda1))) (cos phi2)) (cos phi1))
282.0ms
(log (exp (+ (* (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda2) (cos lambda1))) (cos phi2)) (cos phi1))))

simplify1.3s

Counts
71 → 71
Iterations

Useful iterations: 3 (559.0ms)

IterNodesCost
01161338
12531292
26641132
320241112
done50021112

prune371.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.1b

regimes487.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02336
13236
done3236

end0.0ms

sample11.4s

Algorithm
intervals
Results
6.2s3555×body1280valid
2.9s2408×body640valid
804.0ms975×body320valid
473.0ms375×body160valid
450.0ms687×body80valid