Details

Time bar (total: 24.2s)

sample362.0ms

Algorithm
intervals
Results
188.0ms119×body1280valid
68.0ms74×body640valid
68.0ms29×body320valid
5.0ms26×body80valid
4.0ms8×body160valid

simplify10.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01420
12020
22120
done2120

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.5b

localize25.0ms

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))))
4.1b
(cos (- lambda1 lambda2))
4.2b
(sin (- lambda1 lambda2))

rewrite95.0ms

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)))))
19.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
57.0ms
(cos (- lambda1 lambda2))
17.0ms
(sin (- lambda1 lambda2))

series211.0ms

Counts
4 → 12
Calls
4 calls:
15.0ms
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
152.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
19.0ms
(cos (- lambda1 lambda2))
25.0ms
(sin (- lambda1 lambda2))

simplify1.2s

Counts
52 → 52
Iterations

Useful iterations: 3 (353.0ms)

IterNodesCost
097702
1207687
2538615
31521613
done5000613

prune461.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 1.2b

localize75.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (cos phi2) (sin (- lambda1 lambda2)))
0.2b
(atan2 (* (cos phi2) (sin (- lambda1 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))))
4.2b
(sin (- lambda1 lambda2))

rewrite90.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt
6×pow1 add-exp-log add-cube-cbrt *-un-lft-identity sin-sum add-cbrt-cube add-log-exp
3×sub-neg associate-*r* associate-*l*
2×distribute-rgt-in distribute-lft-in
1×+-commutative flip3-+ pow-prod-down prod-exp sum-log sin-diff *-commutative cbrt-unprod flip-+ unswap-sqr
Counts
4 → 50
Calls
4 calls:
51.0ms
(* (cos phi2) (sin (- lambda1 lambda2)))
0.0ms
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (+ (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2)))) (* (cos phi2) (* (sin lambda1) (sin lambda2)))))
16.0ms
(+ (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2))))
21.0ms
(sin (- lambda1 lambda2))

series391.0ms

Counts
4 → 12
Calls
4 calls:
91.0ms
(* (cos phi2) (sin (- lambda1 lambda2)))
40.0ms
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (+ (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2)))) (* (cos phi2) (* (sin lambda1) (sin lambda2)))))
220.0ms
(+ (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2))))
41.0ms
(sin (- lambda1 lambda2))

simplify751.0ms

Counts
62 → 62
Iterations

Useful iterations: done (748.0ms)

IterNodesCost
01121002
1266981
2985836
done5000834

prune536.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize54.0ms

Local error

Found 4 expressions with local error:

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

rewrite63.0ms

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-+ sum-log flip-+ sin-mult
Counts
4 → 55
Calls
4 calls:
26.0ms
(* (sin lambda1) (sin lambda2))
24.0ms
(* (cos lambda1) (sin lambda2))
0.0ms
(atan2 (* (cos phi2) (+ (* (cos lambda2) (sin lambda1)) (- (* (cos lambda1) (sin lambda2))))) (+ (+ (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2)))) (* (cos phi2) (* (sin lambda1) (sin lambda2)))))
10.0ms
(+ (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2))))

series337.0ms

Counts
4 → 12
Calls
4 calls:
64.0ms
(* (sin lambda1) (sin lambda2))
68.0ms
(* (cos lambda1) (sin lambda2))
21.0ms
(atan2 (* (cos phi2) (+ (* (cos lambda2) (sin lambda1)) (- (* (cos lambda1) (sin lambda2))))) (+ (+ (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2)))) (* (cos phi2) (* (sin lambda1) (sin lambda2)))))
184.0ms
(+ (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2))))

simplify834.0ms

Counts
67 → 67
Iterations

Useful iterations: done (831.0ms)

IterNodesCost
01331054
13311026
21207865
done5001861

prune571.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize85.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (+ (pow (cos phi1) 3) (pow (* (cos phi2) (* (cos lambda1) (cos lambda2))) 3)) (+ (* (cos phi1) (cos phi1)) (* (* (cos phi2) (* (cos lambda1) (cos lambda2))) (- (* (cos phi2) (* (cos lambda1) (cos lambda2))) (cos phi1)))))
0.4b
(+ (pow (cos phi1) 3) (pow (* (cos phi2) (* (cos lambda1) (cos lambda2))) 3))
0.6b
(pow (* (cos phi2) (* (cos lambda1) (cos lambda2))) 3)
1.9b
(- (* (cos phi2) (* (cos lambda1) (cos lambda2))) (cos phi1))

rewrite270.0ms

Algorithm
rewrite-expression-head
Rules
25×*-un-lft-identity
15×add-sqr-sqrt add-cube-cbrt times-frac
12×add-exp-log add-cbrt-cube
10×pow1
9×cos-mult
8×add-log-exp
7×associate-/r/
6×associate-*r/
5×frac-add sum-cubes distribute-lft-out associate-/l*
3×pow-unpow flip3-- pow-pow flip3-+ pow-prod-down pow-exp prod-exp associate-/r* flip-- cbrt-unprod flip-+ rem-cube-cbrt
2×frac-times associate-/l/
1×cbrt-undiv +-commutative cube-div cube-mult pow-to-exp sub-neg unpow-prod-down frac-2neg diff-log unpow3 cube-prod div-exp associate-*l/ clear-num sum-log div-inv sqr-pow
Counts
4 → 95
Calls
4 calls:
190.0ms
(/ (+ (pow (cos phi1) 3) (pow (* (cos phi2) (* (cos lambda1) (cos lambda2))) 3)) (+ (* (cos phi1) (cos phi1)) (* (* (cos phi2) (* (cos lambda1) (cos lambda2))) (- (* (cos phi2) (* (cos lambda1) (cos lambda2))) (cos phi1)))))
24.0ms
(+ (pow (cos phi1) 3) (pow (* (cos phi2) (* (cos lambda1) (cos lambda2))) 3))
21.0ms
(pow (* (cos phi2) (* (cos lambda1) (cos lambda2))) 3)
30.0ms
(- (* (cos phi2) (* (cos lambda1) (cos lambda2))) (cos phi1))

series1.8s

Counts
4 → 12
Calls
4 calls:
1.1s
(/ (+ (pow (cos phi1) 3) (pow (* (cos phi2) (* (cos lambda1) (cos lambda2))) 3)) (+ (* (cos phi1) (cos phi1)) (* (* (cos phi2) (* (cos lambda1) (cos lambda2))) (- (* (cos phi2) (* (cos lambda1) (cos lambda2))) (cos phi1)))))
279.0ms
(+ (pow (cos phi1) 3) (pow (* (cos phi2) (* (cos lambda1) (cos lambda2))) 3))
213.0ms
(pow (* (cos phi2) (* (cos lambda1) (cos lambda2))) 3)
197.0ms
(- (* (cos phi2) (* (cos lambda1) (cos lambda2))) (cos phi1))

simplify2.4s

Counts
107 → 107
Iterations

Useful iterations: 2 (672.0ms)

IterNodesCost
02274111
16793857
236373546
done50003546

prune979.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

regimes838.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify9.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
042102
167102
269102
done69102

end0.0ms

sample11.7s

Algorithm
intervals
Results
6.8s3552×body1280valid
2.9s2372×body640valid
963.0ms932×body320valid
308.0ms445×body160valid
253.0ms699×body80valid