Details

Time bar (total: 25.2s)

sample397.0ms

Algorithm
intervals
Results
257.0ms114×body1280valid
69.0ms74×body640valid
33.0ms34×body320valid
5.0ms12×body160valid
5.0ms22×body80valid

simplify8.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01420
12020
22120
done2120

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.0b

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)))))
0.4b
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
5.4b
(sin (- lambda1 lambda2))
5.6b
(cos (- lambda1 lambda2))

rewrite46.0ms

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)))))
23.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
10.0ms
(sin (- lambda1 lambda2))
11.0ms
(cos (- lambda1 lambda2))

series235.0ms

Counts
4 → 12
Calls
4 calls:
25.0ms
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
157.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
33.0ms
(sin (- lambda1 lambda2))
21.0ms
(cos (- lambda1 lambda2))

simplify1.0s

Counts
52 → 52
Iterations

Useful iterations: 3 (321.0ms)

IterNodesCost
097702
1207687
2532615
31518613
done5000613

prune352.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.8b

localize51.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (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)))))
0.4b
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
5.6b
(cos (- lambda1 lambda2))

rewrite114.0ms

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×distribute-rgt-in cos-sum associate-+r+ distribute-lft-in flip3-+ associate-*r/ flip-+
1×+-commutative sub-neg pow-prod-down prod-exp sum-log *-commutative cbrt-unprod unswap-sqr
Counts
4 → 52
Calls
4 calls:
91.0ms
(* (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)))))
10.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
11.0ms
(cos (- lambda1 lambda2))

series390.0ms

Counts
4 → 12
Calls
4 calls:
211.0ms
(* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))))
29.0ms
(atan2 (* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
125.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
24.0ms
(cos (- lambda1 lambda2))

simplify976.0ms

Counts
64 → 64
Iterations

Useful iterations: done (974.0ms)

IterNodesCost
01271191
13491173
215721033
done50021031

prune559.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize61.0ms

Local error

Found 4 expressions with local error:

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

rewrite66.0ms

Algorithm
rewrite-expression-head
Rules
11×pow1 add-exp-log add-cbrt-cube
9×add-sqr-sqrt
7×add-cube-cbrt *-un-lft-identity
6×associate-*l* add-log-exp
4×associate-*r* pow-prod-down prod-exp cbrt-unprod
2×*-commutative
1×+-commutative flip3-+ associate-*r/ sum-log cos-mult flip-+ sin-mult unswap-sqr
Counts
4 → 56
Calls
4 calls:
25.0ms
(* (cos phi2) (* (cos lambda1) (cos lambda2)))
0.0ms
(atan2 (* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))) (+ (+ (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2)))) (* (* (sin lambda1) (sin lambda2)) (cos phi2))))
24.0ms
(* (sin lambda1) (sin lambda2))
15.0ms
(+ (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2))))

series397.0ms

Counts
4 → 12
Calls
4 calls:
102.0ms
(* (cos phi2) (* (cos lambda1) (cos lambda2)))
21.0ms
(atan2 (* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))) (+ (+ (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2)))) (* (* (sin lambda1) (sin lambda2)) (cos phi2))))
77.0ms
(* (sin lambda1) (sin lambda2))
198.0ms
(+ (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2))))

simplify926.0ms

Counts
68 → 68
Iterations

Useful iterations: 2 (242.0ms)

IterNodesCost
01431144
13471107
21222928
done5001928

prune935.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize98.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (cos phi1) (cos phi1))
0.4b
(pow (cos phi1) 3)
0.6b
(pow (* (cos phi2) (* (cos lambda1) (cos lambda2))) 3)
1.3b
(- (* (cos lambda1) (* (cos phi2) (cos lambda2))) (cos phi1))

rewrite95.0ms

Algorithm
rewrite-expression-head
Rules
18×pow1
14×add-sqr-sqrt
13×add-exp-log add-cbrt-cube
12×add-cube-cbrt *-un-lft-identity
6×pow-unpow add-log-exp
4×unpow-prod-down pow-pow cube-prod pow-prod-down pow-exp prod-exp cbrt-unprod rem-cube-cbrt
3×swap-sqr associate-*r* associate-*l*
2×cube-mult pow-to-exp unpow3 cos-mult sqr-pow
1×cube-div pow2 sub-neg sqr-cos flip3-- pow-plus diff-log associate-*r/ pow-sqr *-commutative pow-prod-up flip-- unswap-sqr
Counts
4 → 88
Calls
4 calls:
11.0ms
(* (cos phi1) (cos phi1))
5.0ms
(pow (cos phi1) 3)
42.0ms
(pow (* (cos phi2) (* (cos lambda1) (cos lambda2))) 3)
35.0ms
(- (* (cos lambda1) (* (cos phi2) (cos lambda2))) (cos phi1))

series423.0ms

Counts
4 → 12
Calls
4 calls:
19.0ms
(* (cos phi1) (cos phi1))
36.0ms
(pow (cos phi1) 3)
169.0ms
(pow (* (cos phi2) (* (cos lambda1) (cos lambda2))) 3)
199.0ms
(- (* (cos lambda1) (* (cos phi2) (cos lambda2))) (cos phi1))

simplify5.5s

Counts
100 → 100
Iterations

Useful iterations: 2 (755.0ms)

IterNodesCost
01561014
1495847
23762746
done5000746

prune842.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

regimes669.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify6.0ms

Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
03985
15585
done5585

end0.0ms

sample10.9s

Algorithm
intervals
Results
6.2s3580×body1280valid
2.9s2341×body640valid
1.1s946×body320valid
191.0ms419×body160valid
115.0ms714×body80valid