Details

Time bar (total: 15.1s)

analyze3.0s

Algorithm
search
Search
TrueOtherFalseIter
0%99.8%0.2%0
0%99.8%0.2%1
0%99.8%0.2%2
0%99.8%0.2%3
0%99.8%0.2%4
0%99.8%0.2%5
0%99.8%0.2%6
0%99.8%0.2%7
0%99.8%0.2%8
0%99.8%0.2%9
0%99.8%0.2%10
0.8%99%0.2%11
1.2%98.6%0.2%12
1.8%98%0.2%13
2%97.7%0.2%14

sample283.0ms

Algorithm
intervals
Results
192.0ms144×body1280valid
52.0ms72×body640valid
14.0ms25×body320valid
4.0ms11×body160valid
1.0msbody80valid

simplify5.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (3.0ms)

IterNodesCost
09519
19519

prune18.0ms

Filtered
1 candidates to 1 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 18.1b

Counts
2 → 2

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
0.3b
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
1.0b
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
3.9b
(cos (- lambda1 lambda2))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
11×pow1 add-exp-log add-cbrt-cube
add-sqr-sqrt
add-cube-cbrt *-un-lft-identity
associate-*r*
associate-*l* pow-prod-down prod-exp cbrt-unprod add-log-exp
cos-diff
*-commutative
distribute-rgt-in acos-asin sub-neg cos-sum distribute-lft-in associate-*l/ cos-mult unswap-sqr
Counts
4 → 56
Calls
4 calls:
6.0ms
(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
3.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
1.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
4.0ms
(cos (- lambda1 lambda2))

series69.0ms

Counts
4 → 12
Calls
4 calls:
26.0ms
(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
30.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
9.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
5.0ms
(cos (- lambda1 lambda2))

simplify47.0ms

Algorithm
egg-herbie
Counts
68 → 68
Iterations

Useful iterations: 0 (40.0ms)

IterNodesCost
049881022
149881022

prune164.0ms

Filtered
48 candidates to 68 candidates (-41.7%)
Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New561268
Fresh101
Picked101
Done000
Total581270

Merged error: 2.9b

Counts
70 → 12

localize34.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin lambda2) (* (cos phi1) (cos phi2)))
0.3b
(* (sin lambda1) (* (sin lambda2) (* (cos phi1) (cos phi2))))
0.3b
(* (acos (+ (* (sin phi1) (sin phi2)) (+ (* (cos lambda1) (* (cos lambda2) (* (cos phi1) (cos phi2)))) (* (sin lambda1) (* (sin lambda2) (* (cos phi1) (cos phi2))))))) R)
1.0b
(acos (+ (* (sin phi1) (sin phi2)) (+ (* (cos lambda1) (* (cos lambda2) (* (cos phi1) (cos phi2)))) (* (sin lambda1) (* (sin lambda2) (* (cos phi1) (cos phi2)))))))

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
20×pow1 add-exp-log add-cbrt-cube
10×add-sqr-sqrt pow-prod-down prod-exp cbrt-unprod
associate-*l*
add-cube-cbrt *-un-lft-identity
associate-*r*
add-log-exp
associate-*r/ *-commutative
cos-mult
acos-asin unswap-sqr
Counts
4 → 67
Calls
4 calls:
6.0ms
(* (sin lambda2) (* (cos phi1) (cos phi2)))
9.0ms
(* (sin lambda1) (* (sin lambda2) (* (cos phi1) (cos phi2))))
3.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (+ (* (cos lambda1) (* (cos lambda2) (* (cos phi1) (cos phi2)))) (* (sin lambda1) (* (sin lambda2) (* (cos phi1) (cos phi2))))))) R)
1.0ms
(acos (+ (* (sin phi1) (sin phi2)) (+ (* (cos lambda1) (* (cos lambda2) (* (cos phi1) (cos phi2)))) (* (sin lambda1) (* (sin lambda2) (* (cos phi1) (cos phi2)))))))

series103.0ms

Counts
4 → 12
Calls
4 calls:
18.0ms
(* (sin lambda2) (* (cos phi1) (cos phi2)))
27.0ms
(* (sin lambda1) (* (sin lambda2) (* (cos phi1) (cos phi2))))
43.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (+ (* (cos lambda1) (* (cos lambda2) (* (cos phi1) (cos phi2)))) (* (sin lambda1) (* (sin lambda2) (* (cos phi1) (cos phi2))))))) R)
15.0ms
(acos (+ (* (sin phi1) (sin phi2)) (+ (* (cos lambda1) (* (cos lambda2) (* (cos phi1) (cos phi2)))) (* (sin lambda1) (* (sin lambda2) (* (cos phi1) (cos phi2)))))))

simplify58.0ms

Algorithm
egg-herbie
Counts
79 → 79
Iterations

Useful iterations: 0 (49.0ms)

IterNodesCost
050561367

prune185.0ms

Filtered
56 candidates to 79 candidates (-41.1%)
Pruning

14 alts after pruning (13 fresh and 1 done)

PrunedKeptTotal
New691079
Fresh8311
Picked011
Done000
Total771491

Merged error: 2.8b

Counts
91 → 14

localize35.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin phi1) (sin phi2))
0.3b
(* (- (/ PI 2) (asin (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2)))))))) R)
0.6b
(asin (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2)))))))
0.7b
(- (/ PI 2) (asin (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))))))))

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
22×add-sqr-sqrt
12×*-un-lft-identity
associate-*l*
pow1 add-exp-log add-cube-cbrt add-cbrt-cube
associate-*r* add-log-exp
difference-of-squares
asin-acos flip3-- times-frac pow-prod-down associate-*l/ prod-exp *-commutative flip-- cbrt-unprod distribute-lft-out-- unswap-sqr
sub-neg diff-log sin-mult associate--r-
Counts
4 → 65
Calls
4 calls:
5.0ms
(* (sin phi1) (sin phi2))
9.0ms
(* (- (/ PI 2) (asin (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2)))))))) R)
1.0ms
(asin (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2)))))))
7.0ms
(- (/ PI 2) (asin (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))))))))

series114.0ms

Counts
4 → 12
Calls
4 calls:
10.0ms
(* (sin phi1) (sin phi2))
66.0ms
(* (- (/ PI 2) (asin (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2)))))))) R)
13.0ms
(asin (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2)))))))
26.0ms
(- (/ PI 2) (asin (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))))))))

simplify43.0ms

Algorithm
egg-herbie
Counts
77 → 77
Iterations

Useful iterations: 0 (32.0ms)

IterNodesCost
056612005

prune240.0ms

Filtered
55 candidates to 77 candidates (-40.0%)
Pruning

20 alts after pruning (19 fresh and 1 done)

PrunedKeptTotal
New661177
Fresh4812
Picked101
Done011
Total712091

Merged error: 2.6b

Counts
91 → 20

localize41.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (- (/ PI 2) (asin (+ (log (pow (exp (sin phi1)) (sin phi2))) (* (cos phi1) (* (cos phi2) (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2)))))))) R)
0.6b
(asin (+ (log (pow (exp (sin phi1)) (sin phi2))) (* (cos phi1) (* (cos phi2) (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2)))))))
0.7b
(- (/ PI 2) (asin (+ (log (pow (exp (sin phi1)) (sin phi2))) (* (cos phi1) (* (cos phi2) (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))))))))
4.3b
(log (pow (exp (sin phi1)) (sin phi2)))

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt
12×*-un-lft-identity
add-cube-cbrt
add-exp-log log-prod
pow1 associate-*l* add-cbrt-cube add-log-exp
difference-of-squares
unpow-prod-down rem-log-exp associate-*r*
asin-acos flip3-- times-frac associate-*l/ flip-- distribute-lft-out--
pow-to-exp sub-neg diff-log pow-prod-down pow-exp prod-exp log-pow *-commutative cbrt-unprod associate--r- unswap-sqr sqr-pow
Counts
4 → 64
Calls
4 calls:
12.0ms
(* (- (/ PI 2) (asin (+ (log (pow (exp (sin phi1)) (sin phi2))) (* (cos phi1) (* (cos phi2) (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2)))))))) R)
2.0ms
(asin (+ (log (pow (exp (sin phi1)) (sin phi2))) (* (cos phi1) (* (cos phi2) (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2)))))))
7.0ms
(- (/ PI 2) (asin (+ (log (pow (exp (sin phi1)) (sin phi2))) (* (cos phi1) (* (cos phi2) (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))))))))
3.0ms
(log (pow (exp (sin phi1)) (sin phi2)))

series136.0ms

Counts
4 → 12
Calls
4 calls:
74.0ms
(* (- (/ PI 2) (asin (+ (log (pow (exp (sin phi1)) (sin phi2))) (* (cos phi1) (* (cos phi2) (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2)))))))) R)
14.0ms
(asin (+ (log (pow (exp (sin phi1)) (sin phi2))) (* (cos phi1) (* (cos phi2) (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2)))))))
26.0ms
(- (/ PI 2) (asin (+ (log (pow (exp (sin phi1)) (sin phi2))) (* (cos phi1) (* (cos phi2) (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))))))))
22.0ms
(log (pow (exp (sin phi1)) (sin phi2)))

simplify43.0ms

Algorithm
egg-herbie
Counts
76 → 76
Iterations

Useful iterations: 0 (32.0ms)

IterNodesCost
049902036
149902036

prune84.0ms

Filtered
52 candidates to 76 candidates (-46.2%)
Pruning

19 alts after pruning (19 fresh and 0 done)

PrunedKeptTotal
New75176
Fresh01818
Picked101
Done101
Total771996

Merged error: 2.6b

Counts
96 → 19

regimes1.5s

Accuracy

0% (0.6b remaining)

Error of 4.1b against oracle of 3.5b and baseline of 4.1b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03428
13428

end0.0ms

sample8.9s

Algorithm
intervals
Results
6.3s4766×body1280valid
1.6s2090×body640valid
382.0ms714×body320valid
118.0ms288×body160valid
42.0ms12×body2560valid
23.0ms130×body80valid
1.0msbody1280invalid

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