Details

Time bar (total: 9.7s)

analyze1.9s

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
9.4%90.4%0.2%9
9.4%90.4%0.2%10
10.9%88.9%0.2%11
10.9%88.9%0.2%12
10.9%88.9%0.2%13
10.9%88.9%0.2%14

sample185.0ms

Algorithm
intervals
Results
103.0ms99×body1280valid
44.0ms76×body640valid
15.0ms40×body320valid
5.0ms22×body160valid
2.0ms19×body80valid

simplify15.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (14.0ms)

IterNodesCost
027020
127020

prune5.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 0.9b

Counts
2 → 1

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
0.5b
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
2.8b
(cos (- lambda1 lambda2))
3.0b
(sin (- lambda1 lambda2))

rewrite13.0ms

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 associate-+r+
1×+-commutative distribute-rgt-in cos-sum distribute-lft-in flip3-+ sin-sum sum-log sin-diff flip-+
Counts
4 → 38
Calls
4 calls:
1.0ms
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
4.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
4.0ms
(cos (- lambda1 lambda2))
4.0ms
(sin (- lambda1 lambda2))

series45.0ms

Counts
4 → 12
Calls
4 calls:
12.0ms
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
23.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
4.0ms
(cos (- lambda1 lambda2))
6.0ms
(sin (- lambda1 lambda2))

simplify44.0ms

Algorithm
egg-herbie
Counts
50 → 50
Iterations

Useful iterations: 0 (39.0ms)

IterNodesCost
04947591
14947591

prune154.0ms

Filtered
42 candidates to 50 candidates (-19.0%)
Pruning

14 alts after pruning (14 fresh and 0 done)

PrunedKeptTotal
New361450
Fresh000
Picked101
Done000
Total371451

Merged error: 0.7b

Counts
51 → 14

localize31.0ms

Local error

Found 4 expressions with local error:

0.1b
(- (* (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)))))
0.5b
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
2.8b
(cos (- lambda1 lambda2))

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
8×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 associate-+r+
1×+-commutative distribute-rgt-in cos-sum flip3-- distribute-lft-in flip3-+ diff-log sum-log flip-- flip-+
Counts
4 → 40
Calls
4 calls:
5.0ms
(- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))
1.0ms
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
4.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
4.0ms
(cos (- lambda1 lambda2))

series54.0ms

Counts
4 → 12
Calls
4 calls:
18.0ms
(- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))
9.0ms
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
23.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
4.0ms
(cos (- lambda1 lambda2))

simplify47.0ms

Algorithm
egg-herbie
Counts
52 → 52
Iterations

Useful iterations: 0 (41.0ms)

IterNodesCost
04907813
14907813

prune126.0ms

Filtered
43 candidates to 52 candidates (-20.9%)
Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New51152
Fresh21113
Picked101
Done000
Total541266

Merged error: 0.1b

Counts
66 → 12

localize32.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (cos lambda1) (* (cos lambda2) (cos phi2)))
0.2b
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (+ (cos phi1) (* (cos lambda1) (* (cos lambda2) (cos phi2)))) (* (cos phi2) (* (sin lambda1) (sin lambda2)))))
0.2b
(* (sin lambda1) (sin lambda2))
0.4b
(+ (cos phi1) (* (cos lambda1) (* (cos lambda2) (cos phi2))))

rewrite16.0ms

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:
6.0ms
(* (cos lambda1) (* (cos lambda2) (cos phi2)))
1.0ms
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (+ (cos phi1) (* (cos lambda1) (* (cos lambda2) (cos phi2)))) (* (cos phi2) (* (sin lambda1) (sin lambda2)))))
5.0ms
(* (sin lambda1) (sin lambda2))
4.0ms
(+ (cos phi1) (* (cos lambda1) (* (cos lambda2) (cos phi2))))

series67.0ms

Counts
4 → 12
Calls
4 calls:
16.0ms
(* (cos lambda1) (* (cos lambda2) (cos phi2)))
13.0ms
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (+ (cos phi1) (* (cos lambda1) (* (cos lambda2) (cos phi2)))) (* (cos phi2) (* (sin lambda1) (sin lambda2)))))
9.0ms
(* (sin lambda1) (sin lambda2))
28.0ms
(+ (cos phi1) (* (cos lambda1) (* (cos lambda2) (cos phi2))))

simplify34.0ms

Algorithm
egg-herbie
Counts
68 → 68
Iterations

Useful iterations: 0 (28.0ms)

IterNodesCost
04993917
14993917

prune141.0ms

Filtered
47 candidates to 68 candidates (-44.7%)
Pruning

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New65368
Fresh11011
Picked101
Done000
Total671380

Merged error: 0.1b

Counts
80 → 13

localize36.0ms

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))))
0.7b
(log (exp (+ (cos phi1) (* (cos lambda1) (* (cos lambda2) (cos phi2))))))

rewrite20.0ms

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:
4.0ms
(* (sin lambda1) (sin lambda2))
5.0ms
(exp (+ (cos phi1) (* (cos lambda1) (* (cos lambda2) (cos phi2)))))
4.0ms
(+ (cos phi1) (* (cos lambda1) (* (cos lambda2) (cos phi2))))
5.0ms
(log (exp (+ (cos phi1) (* (cos lambda1) (* (cos lambda2) (cos phi2))))))

series102.0ms

Counts
4 → 12
Calls
4 calls:
9.0ms
(* (sin lambda1) (sin lambda2))
38.0ms
(exp (+ (cos phi1) (* (cos lambda1) (* (cos lambda2) (cos phi2)))))
27.0ms
(+ (cos phi1) (* (cos lambda1) (* (cos lambda2) (cos phi2))))
29.0ms
(log (exp (+ (cos phi1) (* (cos lambda1) (* (cos lambda2) (cos phi2))))))

simplify40.0ms

Algorithm
egg-herbie
Counts
71 → 71
Iterations

Useful iterations: 0 (33.0ms)

IterNodesCost
04988813
14988813

prune86.0ms

Filtered
51 candidates to 71 candidates (-39.2%)
Pruning

13 alts after pruning (12 fresh and 1 done)

PrunedKeptTotal
New71071
Fresh01212
Picked011
Done000
Total711384

Merged error: 0.1b

Counts
84 → 13

regimes653.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
06039
16039

end0.0ms

sample5.8s

Algorithm
intervals
Results
3.6s3539×body1280valid
1.4s2315×body640valid
379.0ms964×body320valid
111.0ms435×body160valid
94.0ms747×body80valid

Profiling

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