Details

Time bar (total: 8.6s)

sample177.0ms

Algorithm
intervals
Results
108.0ms113×body1280valid
42.0ms84×body640valid
8.0ms23×body320valid
3.0ms25×body80valid
2.0ms11×body160valid

simplify5.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02012
12312
22312

prune3.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 0.4b

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))

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
18×prod-diff
17×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
11×cos-sum sin-sum
6×add-log-exp
4×pow1 add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u
3×cos-diff fma-def
2×sub-neg associate-+r+
1×+-commutative distribute-rgt-in distribute-lft-in flip3-+ sum-log sin-diff flip-+
Counts
4 → 69
Calls
4 calls:
1.0ms
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
10.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
5.0ms
(cos (- lambda1 lambda2))
5.0ms
(sin (- lambda1 lambda2))

series143.0ms

Counts
4 → 12
Calls
4 calls:
9.0ms
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
96.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
16.0ms
(cos (- lambda1 lambda2))
22.0ms
(sin (- lambda1 lambda2))

simplify66.0ms

Algorithm
egg-herbie
Counts
81 → 81
Iterations

Useful iterations: 3 (58.0ms)

IterNodesCost
03651011
1800787
22597784
35002735

prune302.0ms

Filtered
81 candidates to 55 candidates (67.9%)
Pruning

15 alts after pruning (15 fresh and 0 done)

PrunedKeptTotal
New661581
Fresh000
Picked101
Done000
Total671582

Merged error: 0.2b

Counts
82 → 15

localize41.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin lambda1) (cos 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))

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
15×add-sqr-sqrt
13×add-cube-cbrt *-un-lft-identity
11×cos-sum
9×prod-diff
6×pow1 add-exp-log add-cbrt-cube add-log-exp
4×expm1-log1p-u log1p-expm1-u
3×cos-diff fma-def associate-*r* associate-*l*
2×associate-+r+
1×+-commutative distribute-rgt-in sub-neg distribute-lft-in flip3-+ pow-prod-down prod-exp sum-log *-commutative sin-cos-mult cbrt-unprod flip-+ unswap-sqr
Counts
4 → 69
Calls
4 calls:
5.0ms
(* (sin lambda1) (cos lambda2))
1.0ms
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
5.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
5.0ms
(cos (- lambda1 lambda2))

series176.0ms

Counts
4 → 12
Calls
4 calls:
45.0ms
(* (sin lambda1) (cos lambda2))
12.0ms
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
102.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
16.0ms
(cos (- lambda1 lambda2))

simplify92.0ms

Algorithm
egg-herbie
Counts
81 → 81
Iterations

Useful iterations: 3 (83.0ms)

IterNodesCost
0390869
11061710
23925707
35001706

prune358.0ms

Filtered
81 candidates to 60 candidates (74.1%)
Pruning

14 alts after pruning (14 fresh and 0 done)

PrunedKeptTotal
New80181
Fresh11314
Picked101
Done000
Total821496

Merged error: 0.1b

Counts
96 → 14

localize30.0ms

Local error

Found 4 expressions with local error:

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

rewrite12.0ms

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*
4×expm1-log1p-u log1p-expm1-u add-log-exp
2×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×sin-cos-mult fma-udef sin-mult
Counts
4 → 61
Calls
4 calls:
5.0ms
(* (sin lambda1) (cos lambda2))
5.0ms
(* (sin lambda1) (sin lambda2))
1.0ms
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1)) (* (cos phi2) (* (sin lambda1) (sin lambda2)))))
1.0ms
(fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))

series226.0ms

Counts
4 → 12
Calls
4 calls:
44.0ms
(* (sin lambda1) (cos lambda2))
42.0ms
(* (sin lambda1) (sin lambda2))
15.0ms
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1)) (* (cos phi2) (* (sin lambda1) (sin lambda2)))))
124.0ms
(fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))

simplify60.0ms

Algorithm
egg-herbie
Counts
73 → 73
Iterations

Useful iterations: 2 (19.0ms)

IterNodesCost
0240677
1726590
22516588
35002588

prune338.0ms

Filtered
73 candidates to 56 candidates (76.7%)
Pruning

14 alts after pruning (13 fresh and 1 done)

PrunedKeptTotal
New73073
Fresh01313
Picked011
Done000
Total731487

Merged error: 0.1b

Counts
87 → 14

localize25.0ms

Local error

Found 4 expressions with local error:

0.5b
(+ (cos phi1) (* (cos phi2) (log (exp (cos (- lambda1 lambda2))))))
0.5b
(log (exp (cos (- lambda1 lambda2))))
2.8b
(cos (- lambda1 lambda2))
3.0b
(sin (- lambda1 lambda2))

rewrite34.0ms

Algorithm
rewrite-expression-head
Rules
27×add-sqr-sqrt add-cube-cbrt *-un-lft-identity prod-diff
22×cos-sum
12×log-prod
11×log-div exp-diff sin-sum
8×associate-+r+
6×add-log-exp
5×pow1
4×add-exp-log distribute-rgt-in cos-diff expm1-log1p-u distribute-lft-in log-pow add-cbrt-cube log1p-expm1-u
3×sub-neg exp-prod fma-def exp-sum
1×+-commutative flip3-+ rem-log-exp sum-log sin-diff flip-+
Counts
4 → 95
Calls
4 calls:
9.0ms
(+ (cos phi1) (* (cos phi2) (log (exp (cos (- lambda1 lambda2))))))
10.0ms
(log (exp (cos (- lambda1 lambda2))))
5.0ms
(cos (- lambda1 lambda2))
5.0ms
(sin (- lambda1 lambda2))

series152.0ms

Counts
4 → 12
Calls
4 calls:
100.0ms
(+ (cos phi1) (* (cos phi2) (log (exp (cos (- lambda1 lambda2))))))
16.0ms
(log (exp (cos (- lambda1 lambda2))))
16.0ms
(cos (- lambda1 lambda2))
20.0ms
(sin (- lambda1 lambda2))

simplify82.0ms

Algorithm
egg-herbie
Counts
107 → 107
Iterations

Useful iterations: 3 (67.0ms)

IterNodesCost
04811306
11054982
23036952
35002852

prune299.0ms

Filtered
107 candidates to 67 candidates (62.6%)
Pruning

14 alts after pruning (12 fresh and 2 done)

PrunedKeptTotal
New1070107
Fresh01212
Picked011
Done011
Total10714121

Merged error: 0.1b

Counts
121 → 14

regimes450.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 0.2b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02923
12923

end0.0ms

sample5.4s

Algorithm
intervals
Results
3.3s3543×body1280valid
1.3s2388×body640valid
337.0ms933×body320valid
110.0ms427×body160valid
87.0ms709×body80valid

Profiling

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