Details

Time bar (total: 8.6s)

sample180.0ms

Algorithm
intervals
Results
105.0ms117×body1280valid
44.0ms84×body640valid
12.0ms23×body320valid
3.0ms24×body80valid
2.0ms8×body160valid

simplify5.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02012
12112
22112

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: 1.0b

Counts
2 → 1

localize20.0ms

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))))
3.0b
(sin (- lambda1 lambda2))
3.0b
(cos (- 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 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:
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
(sin (- lambda1 lambda2))
4.0ms
(cos (- lambda1 lambda2))

series150.0ms

Counts
4 → 12
Calls
4 calls:
10.0ms
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
99.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
24.0ms
(sin (- lambda1 lambda2))
18.0ms
(cos (- lambda1 lambda2))

simplify117.0ms

Algorithm
egg-herbie
Counts
52 → 52
Iterations

Useful iterations: 1 (5.0ms)

IterNodesCost
0205421
1508374
21327374
33684374
45001374

prune235.0ms

Filtered
52 candidates to 42 candidates (80.8%)
Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New401252
Fresh000
Picked101
Done000
Total411253

Merged error: 0.7b

Counts
53 → 12

localize29.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (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))))
3.0b
(cos (- lambda1 lambda2))

rewrite18.0ms

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×distribute-rgt-in cos-diff sub-neg distribute-lft-in associate-*r* associate-*l*
2×cos-sum associate-+r+ associate-*r/
1×+-commutative flip3-- flip3-+ pow-prod-down prod-exp sum-log *-commutative flip-- cbrt-unprod flip-+ unswap-sqr
Counts
4 → 54
Calls
4 calls:
8.0ms
(* (cos phi2) (- (* (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))

series269.0ms

Counts
4 → 12
Calls
4 calls:
138.0ms
(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
12.0ms
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
98.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
20.0ms
(cos (- lambda1 lambda2))

simplify121.0ms

Algorithm
egg-herbie
Counts
66 → 66
Iterations

Useful iterations: 1 (8.0ms)

IterNodesCost
0289748
11037658
24438658
35002658

prune300.0ms

Filtered
66 candidates to 48 candidates (72.7%)
Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New63366
Fresh2911
Picked101
Done000
Total661278

Merged error: 0.1b

Counts
78 → 12

localize28.0ms

Local error

Found 4 expressions with local error:

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

rewrite22.0ms

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
3×distribute-rgt-in distribute-lft-in
2×sub-neg associate-+r+ associate-*r/ pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×+-commutative flip3-- flip3-+ sum-log flip-- flip-+ sin-mult
Counts
4 → 63
Calls
4 calls:
11.0ms
(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
5.0ms
(* (sin lambda1) (sin lambda2))
1.0ms
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
4.0ms
(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

series440.0ms

Counts
4 → 12
Calls
4 calls:
150.0ms
(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
57.0ms
(* (sin lambda1) (sin lambda2))
16.0ms
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
215.0ms
(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

simplify45.0ms

Algorithm
egg-herbie
Counts
75 → 75
Iterations

Useful iterations: 1 (10.0ms)

IterNodesCost
0345962
11380833
25001833

prune306.0ms

Filtered
75 candidates to 52 candidates (69.3%)
Pruning

12 alts after pruning (11 fresh and 1 done)

PrunedKeptTotal
New75075
Fresh01111
Picked011
Done000
Total751287

Merged error: 0.1b

Counts
87 → 12

localize30.0ms

Local error

Found 4 expressions with local error:

3.0b
(sin (- lambda1 lambda2))
3.0b
(cos (- lambda1 lambda2))
3.0b
(cos (- lambda1 lambda2))
3.0b
(cos (- lambda1 lambda2))

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
6×cos-sum
4×pow1 add-exp-log add-sqr-sqrt add-cube-cbrt sub-neg *-un-lft-identity add-cbrt-cube add-log-exp
3×cos-diff
2×sin-sum
1×sin-diff
Counts
4 → 40
Calls
4 calls:
4.0ms
(sin (- lambda1 lambda2))
6.0ms
(cos (- lambda1 lambda2))
4.0ms
(cos (- lambda1 lambda2))
4.0ms
(cos (- lambda1 lambda2))

series70.0ms

Counts
4 → 12
Calls
4 calls:
20.0ms
(sin (- lambda1 lambda2))
16.0ms
(cos (- lambda1 lambda2))
17.0ms
(cos (- lambda1 lambda2))
17.0ms
(cos (- lambda1 lambda2))

simplify55.0ms

Algorithm
egg-herbie
Counts
52 → 52
Iterations

Useful iterations: 4 (51.0ms)

IterNodesCost
083235
1149215
2390215
31140215
45001212

prune223.0ms

Filtered
52 candidates to 40 candidates (76.9%)
Pruning

12 alts after pruning (10 fresh and 2 done)

PrunedKeptTotal
New52052
Fresh01010
Picked011
Done011
Total521264

Merged error: 0.1b

Counts
64 → 12

regimes400.0ms

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
03022
13022

end0.0ms

sample5.5s

Algorithm
intervals
Results
3.3s3557×body1280valid
1.3s2428×body640valid
345.0ms958×body320valid
96.0ms382×body160valid
77.0ms675×body80valid

Profiling

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