Details

Time bar (total: 7.6s)

sample184.0ms

Algorithm
intervals
Results
99.0ms107×body1280valid
46.0ms79×body640valid
10.0ms28×body320valid
4.0ms19×body160valid
2.0ms23×body80valid

simplify4.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02012
12112
22112

prune5.0ms

Filtered
1 candidates to 0 candidates (100.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 1.1b

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))))
4.1b
(cos (- lambda1 lambda2))
4.1b
(sin (- lambda1 lambda2))

rewrite12.0ms

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
(cos (- lambda1 lambda2))
4.0ms
(sin (- lambda1 lambda2))

series41.0ms

Counts
4 → 12
Calls
4 calls:
8.0ms
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
24.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
4.0ms
(cos (- lambda1 lambda2))
4.0ms
(sin (- lambda1 lambda2))

simplify120.0ms

Algorithm
egg-herbie
Counts
52 → 52
Iterations

Useful iterations: 1 (5.0ms)

IterNodesCost
0205421
1508374
21327374
33685374
45001374

prune137.0ms

Filtered
52 candidates to 42 candidates (19.2%)
Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New401252
Fresh000
Picked101
Done000
Total411253

Merged error: 0.9b

Counts
53 → 12

localize30.0ms

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)))))
0.5b
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
4.1b
(cos (- lambda1 lambda2))

rewrite19.0ms

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:
9.0ms
(* (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))

series66.0ms

Counts
4 → 12
Calls
4 calls:
29.0ms
(* (cos phi2) (- (* (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))

simplify118.0ms

Algorithm
egg-herbie
Counts
66 → 66
Iterations

Useful iterations: 1 (7.0ms)

IterNodesCost
0289748
11037658
24438658
35002658

prune126.0ms

Filtered
66 candidates to 48 candidates (27.3%)
Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New63366
Fresh5611
Picked101
Done000
Total69978

Merged error: 0.1b

Counts
78 → 9

localize30.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (cos lambda1) (sin lambda2))
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) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
0.6b
(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

rewrite18.0ms

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-+
Counts
4 → 62
Calls
4 calls:
4.0ms
(* (cos lambda1) (sin lambda2))
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) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
4.0ms
(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

series105.0ms

Counts
4 → 12
Calls
4 calls:
9.0ms
(* (cos lambda1) (sin lambda2))
30.0ms
(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
14.0ms
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
53.0ms
(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

simplify44.0ms

Algorithm
egg-herbie
Counts
74 → 74
Iterations

Useful iterations: 1 (9.0ms)

IterNodesCost
0354956
11394834
25001834

prune115.0ms

Filtered
74 candidates to 51 candidates (31.1%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New74074
Fresh088
Picked011
Done000
Total74983

Merged error: 0.1b

Counts
83 → 9

localize33.0ms

Local error

Found 4 expressions with local error:

4.1b
(cos (- lambda1 lambda2))
4.1b
(cos (- lambda1 lambda2))
4.1b
(cos (- lambda1 lambda2))
4.1b
(sin (- lambda1 lambda2))

rewrite16.0ms

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
(cos (- lambda1 lambda2))
4.0ms
(cos (- lambda1 lambda2))
4.0ms
(cos (- lambda1 lambda2))
4.0ms
(sin (- lambda1 lambda2))

series16.0ms

Counts
4 → 12
Calls
4 calls:
4.0ms
(cos (- lambda1 lambda2))
4.0ms
(cos (- lambda1 lambda2))
4.0ms
(cos (- lambda1 lambda2))
4.0ms
(sin (- lambda1 lambda2))

simplify52.0ms

Algorithm
egg-herbie
Counts
52 → 52
Iterations

Useful iterations: 4 (48.0ms)

IterNodesCost
083235
1149215
2390215
31141215
45001212

prune82.0ms

Filtered
52 candidates to 40 candidates (23.1%)
Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New52052
Fresh077
Picked011
Done011
Total52961

Merged error: 0.1b

Counts
61 → 9

regimes526.0ms

Accuracy

0% (0.1b 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 (0.0ms)

IterNodesCost
03022
13022

end0.0ms

sample5.7s

Algorithm
intervals
Results
3.4s3633×body1280valid
1.3s2319×body640valid
341.0ms927×body320valid
102.0ms416×body160valid
77.0ms705×body80valid

Profiling

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