Details

Time bar (total: 7.9s)

sample188.0ms

Algorithm
intervals
Results
101.0ms110×body1280valid
43.0ms80×body640valid
12.0ms34×body320valid
3.0ms13×body160valid
2.0ms19×body80valid

simplify5.0ms

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: 0.9b

Counts
2 → 1

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
0.6b
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
3.8b
(cos (- lambda1 lambda2))
4.1b
(sin (- lambda1 lambda2))

rewrite18.0ms

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)))))
8.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
4.0ms
(cos (- lambda1 lambda2))
4.0ms
(sin (- lambda1 lambda2))

series43.0ms

Counts
4 → 12
Calls
4 calls:
9.0ms
(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))
6.0ms
(sin (- lambda1 lambda2))

simplify127.0ms

Algorithm
egg-herbie
Counts
52 → 52
Iterations

Useful iterations: 1 (6.0ms)

IterNodesCost
0205421
1508374
21327374
33685374
45001374

prune151.0ms

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: 0.7b

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)))))
0.6b
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
3.8b
(cos (- lambda1 lambda2))

rewrite17.0ms

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))

series68.0ms

Counts
4 → 12
Calls
4 calls:
30.0ms
(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
11.0ms
(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))

simplify125.0ms

Algorithm
egg-herbie
Counts
66 → 66
Iterations

Useful iterations: 1 (8.0ms)

IterNodesCost
0289748
11037658
24438658
35002658

prune141.0ms

Filtered
66 candidates to 48 candidates (27.3%)
Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New64266
Fresh11011
Picked101
Done000
Total661278

Merged error: 0.1b

Counts
78 → 12

localize33.0ms

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))))))
0.7b
(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

rewrite19.0ms

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:
8.0ms
(* (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)))))

series105.0ms

Counts
4 → 12
Calls
4 calls:
30.0ms
(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
12.0ms
(* (sin lambda1) (sin lambda2))
13.0ms
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
49.0ms
(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

simplify47.0ms

Algorithm
egg-herbie
Counts
75 → 75
Iterations

Useful iterations: 1 (10.0ms)

IterNodesCost
0345962
11380833
25001833

prune142.0ms

Filtered
75 candidates to 52 candidates (30.7%)
Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New72375
Fresh3811
Picked101
Done000
Total761187

Merged error: 0.1b

Counts
87 → 11

localize34.0ms

Local error

Found 4 expressions with local error:

3.8b
(cos (- lambda1 lambda2))
3.8b
(cos (- lambda1 lambda2))
3.8b
(cos (- lambda1 lambda2))
4.1b
(sin (- lambda1 lambda2))

rewrite17.0ms

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))

series17.0ms

Counts
4 → 12
Calls
4 calls:
4.0ms
(cos (- lambda1 lambda2))
4.0ms
(cos (- lambda1 lambda2))
4.0ms
(cos (- lambda1 lambda2))
5.0ms
(sin (- lambda1 lambda2))

simplify57.0ms

Algorithm
egg-herbie
Counts
52 → 52
Iterations

Useful iterations: 4 (53.0ms)

IterNodesCost
083235
1149215
2390215
31141215
45001212

prune86.0ms

Filtered
52 candidates to 40 candidates (23.1%)
Pruning

12 alts after pruning (11 fresh and 1 done)

PrunedKeptTotal
New50252
Fresh1910
Picked011
Done000
Total511263

Merged error: 0.1b

Counts
63 → 12

regimes677.0ms

Accuracy

0% (0.8b remaining)

Error of 1.0b against oracle of 0.1b and baseline of 1.0b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02830
12830

end0.0ms

sample5.8s

Algorithm
intervals
Results
3.4s3581×body1280valid
1.3s2363×body640valid
337.0ms945×body320valid
97.0ms416×body160valid
86.0ms695×body80valid

Profiling

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