Details

Time bar (total: 7.7s)

sample195.0ms

Algorithm
intervals
Results
117.0ms120×body1280valid
38.0ms71×body640valid
12.0ms32×body320valid
4.0ms15×body160valid
2.0ms18×body80valid

simplify2.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02120
12120

prune5.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 0.4b

Counts
2 → 1

localize25.0ms

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))))
4.5b
(sin (- lambda1 lambda2))
4.6b
(cos (- lambda1 lambda2))

rewrite15.0ms

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))
5.0ms
(cos (- lambda1 lambda2))

series48.0ms

Counts
4 → 12
Calls
4 calls:
9.0ms
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
27.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
5.0ms
(sin (- lambda1 lambda2))
6.0ms
(cos (- lambda1 lambda2))

simplify33.0ms

Algorithm
egg-herbie
Counts
52 → 52
Iterations

Useful iterations: 0 (28.0ms)

IterNodesCost
05089613

prune150.0ms

Filtered
42 candidates to 52 candidates (-23.8%)
Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New421052
Fresh000
Picked101
Done000
Total431053

Merged error: 0.2b

Counts
53 → 10

localize28.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (cos lambda2) (sin lambda1))
0.2b
(atan2 (* (cos phi2) (- (* (cos lambda2) (sin lambda1)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
0.6b
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
4.6b
(cos (- lambda1 lambda2))

rewrite16.0ms

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×cos-diff associate-*r* associate-*l*
2×cos-sum associate-+r+
1×+-commutative distribute-rgt-in sub-neg distribute-lft-in flip3-+ pow-prod-down prod-exp sum-log *-commutative cbrt-unprod flip-+ unswap-sqr
Counts
4 → 48
Calls
4 calls:
5.0ms
(* (cos lambda2) (sin lambda1))
1.0ms
(atan2 (* (cos phi2) (- (* (cos lambda2) (sin lambda1)) (* (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))

series55.0ms

Counts
4 → 12
Calls
4 calls:
10.0ms
(* (cos lambda2) (sin lambda1))
11.0ms
(atan2 (* (cos phi2) (- (* (cos lambda2) (sin lambda1)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
29.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
4.0ms
(cos (- lambda1 lambda2))

simplify43.0ms

Algorithm
egg-herbie
Counts
60 → 60
Iterations

Useful iterations: 0 (37.0ms)

IterNodesCost
04890741
14890741

prune123.0ms

Filtered
45 candidates to 60 candidates (-33.3%)
Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New59160
Fresh189
Picked101
Done000
Total61970

Merged error: 0.1b

Counts
70 → 9

localize28.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
0.2b
(atan2 (* (cos phi2) (- (* (cos lambda2) (sin lambda1)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
0.2b
(* (sin lambda1) (sin lambda2))
0.6b
(+ (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×associate-*r/
2×distribute-rgt-in associate-+r+ distribute-lft-in flip3-+ pow-prod-down prod-exp *-commutative cbrt-unprod flip-+ sin-mult unswap-sqr
1×+-commutative frac-add sum-log cos-mult
Counts
4 → 62
Calls
4 calls:
10.0ms
(* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
1.0ms
(atan2 (* (cos phi2) (- (* (cos lambda2) (sin lambda1)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
6.0ms
(* (sin lambda1) (sin lambda2))
5.0ms
(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

series119.0ms

Counts
4 → 12
Calls
4 calls:
34.0ms
(* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
15.0ms
(atan2 (* (cos phi2) (- (* (cos lambda2) (sin lambda1)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
11.0ms
(* (sin lambda1) (sin lambda2))
59.0ms
(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

simplify46.0ms

Algorithm
egg-herbie
Counts
74 → 74
Iterations

Useful iterations: 0 (38.0ms)

IterNodesCost
049291262
149291262

prune127.0ms

Filtered
53 candidates to 74 candidates (-39.6%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New74074
Fresh088
Picked011
Done000
Total74983

Merged error: 0.1b

Counts
83 → 9

localize27.0ms

Local error

Found 4 expressions with local error:

4.5b
(sin (- lambda1 lambda2))
4.6b
(cos (- lambda1 lambda2))
4.6b
(cos (- lambda1 lambda2))
4.6b
(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))
5.0ms
(cos (- lambda1 lambda2))
5.0ms
(cos (- lambda1 lambda2))
5.0ms
(cos (- lambda1 lambda2))

series18.0ms

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

simplify59.0ms

Algorithm
egg-herbie
Counts
52 → 52
Iterations

Useful iterations: 0 (54.0ms)

IterNodesCost
04964364
14964364

prune67.0ms

Filtered
40 candidates to 52 candidates (-30.0%)
Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New52052
Fresh077
Picked011
Done011
Total52961

Merged error: 0.1b

Counts
61 → 9

regimes545.0ms

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
03034
13034

end0.0ms

sample5.9s

Algorithm
intervals
Results
3.4s3685×body1280valid
1.5s2281×body640valid
365.0ms952×body320valid
108.0ms413×body160valid
83.0ms669×body80valid

Profiling

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