Details

Time bar (total: 7.8s)

sample204.0ms

Algorithm
intervals
Results
107.0ms121×body1280valid
40.0ms76×body640valid
16.0ms30×body320valid
2.0ms20×body80valid
2.0ms9×body160valid

simplify6.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02012
12112
22112

prune10.0ms

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: 1.0b

Counts
2 → 1

localize23.0ms

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))
4.5b
(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))

series42.0ms

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

simplify122.0ms

Algorithm
egg-herbie
Counts
52 → 52
Iterations

Useful iterations: 1 (7.0ms)

IterNodesCost
0205421
1508374
21327374
33684374
45001374

prune160.0ms

Filtered
52 candidates to 42 candidates (19.2%)
Pruning

15 alts after pruning (15 fresh and 0 done)

PrunedKeptTotal
New371552
Fresh000
Picked101
Done000
Total381553

Merged error: 0.8b

Counts
53 → 15

localize32.0ms

Local error

Found 4 expressions with local error:

0.2b
(atan2 (* (cos phi2) (sin (- lambda1 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)))))
4.5b
(sin (- lambda1 lambda2))

rewrite14.0ms

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×associate-*r* associate-*l*
2×associate-+r+ sin-sum
1×+-commutative distribute-rgt-in sub-neg distribute-lft-in flip3-+ pow-prod-down prod-exp sum-log sin-diff *-commutative cbrt-unprod flip-+ sin-mult unswap-sqr
Counts
4 → 49
Calls
4 calls:
1.0ms
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
5.0ms
(* (sin lambda1) (sin lambda2))
4.0ms
(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))
4.0ms
(sin (- lambda1 lambda2))

series79.0ms

Counts
4 → 12
Calls
4 calls:
13.0ms
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
13.0ms
(* (sin lambda1) (sin lambda2))
49.0ms
(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))
4.0ms
(sin (- lambda1 lambda2))

simplify98.0ms

Algorithm
egg-herbie
Counts
61 → 61
Iterations

Useful iterations: 1 (7.0ms)

IterNodesCost
0266635
1830549
23809549
35002549

prune137.0ms

Filtered
61 candidates to 45 candidates (26.2%)
Pruning

14 alts after pruning (14 fresh and 0 done)

PrunedKeptTotal
New60161
Fresh11314
Picked101
Done000
Total621476

Merged error: 0.1b

Counts
76 → 14

localize29.0ms

Local error

Found 4 expressions with local error:

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

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt add-log-exp
6×pow1 add-exp-log add-cube-cbrt *-un-lft-identity add-cbrt-cube
3×associate-*r* associate-*l*
2×+-commutative associate-+r+ flip3-+ sum-log flip-+ sin-mult
1×distribute-rgt-in distribute-lft-in pow-prod-down frac-add prod-exp cos-mult *-commutative cbrt-unprod unswap-sqr
Counts
4 → 51
Calls
4 calls:
5.0ms
(+ (* (cos lambda1) (cos lambda2)) (* (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))))))
5.0ms
(* (sin lambda1) (sin lambda2))
4.0ms
(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

series88.0ms

Counts
4 → 12
Calls
4 calls:
15.0ms
(+ (* (cos lambda1) (cos lambda2)) (* (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))))))
9.0ms
(* (sin lambda1) (sin lambda2))
50.0ms
(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

simplify40.0ms

Algorithm
egg-herbie
Counts
63 → 63
Iterations

Useful iterations: 1 (9.0ms)

IterNodesCost
0330805
11122705
25001705

prune131.0ms

Filtered
63 candidates to 47 candidates (25.4%)
Pruning

14 alts after pruning (13 fresh and 1 done)

PrunedKeptTotal
New63063
Fresh01313
Picked011
Done000
Total631477

Merged error: 0.1b

Counts
77 → 14

localize30.0ms

Local error

Found 4 expressions with local error:

4.5b
(sin (- lambda1 lambda2))
4.5b
(cos (- lambda1 lambda2))
4.5b
(cos (- lambda1 lambda2))
4.5b
(cos (- 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
(sin (- lambda1 lambda2))
4.0ms
(cos (- lambda1 lambda2))
4.0ms
(cos (- lambda1 lambda2))
4.0ms
(cos (- lambda1 lambda2))

series16.0ms

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

simplify53.0ms

Algorithm
egg-herbie
Counts
52 → 52
Iterations

Useful iterations: 4 (50.0ms)

IterNodesCost
083235
1149215
2390215
31140215
45001212

prune82.0ms

Filtered
52 candidates to 40 candidates (23.1%)
Pruning

15 alts after pruning (13 fresh and 2 done)

PrunedKeptTotal
New50252
Fresh11112
Picked011
Done011
Total511566

Merged error: 0.1b

Counts
66 → 15

regimes738.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03022
13022

end0.0ms

sample5.6s

Algorithm
intervals
Results
3.3s3497×body1280valid
1.3s2321×body640valid
366.0ms1002×body320valid
105.0ms433×body160valid
86.0ms747×body80valid

Profiling

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