Details

Time bar (total: 16.4s)

sample4.0s

Algorithm
intervals
sampling

Space saved by range analysis: 0%

Space saved by search: 0%

Guaranteed chance to sample good point: 0%

Results
102.0ms107×body1280valid
48.0ms76×body640valid
13.0ms35×body320valid
3.0ms26×body80valid
3.0ms12×body160valid

simplify5.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02012
12112
22112

prune5.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 1.3b

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))))
3.9b
(cos (- lambda1 lambda2))
4.1b
(sin (- lambda1 lambda2))

rewrite14.0ms

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))

series48.0ms

Counts
4 → 12
Calls
4 calls:
9.0ms
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
30.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
4.0ms
(cos (- lambda1 lambda2))
5.0ms
(sin (- lambda1 lambda2))

simplify126.0ms

Algorithm
egg-herbie
Counts
52 → 52
Iterations

Useful iterations: 1 (6.0ms)

IterNodesCost
0205421
1508374
21327374
33685374
45001374

prune139.0ms

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: 0.9b

Counts
53 → 10

localize33.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (cos phi2) (cos (- lambda1 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))))
3.9b
(cos (- lambda1 lambda2))

rewrite15.0ms

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
5×cos-diff
3×associate-*r* associate-*l*
2×distribute-rgt-in cos-sum associate-+r+ distribute-lft-in
1×+-commutative sub-neg flip3-+ pow-prod-down prod-exp sum-log cos-mult *-commutative cbrt-unprod flip-+ unswap-sqr
Counts
4 → 51
Calls
4 calls:
5.0ms
(* (cos phi2) (cos (- lambda1 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))

series54.0ms

Counts
4 → 12
Calls
4 calls:
14.0ms
(* (cos phi2) (cos (- lambda1 lambda2)))
10.0ms
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
25.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
4.0ms
(cos (- lambda1 lambda2))

simplify75.0ms

Algorithm
egg-herbie
Counts
63 → 63
Iterations

Useful iterations: 1 (7.0ms)

IterNodesCost
0242574
1728512
22584512
35002512

prune124.0ms

Filtered
46 candidates to 63 candidates (-37.0%)
Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New62163
Fresh189
Picked101
Done000
Total64973

Merged error: 0.1b

Counts
73 → 9

localize34.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (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))))))
0.6b
(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

rewrite16.0ms

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
2×associate-+r+ pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×+-commutative distribute-rgt-in distribute-lft-in flip3-+ sum-log flip-+ sin-mult
Counts
4 → 57
Calls
4 calls:
5.0ms
(* (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)))))

series89.0ms

Counts
4 → 12
Calls
4 calls:
10.0ms
(* (cos lambda1) (sin lambda2))
12.0ms
(* (sin 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)))))

simplify128.0ms

Algorithm
egg-herbie
Counts
69 → 69
Iterations

Useful iterations: 1 (8.0ms)

IterNodesCost
0309746
11069641
24897641
35001641

prune127.0ms

Filtered
49 candidates to 69 candidates (-40.8%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New67269
Fresh268
Picked101
Done000
Total70878

Merged error: 0.1b

Counts
78 → 8

localize40.0ms

Local error

Found 4 expressions with local error:

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

rewrite12.0ms

Algorithm
rewrite-expression-head
Rules
25×cbrt-prod
23×add-sqr-sqrt
15×add-cube-cbrt *-un-lft-identity
11×pow1
9×pow1/3
6×add-exp-log swap-sqr associate-*r* associate-*l*
4×add-cbrt-cube add-log-exp unswap-sqr
2×pow-prod-down pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 73
Calls
4 calls:
6.0ms
(* (cbrt (atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))) (cbrt (atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))))
1.0ms
(cbrt (atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))
1.0ms
(cbrt (atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))
1.0ms
(cbrt (atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))

series296.0ms

Counts
4 → 12
Calls
4 calls:
100.0ms
(* (cbrt (atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))) (cbrt (atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))))
66.0ms
(cbrt (atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))
65.0ms
(cbrt (atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))
65.0ms
(cbrt (atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))

simplify80.0ms

Algorithm
egg-herbie
Counts
85 → 85
Iterations

Useful iterations: 3 (59.0ms)

IterNodesCost
01553332
13972959
217352692
350012656

prune89.0ms

Filtered
52 candidates to 85 candidates (-63.5%)
Pruning

11 alts after pruning (10 fresh and 1 done)

PrunedKeptTotal
New82385
Fresh077
Picked011
Done000
Total821193

Merged error: 0.1b

Counts
93 → 11

regimes682.0ms

Accuracy

0% (0.6b remaining)

Error of 0.7b against oracle of 0.1b and baseline of 0.7b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03469
13469

end0.0ms

sample10.1s

Algorithm
intervals
sampling

Space saved by range analysis: 0%

Space saved by search: 0%

Guaranteed chance to sample good point: 0%

Results
3.7s3623×body1280valid
1.4s2342×body640valid
342.0ms890×body320valid
126.0ms441×body160valid
82.0ms704×body80valid

Profiling

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