Details

Time bar (total: 11.1s)

sample322.0ms

Algorithm
intervals
Results
137.0ms86×body1280valid
58.0ms59×body640valid
26.0ms31×body320valid
13.0ms75×body80valid
2.0ms5×body160valid

simplify6.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03522
15622
25922
35922

prune6.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 0.1b

Counts
2 → 1

localize31.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin theta) (sin delta))
0.3b
(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
0.3b
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
0.4b
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

rewrite20.0ms

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×pow-prod-down prod-exp *-commutative cbrt-unprod sin-mult unswap-sqr
1×sub-neg asin-acos flip3-- diff-log flip--
Counts
4 → 58
Calls
4 calls:
5.0ms
(* (sin theta) (sin delta))
5.0ms
(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
2.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
7.0ms
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

series97.0ms

Counts
4 → 12
Calls
4 calls:
9.0ms
(* (sin theta) (sin delta))
37.0ms
(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
5.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
44.0ms
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

simplify89.0ms

Algorithm
egg-herbie
Counts
70 → 70
Iterations

Useful iterations: 2 (24.0ms)

IterNodesCost
0289930
1894837
23513835
35002835

prune156.0ms

Filtered
51 candidates to 70 candidates (-37.3%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New62870
Fresh000
Picked101
Done000
Total63871

Merged error: 0.0b

Counts
71 → 8

localize35.0ms

Local error

Found 4 expressions with local error:

0.3b
(asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta))))
0.4b
(- (cos delta) (* (sin phi1) (sin (cbrt (pow (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta)))) 3)))))
0.6b
(pow (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta)))) 3)
8.9b
(cbrt (pow (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta)))) 3))

rewrite12.0ms

Algorithm
rewrite-expression-head
Rules
12×cbrt-prod
10×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
6×unpow-prod-down cube-prod add-log-exp
5×pow1 add-exp-log add-cbrt-cube
3×pow-unpow
2×cube-mult unpow3 sqr-pow
1×pow-to-exp sub-neg asin-acos flip3-- pow-pow pow1/3 diff-log pow-exp flip-- rem-cbrt-cube rem-cube-cbrt
Counts
4 → 64
Calls
4 calls:
2.0ms
(asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta))))
3.0ms
(- (cos delta) (* (sin phi1) (sin (cbrt (pow (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta)))) 3)))))
3.0ms
(pow (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta)))) 3)
2.0ms
(cbrt (pow (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta)))) 3))

series78.0ms

Counts
4 → 12
Calls
4 calls:
5.0ms
(asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta))))
46.0ms
(- (cos delta) (* (sin phi1) (sin (cbrt (pow (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta)))) 3)))))
20.0ms
(pow (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta)))) 3)
6.0ms
(cbrt (pow (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta)))) 3))

simplify156.0ms

Algorithm
egg-herbie
Counts
76 → 76
Iterations

Useful iterations: 2 (24.0ms)

IterNodesCost
02261298
17421202
241271196
350021196

prune143.0ms

Filtered
43 candidates to 76 candidates (-76.7%)
Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New75176
Fresh167
Picked011
Done000
Total76884

Merged error: 0.0b

Counts
84 → 8

localize28.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin theta) (sin delta))
0.2b
(* (sin phi1) (* (cos phi1) (* (cos theta) (sin delta))))
0.3b
(pow (sin phi1) 2)
0.4b
(- (cos delta) (+ (* (pow (sin phi1) 2) (cos delta)) (* (sin phi1) (* (cos phi1) (* (cos theta) (sin delta))))))

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
16×pow1 add-exp-log
15×add-cbrt-cube
13×add-sqr-sqrt
11×*-un-lft-identity
9×add-cube-cbrt add-log-exp
7×pow-prod-down prod-exp cbrt-unprod
6×associate-*l*
4×associate-*r*
3×unpow-prod-down pow-unpow
2×diff-log *-commutative
1×pow-to-exp sub-neg flip3-- pow-pow pow-exp sum-log flip-- sin-mult associate--r+ distribute-lft-out-- unpow2 difference-of-squares unswap-sqr sqr-pow
Counts
4 → 74
Calls
4 calls:
5.0ms
(* (sin theta) (sin delta))
9.0ms
(* (sin phi1) (* (cos phi1) (* (cos theta) (sin delta))))
3.0ms
(pow (sin phi1) 2)
7.0ms
(- (cos delta) (+ (* (pow (sin phi1) 2) (cos delta)) (* (sin phi1) (* (cos phi1) (* (cos theta) (sin delta))))))

series82.0ms

Counts
4 → 12
Calls
4 calls:
9.0ms
(* (sin theta) (sin delta))
22.0ms
(* (sin phi1) (* (cos phi1) (* (cos theta) (sin delta))))
4.0ms
(pow (sin phi1) 2)
47.0ms
(- (cos delta) (+ (* (pow (sin phi1) 2) (cos delta)) (* (sin phi1) (* (cos phi1) (* (cos theta) (sin delta))))))

simplify50.0ms

Algorithm
egg-herbie
Counts
86 → 86
Iterations

Useful iterations: 2 (42.0ms)

IterNodesCost
0400786
11562674
25001673

prune146.0ms

Filtered
54 candidates to 86 candidates (-59.3%)
Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New83386
Fresh336
Picked101
Done011
Total87794

Merged error: 0.0b

Counts
94 → 7

localize38.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow (sin phi1) 2)
0.4b
(/ (* (- (cos delta) (+ (* (pow (sin phi1) 2) (cos delta)) (* (sin phi1) (* (cos phi1) (* (cos theta) (sin delta)))))) (+ (* (sin phi1) (* (cos phi1) (* (cos theta) (sin delta)))) (* (+ (pow (sin phi1) 2) 1) (cos delta)))) (+ (* (sin phi1) (* (cos phi1) (* (cos theta) (sin delta)))) (* (+ (pow (sin phi1) 2) 1) (cos delta))))
0.4b
(* (- (cos delta) (+ (* (pow (sin phi1) 2) (cos delta)) (* (sin phi1) (* (cos phi1) (* (cos theta) (sin delta)))))) (+ (* (sin phi1) (* (cos phi1) (* (cos theta) (sin delta)))) (* (+ (pow (sin phi1) 2) 1) (cos delta))))
0.4b
(- (cos delta) (+ (* (pow (sin phi1) 2) (cos delta)) (* (sin phi1) (* (cos phi1) (* (cos theta) (sin delta))))))

rewrite53.0ms

Algorithm
rewrite-expression-head
Rules
16×add-sqr-sqrt
14×*-un-lft-identity
12×add-exp-log
11×add-cbrt-cube
10×add-cube-cbrt
9×add-log-exp
8×frac-times associate-/l/
7×pow1 flip3-- flip3-+ flip-- flip-+
5×associate-*l*
4×associate-*r/ associate-*l/
3×unpow-prod-down pow-unpow times-frac associate-*r* associate-/r*
2×cbrt-undiv diff-log div-exp prod-exp associate-/r/ cbrt-unprod distribute-lft-out-- difference-of-squares
1×distribute-rgt-in pow-to-exp sub-neg pow-pow frac-2neg distribute-lft-in pow-prod-down pow-exp clear-num sum-log *-commutative div-inv associate-/l* associate--r+ unpow2 unswap-sqr sqr-pow
Counts
4 → 95
Calls
4 calls:
3.0ms
(pow (sin phi1) 2)
23.0ms
(/ (* (- (cos delta) (+ (* (pow (sin phi1) 2) (cos delta)) (* (sin phi1) (* (cos phi1) (* (cos theta) (sin delta)))))) (+ (* (sin phi1) (* (cos phi1) (* (cos theta) (sin delta)))) (* (+ (pow (sin phi1) 2) 1) (cos delta)))) (+ (* (sin phi1) (* (cos phi1) (* (cos theta) (sin delta)))) (* (+ (pow (sin phi1) 2) 1) (cos delta))))
17.0ms
(* (- (cos delta) (+ (* (pow (sin phi1) 2) (cos delta)) (* (sin phi1) (* (cos phi1) (* (cos theta) (sin delta)))))) (+ (* (sin phi1) (* (cos phi1) (* (cos theta) (sin delta)))) (* (+ (pow (sin phi1) 2) 1) (cos delta))))
7.0ms
(- (cos delta) (+ (* (pow (sin phi1) 2) (cos delta)) (* (sin phi1) (* (cos phi1) (* (cos theta) (sin delta))))))

series201.0ms

Counts
4 → 12
Calls
4 calls:
4.0ms
(pow (sin phi1) 2)
48.0ms
(/ (* (- (cos delta) (+ (* (pow (sin phi1) 2) (cos delta)) (* (sin phi1) (* (cos phi1) (* (cos theta) (sin delta)))))) (+ (* (sin phi1) (* (cos phi1) (* (cos theta) (sin delta)))) (* (+ (pow (sin phi1) 2) 1) (cos delta)))) (+ (* (sin phi1) (* (cos phi1) (* (cos theta) (sin delta)))) (* (+ (pow (sin phi1) 2) 1) (cos delta))))
104.0ms
(* (- (cos delta) (+ (* (pow (sin phi1) 2) (cos delta)) (* (sin phi1) (* (cos phi1) (* (cos theta) (sin delta)))))) (+ (* (sin phi1) (* (cos phi1) (* (cos theta) (sin delta)))) (* (+ (pow (sin phi1) 2) 1) (cos delta))))
45.0ms
(- (cos delta) (+ (* (pow (sin phi1) 2) (cos delta)) (* (sin phi1) (* (cos phi1) (* (cos theta) (sin delta))))))

simplify119.0ms

Algorithm
egg-herbie
Counts
107 → 107
Iterations

Useful iterations: 1 (16.0ms)

IterNodesCost
05773164
134622690
250012690

prune245.0ms

Filtered
76 candidates to 107 candidates (-40.8%)
Pruning

7 alts after pruning (5 fresh and 2 done)

PrunedKeptTotal
New1070107
Fresh055
Picked011
Done011
Total1077114

Merged error: 0.0b

Counts
114 → 7

regimes487.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04249
14249

end0.0ms

sample8.4s

Algorithm
intervals
Results
5.2s3052×body1280valid
1.8s1846×body640valid
454.0ms708×body320valid
364.0ms2082×body80valid
134.0ms312×body160valid

Profiling

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