Details

Time bar (total: 10.6s)

sample298.0ms

Algorithm
intervals
Results
177.0ms107×body1280valid
62.0ms68×body640valid
19.0ms30×body320valid
8.0ms46×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

localize32.0ms

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))))
0.5b
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

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×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:
4.0ms
(* (sin theta) (sin delta))
5.0ms
(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
1.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
3.0ms
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

series94.0ms

Counts
4 → 12
Calls
4 calls:
9.0ms
(* (sin theta) (sin delta))
34.0ms
(* (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))))
46.0ms
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

simplify88.0ms

Algorithm
egg-herbie
Counts
70 → 70
Iterations

Useful iterations: 2 (23.0ms)

IterNodesCost
0289930
1894837
23513835
35002835

prune172.0ms

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

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New601070
Fresh000
Picked101
Done000
Total611071

Merged error: 0.0b

Counts
71 → 10

localize37.0ms

Local error

Found 4 expressions with local error:

0.3b
(asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta))))
0.5b
(- (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)
5.8b
(cbrt (pow (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta)))) 3))

rewrite24.0ms

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:
3.0ms
(asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta))))
6.0ms
(- (cos delta) (* (sin phi1) (sin (cbrt (pow (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta)))) 3)))))
6.0ms
(pow (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta)))) 3)
5.0ms
(cbrt (pow (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta)))) 3))

series81.0ms

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)
9.0ms
(cbrt (pow (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta)))) 3))

simplify155.0ms

Algorithm
egg-herbie
Counts
76 → 76
Iterations

Useful iterations: 2 (25.0ms)

IterNodesCost
02261298
17421202
241271196
350021196

prune160.0ms

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

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New74276
Fresh369
Picked101
Done000
Total78886

Merged error: 0.0b

Counts
86 → 8

localize28.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin theta) (sin delta))
0.3b
(* (sin phi1) (* (cos phi1) (* (cos theta) (sin delta))))
0.3b
(pow (sin phi1) 2)
0.5b
(- (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))))))

series77.0ms

Counts
4 → 12
Calls
4 calls:
9.0ms
(* (sin theta) (sin delta))
20.0ms
(* (sin phi1) (* (cos phi1) (* (cos theta) (sin delta))))
3.0ms
(pow (sin phi1) 2)
44.0ms
(- (cos delta) (+ (* (pow (sin phi1) 2) (cos delta)) (* (sin phi1) (* (cos phi1) (* (cos theta) (sin delta))))))

simplify49.0ms

Algorithm
egg-herbie
Counts
86 → 86
Iterations

Useful iterations: 2 (42.0ms)

IterNodesCost
0400786
11562674
25001673

prune166.0ms

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

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New83386
Fresh347
Picked101
Done000
Total87794

Merged error: 0.0b

Counts
94 → 7

localize28.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin theta) (sin delta))
0.3b
(* (sin phi1) (* (cos phi1) (* (cos theta) (sin delta))))
0.3b
(pow (sin phi1) 2)
0.6b
(- (cos delta) (* (pow (sin phi1) 2) (cos delta)))

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
16×pow1 add-exp-log
15×add-cbrt-cube
11×add-sqr-sqrt
10×*-un-lft-identity
9×add-cube-cbrt
7×pow-prod-down prod-exp cbrt-unprod
6×associate-*l* add-log-exp
4×associate-*r*
3×unpow-prod-down pow-unpow
2×*-commutative
1×pow-to-exp sub-neg flip3-- distribute-rgt-out-- pow-pow diff-log pow-exp flip-- sin-mult unpow2 unswap-sqr sqr-pow
Counts
4 → 71
Calls
4 calls:
6.0ms
(* (sin theta) (sin delta))
8.0ms
(* (sin phi1) (* (cos phi1) (* (cos theta) (sin delta))))
2.0ms
(pow (sin phi1) 2)
3.0ms
(- (cos delta) (* (pow (sin phi1) 2) (cos delta)))

series47.0ms

Counts
4 → 12
Calls
4 calls:
9.0ms
(* (sin theta) (sin delta))
20.0ms
(* (sin phi1) (* (cos phi1) (* (cos theta) (sin delta))))
3.0ms
(pow (sin phi1) 2)
14.0ms
(- (cos delta) (* (pow (sin phi1) 2) (cos delta)))

simplify45.0ms

Algorithm
egg-herbie
Counts
83 → 83
Iterations

Useful iterations: 2 (39.0ms)

IterNodesCost
0372553
11482456
25002444

prune111.0ms

Filtered
52 candidates to 83 candidates (-59.6%)
Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New81283
Fresh246
Picked101
Done000
Total84690

Merged error: 0.0b

Counts
90 → 6

regimes462.0ms

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
03546
13546

end0.0ms

sample8.4s

Algorithm
intervals
Results
5.1s3112×body1280valid
1.8s1812×body640valid
467.0ms734×body320valid
370.0ms2014×body80valid
138.0ms328×body160valid

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