Details

Time bar (total: 12.6s)

sample296.0ms

Algorithm
intervals
Results
178.0ms105×body1280valid
51.0ms55×body640valid
15.0ms24×body320valid
12.0ms66×body80valid
2.0ms6×body160valid

simplify7.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03522
15622
25922
35922

prune9.0ms

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: 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))))
0.6b
(- (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:
5.0ms
(* (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))))
4.0ms
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

series96.0ms

Counts
4 → 12
Calls
4 calls:
10.0ms
(* (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))))
47.0ms
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

simplify94.0ms

Algorithm
egg-herbie
Counts
70 → 70
Iterations

Useful iterations: 2 (25.0ms)

IterNodesCost
0289930
1894837
23513835
35002835

prune502.0ms

Filtered
70 candidates to 51 candidates (27.1%)
Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New63770
Fresh000
Picked101
Done000
Total64771

Merged error: 0.0b

Counts
71 → 7

localize39.0ms

Local error

Found 4 expressions with local error:

0.6b
(- (cos delta) (* (* (cbrt (sin phi1)) (cbrt (sin phi1))) (* (cbrt (sin phi1)) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))
0.6b
(cbrt (sin phi1))
0.6b
(cbrt (sin phi1))
0.6b
(cbrt (sin phi1))

rewrite9.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod
7×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
6×add-log-exp
4×pow1 add-exp-log add-cbrt-cube
3×pow1/3
1×sub-neg flip3-- diff-log flip--
Counts
4 → 45
Calls
4 calls:
4.0ms
(- (cos delta) (* (* (cbrt (sin phi1)) (cbrt (sin phi1))) (* (cbrt (sin phi1)) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))
1.0ms
(cbrt (sin phi1))
1.0ms
(cbrt (sin phi1))
2.0ms
(cbrt (sin phi1))

series103.0ms

Counts
4 → 12
Calls
4 calls:
44.0ms
(- (cos delta) (* (* (cbrt (sin phi1)) (cbrt (sin phi1))) (* (cbrt (sin phi1)) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))
22.0ms
(cbrt (sin phi1))
18.0ms
(cbrt (sin phi1))
18.0ms
(cbrt (sin phi1))

simplify139.0ms

Algorithm
egg-herbie
Counts
57 → 57
Iterations

Useful iterations: 3 (133.0ms)

IterNodesCost
0211691
1672617
23481585
35002582

prune410.0ms

Filtered
57 candidates to 45 candidates (21.1%)
Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New56157
Fresh156
Picked011
Done000
Total57764

Merged error: 0.0b

Counts
64 → 7

localize42.0ms

Local error

Found 4 expressions with local error:

0.6b
(- (cos delta) (* (* (sin phi1) (* (cbrt (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) (cbrt (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))) (cbrt (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))
0.6b
(cbrt (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
0.6b
(cbrt (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
0.6b
(cbrt (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))

rewrite9.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod
7×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
6×add-log-exp
4×pow1 add-exp-log add-cbrt-cube
3×pow1/3
1×sub-neg flip3-- diff-log flip--
Counts
4 → 45
Calls
4 calls:
3.0ms
(- (cos delta) (* (* (sin phi1) (* (cbrt (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) (cbrt (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))) (cbrt (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))
2.0ms
(cbrt (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
2.0ms
(cbrt (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
2.0ms
(cbrt (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))

series231.0ms

Counts
4 → 12
Calls
4 calls:
47.0ms
(- (cos delta) (* (* (sin phi1) (* (cbrt (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) (cbrt (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))) (cbrt (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))
61.0ms
(cbrt (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
60.0ms
(cbrt (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
63.0ms
(cbrt (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))

simplify91.0ms

Algorithm
egg-herbie
Counts
57 → 57
Iterations

Useful iterations: 3 (80.0ms)

IterNodesCost
02191599
16051339
226811232
350011229

prune435.0ms

Filtered
57 candidates to 45 candidates (21.1%)
Pruning

7 alts after pruning (5 fresh and 2 done)

PrunedKeptTotal
New57057
Fresh055
Picked011
Done011
Total57764

Merged error: 0.0b

Counts
64 → 7

localize46.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (sin phi1))
0.6b
(cbrt (sin phi1))
0.6b
(cbrt (sin phi1))
0.6b
(cbrt (sin phi1))

rewrite7.0ms

Algorithm
rewrite-expression-head
Rules
12×cbrt-prod
8×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
4×pow1 add-exp-log pow1/3 add-cbrt-cube add-log-exp
Counts
4 → 44
Calls
4 calls:
1.0ms
(cbrt (sin phi1))
2.0ms
(cbrt (sin phi1))
2.0ms
(cbrt (sin phi1))
2.0ms
(cbrt (sin phi1))

series75.0ms

Counts
4 → 12
Calls
4 calls:
20.0ms
(cbrt (sin phi1))
18.0ms
(cbrt (sin phi1))
18.0ms
(cbrt (sin phi1))
18.0ms
(cbrt (sin phi1))

simplify195.0ms

Algorithm
egg-herbie
Counts
56 → 56
Iterations

Useful iterations: 3 (30.0ms)

IterNodesCost
070300
1189280
2652256
33901208
45001208

prune431.0ms

Filtered
56 candidates to 44 candidates (21.4%)
Pruning

7 alts after pruning (4 fresh and 3 done)

PrunedKeptTotal
New56056
Fresh044
Picked011
Done022
Total56763

Merged error: 0.0b

Counts
63 → 7

regimes590.0ms

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
03429
13429

end0.0ms

sample8.7s

Algorithm
intervals
Results
5.3s3078×body1280valid
1.8s1900×body640valid
453.0ms707×body320valid
371.0ms2022×body80valid
130.0ms293×body160valid

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