Details

Time bar (total: 11.1s)

sample282.0ms

Algorithm
intervals
Results
169.0ms105×body1280valid
58.0ms57×body640valid
18.0ms28×body320valid
11.0ms58×body80valid
3.0ms8×body160valid

simplify6.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03522
15622
25922
35922

prune6.0ms

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: 0.2b

Counts
2 → 1

localize32.0ms

Local error

Found 4 expressions with local error:

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

rewrite15.0ms

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))
1.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
5.0ms
(* (sin phi1) (sin (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)))))))

series95.0ms

Counts
4 → 12
Calls
4 calls:
9.0ms
(* (sin theta) (sin delta))
6.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
34.0ms
(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
45.0ms
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

simplify92.0ms

Algorithm
egg-herbie
Counts
70 → 70
Iterations

Useful iterations: 2 (25.0ms)

IterNodesCost
0289930
1894837
23513835
35002835

prune149.0ms

Filtered
70 candidates to 51 candidates (27.1%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New62870
Fresh000
Picked101
Done000
Total63871

Merged error: 0.1b

Counts
71 → 8

localize38.0ms

Local error

Found 4 expressions with local error:

0.3b
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
0.3b
(* (sin phi1) (sin (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)))))))
0.7b
(log (exp (- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))))

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
8×add-cube-cbrt *-un-lft-identity
7×pow1
6×add-exp-log add-cbrt-cube add-log-exp
5×log-prod
4×log-pow
3×exp-prod associate-*r* associate-*l*
2×sub-neg exp-sum
1×log-div asin-acos flip3-- exp-diff diff-log rem-log-exp pow-prod-down prod-exp *-commutative flip-- cbrt-unprod sin-mult unswap-sqr
Counts
4 → 57
Calls
4 calls:
1.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
6.0ms
(* (sin phi1) (sin (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)))))))
3.0ms
(log (exp (- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))))

series126.0ms

Counts
4 → 12
Calls
4 calls:
5.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
33.0ms
(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
45.0ms
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))
42.0ms
(log (exp (- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))))

simplify85.0ms

Algorithm
egg-herbie
Counts
69 → 69
Iterations

Useful iterations: 2 (21.0ms)

IterNodesCost
02531234
17641106
229491102
350011102

prune152.0ms

Filtered
69 candidates to 51 candidates (26.1%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New67269
Fresh167
Picked011
Done000
Total68977

Merged error: 0.1b

Counts
77 → 9

localize35.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
0.4b
(- (cos delta) (cbrt (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)))
0.4b
(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)
17.0b
(cbrt (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3))

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
15×add-sqr-sqrt
10×cbrt-prod *-un-lft-identity
9×pow1 add-exp-log add-cbrt-cube
8×add-cube-cbrt
6×add-log-exp
3×pow-unpow associate-*r* associate-*l* sin-mult difference-of-squares sqr-pow
2×cube-div cube-mult unpow-prod-down pow-pow unpow3 cube-prod pow-prod-down pow-exp prod-exp cbrt-unprod rem-cube-cbrt
1×pow-to-exp sub-neg cbrt-div flip3-- pow1/3 diff-log *-commutative flip-- rem-cbrt-cube distribute-lft-out-- unswap-sqr
Counts
4 → 76
Calls
4 calls:
5.0ms
(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
6.0ms
(- (cos delta) (cbrt (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)))
5.0ms
(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)
3.0ms
(cbrt (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3))

series178.0ms

Counts
4 → 12
Calls
4 calls:
35.0ms
(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
42.0ms
(- (cos delta) (cbrt (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)))
64.0ms
(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)
36.0ms
(cbrt (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3))

simplify53.0ms

Algorithm
egg-herbie
Counts
88 → 88
Iterations

Useful iterations: 2 (40.0ms)

IterNodesCost
03341587
113101468
250021463

prune187.0ms

Filtered
88 candidates to 62 candidates (29.5%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New85388
Fresh257
Picked101
Done011
Total88997

Merged error: 0.0b

Counts
97 → 9

localize31.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow (sin phi1) 3)
0.4b
(- (cos delta) (cbrt (* (pow (sin phi1) 3) (pow (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta))) 3))))
0.6b
(pow (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta))) 3)
17.0b
(cbrt (* (pow (sin phi1) 3) (pow (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta))) 3)))

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt *-un-lft-identity
10×add-cube-cbrt
6×pow1 add-exp-log cube-div unpow-prod-down pow-unpow cube-prod add-cbrt-cube add-log-exp
5×associate-*r/
3×cbrt-div
2×cube-mult pow-to-exp pow-pow flip3-+ unpow3 frac-add pow-exp cos-mult sin-cos-mult flip-+ rem-cube-cbrt sqr-pow
1×cbrt-prod sub-neg flip3-- pow1/3 diff-log pow-prod-down flip-- rem-cbrt-cube distribute-lft-out-- difference-of-squares
Counts
4 → 76
Calls
4 calls:
3.0ms
(pow (sin phi1) 3)
4.0ms
(- (cos delta) (cbrt (* (pow (sin phi1) 3) (pow (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta))) 3))))
8.0ms
(pow (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta))) 3)
12.0ms
(cbrt (* (pow (sin phi1) 3) (pow (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta))) 3)))

series129.0ms

Counts
4 → 12
Calls
4 calls:
5.0ms
(pow (sin phi1) 3)
43.0ms
(- (cos delta) (cbrt (* (pow (sin phi1) 3) (pow (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta))) 3))))
47.0ms
(pow (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta))) 3)
34.0ms
(cbrt (* (pow (sin phi1) 3) (pow (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta))) 3)))

simplify73.0ms

Algorithm
egg-herbie
Counts
88 → 88
Iterations

Useful iterations: 2 (62.0ms)

IterNodesCost
04591170
120111074
250021065

prune133.0ms

Filtered
88 candidates to 54 candidates (38.6%)
Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New86288
Fresh257
Picked011
Done011
Total88997

Merged error: 0.0b

Counts
97 → 9

regimes560.0ms

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
03021
13021

end0.0ms

sample8.6s

Algorithm
intervals
Results
5.2s3116×body1280valid
1.9s1827×body640valid
452.0ms728×body320valid
360.0ms2030×body80valid
132.0ms299×body160valid

Profiling

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