Details

Time bar (total: 19.7s)

analyze3.6s

Algorithm
search

sample316.0ms

Algorithm
intervals
Results
203.0ms110×body1280valid
63.0ms57×body640valid
15.0ms21×body320valid
13.0ms64×body80valid
2.0ms4×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))))
0.5b
(- (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))
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))
33.0ms
(* (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)))))))

simplify89.0ms

Algorithm
egg-herbie
Counts
70 → 70
Iterations

Useful iterations: 2 (24.0ms)

IterNodesCost
0289930
1894837
23513835
35002835

prune136.0ms

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

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New65570
Fresh000
Picked101
Done000
Total66571

Merged error: 0.0b

Counts
71 → 5

localize36.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
0.3b
(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)))))))
0.8b
(log (exp (- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))))

rewrite14.0ms

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:
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)))))))
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:
33.0ms
(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
7.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
42.0ms
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))
44.0ms
(log (exp (- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))))

simplify84.0ms

Algorithm
egg-herbie
Counts
69 → 69
Iterations

Useful iterations: 2 (20.0ms)

IterNodesCost
02531234
17641106
229491102
350011102

prune129.0ms

Filtered
52 candidates to 69 candidates (-32.7%)
Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New68169
Fresh044
Picked011
Done000
Total68674

Merged error: 0.0b

Counts
74 → 6

localize46.0ms

Local error

Found 4 expressions with local error:

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

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
18×add-sqr-sqrt
10×*-un-lft-identity
8×pow1 add-exp-log add-cube-cbrt add-cbrt-cube difference-of-squares sqr-pow
6×unpow-prod-down pow-unpow cube-prod add-log-exp
3×pow-pow pow-exp rem-cube-cbrt
2×cube-mult pow-to-exp unpow3
1×difference-cubes cube-div sub-neg asin-acos flip3-- diff-log pow-prod-down prod-exp flip-- cbrt-unprod sin-mult distribute-lft-out--
Counts
4 → 76
Calls
4 calls:
1.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
9.0ms
(- (pow (cos delta) 3) (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3))
2.0ms
(pow (cos delta) 3)
5.0ms
(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)

series307.0ms

Counts
4 → 12
Calls
4 calls:
5.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
233.0ms
(- (pow (cos delta) 3) (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3))
5.0ms
(pow (cos delta) 3)
65.0ms
(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)

simplify90.0ms

Algorithm
egg-herbie
Counts
88 → 88
Iterations

Useful iterations: 2 (78.0ms)

IterNodesCost
04871373
124471276
250011264

prune191.0ms

Filtered
56 candidates to 88 candidates (-57.1%)
Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New85388
Fresh044
Picked101
Done011
Total86894

Merged error: 0.0b

Counts
94 → 8

localize50.0ms

Local error

Found 4 expressions with local error:

0.4b
(pow (cos delta) 3)
0.4b
(pow (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3) 3)
0.4b
(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)
6.4b
(cbrt (pow (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3) 3))

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
24×unpow-prod-down cube-prod
22×cbrt-prod
14×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
12×add-exp-log
9×pow-unpow pow-exp add-cbrt-cube
8×pow1 cube-mult unpow3 sqr-pow
5×cube-div
4×pow-to-exp pow-pow add-log-exp rem-cube-cbrt
3×sin-mult
2×prod-exp
1×cbrt-div pow1/3 pow-prod-down rem-cbrt-cube cbrt-unprod
Counts
4 → 115
Calls
4 calls:
2.0ms
(pow (cos delta) 3)
6.0ms
(pow (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3) 3)
5.0ms
(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)
5.0ms
(cbrt (pow (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3) 3))

series709.0ms

Counts
4 → 12
Calls
4 calls:
5.0ms
(pow (cos delta) 3)
578.0ms
(pow (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3) 3)
61.0ms
(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)
66.0ms
(cbrt (pow (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3) 3))

simplify68.0ms

Algorithm
egg-herbie
Counts
127 → 127
Iterations

Useful iterations: 2 (50.0ms)

IterNodesCost
03912026
116761835
250021825

prune170.0ms

Filtered
64 candidates to 127 candidates (-98.4%)
Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New1270127
Fresh066
Picked011
Done011
Total1278135

Merged error: 0.0b

Counts
135 → 8

regimes535.0ms

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
03224
13224

end0.0ms

analyze3.6s

Algorithm
search

sample9.2s

Algorithm
intervals
Results
5.7s3136×body1280valid
2.0s1834×body640valid
508.0ms714×body320valid
414.0ms1980×body80valid
153.0ms336×body160valid

Profiling

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