Details

Time bar (total: 12.8s)

sample272.0ms

Algorithm
intervals
Results
170.0ms98×body1280valid
50.0ms54×body640valid
16.0ms25×body320valid
12.0ms66×body80valid
5.0ms13×body160valid

simplify9.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
03522
15622
25922
35922

prune5.0ms

Filtered
1 candidates to 0 candidates (0.0%)
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))))))
0.4b
(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:
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)))))))

series401.0ms

Counts
4 → 12
Calls
4 calls:
44.0ms
(* (sin theta) (sin delta))
160.0ms
(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
8.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
189.0ms
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

simplify99.0ms

Algorithm
egg-herbie
Counts
70 → 70
Iterations

Useful iterations: 2 (28.0ms)

IterNodesCost
0289930
1894837
23513835
35002835

prune378.0ms

Filtered
70 candidates to 51 candidates (72.9%)
Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New61970
Fresh000
Picked101
Done000
Total62971

Merged error: 0.1b

Counts
71 → 9

localize38.0ms

Local error

Found 4 expressions with local error:

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

rewrite13.0ms

Algorithm
rewrite-expression-head
Rules
6×sin-mult add-log-exp
5×cos-mult
4×pow1 add-exp-log add-sqr-sqrt add-cube-cbrt *-un-lft-identity add-cbrt-cube
3×asin-acos frac-sub
2×associate-*r/ associate-*l/ sub-div
1×frac-times sub-neg sqr-cos flip3-- diff-log associate--l+ flip-- difference-of-squares
Counts
4 → 43
Calls
4 calls:
7.0ms
(- (* (cos delta) (cos delta)) (* (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) (* (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))))
2.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
1.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))

series519.0ms

Counts
4 → 12
Calls
4 calls:
499.0ms
(- (* (cos delta) (cos delta)) (* (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) (* (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))))
7.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
7.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))

simplify53.0ms

Algorithm
egg-herbie
Counts
55 → 55
Iterations

Useful iterations: 2 (42.0ms)

IterNodesCost
03261426
113981256
250011223

prune400.0ms

Filtered
55 candidates to 44 candidates (80.0%)
Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New52355
Fresh178
Picked101
Done000
Total541064

Merged error: 0.0b

Counts
64 → 10

localize56.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow (sin phi1) 3)
0.4b
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
0.4b
(pow (sin phi1) 4)
0.4b
(- (pow (cos delta) 2) (* (pow (sin phi1) 4) (pow (cos delta) 2)))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
11×*-un-lft-identity
9×add-sqr-sqrt add-cube-cbrt
7×unpow-prod-down
6×pow1 add-exp-log pow-unpow add-log-exp
5×add-cbrt-cube
3×cube-prod
2×pow-to-exp distribute-rgt-out-- pow-pow pow-exp sqr-pow
1×cube-mult sub-neg asin-acos flip3-- diff-log unpow3 flip-- rem-cube-cbrt
Counts
4 → 62
Calls
4 calls:
3.0ms
(pow (sin phi1) 3)
1.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
3.0ms
(pow (sin phi1) 4)
8.0ms
(- (pow (cos delta) 2) (* (pow (sin phi1) 4) (pow (cos delta) 2)))

series162.0ms

Counts
4 → 12
Calls
4 calls:
30.0ms
(pow (sin phi1) 3)
7.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
31.0ms
(pow (sin phi1) 4)
94.0ms
(- (pow (cos delta) 2) (* (pow (sin phi1) 4) (pow (cos delta) 2)))

simplify47.0ms

Algorithm
egg-herbie
Counts
74 → 74
Iterations

Useful iterations: 2 (40.0ms)

IterNodesCost
0291484
11129424
25001402

prune598.0ms

Filtered
74 candidates to 47 candidates (63.5%)
Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New73174
Fresh189
Picked101
Done000
Total75984

Merged error: 0.0b

Counts
84 → 9

localize70.0ms

Local error

Found 4 expressions with local error:

0.4b
(pow (sin phi1) 4)
0.4b
(pow (cos delta) 4)
0.6b
(pow (cos delta) 6)
0.7b
(pow (sin phi1) 8)

rewrite12.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt add-cube-cbrt unpow-prod-down pow-unpow *-un-lft-identity
8×pow1 add-exp-log
4×pow-to-exp pow-pow pow-exp add-cbrt-cube add-log-exp sqr-pow
Counts
4 → 68
Calls
4 calls:
3.0ms
(pow (sin phi1) 4)
2.0ms
(pow (cos delta) 4)
2.0ms
(pow (cos delta) 6)
3.0ms
(pow (sin phi1) 8)

series155.0ms

Counts
4 → 12
Calls
4 calls:
31.0ms
(pow (sin phi1) 4)
35.0ms
(pow (cos delta) 4)
40.0ms
(pow (cos delta) 6)
50.0ms
(pow (sin phi1) 8)

simplify173.0ms

Algorithm
egg-herbie
Counts
80 → 80
Iterations

Useful iterations: 2 (31.0ms)

IterNodesCost
0270294
1931265
24216258
35001258

prune708.0ms

Filtered
80 candidates to 48 candidates (60.0%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New80080
Fresh088
Picked011
Done000
Total80989

Merged error: 0.0b

Counts
89 → 9

regimes410.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 0.2b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
08064
18064

end0.0ms

sample8.1s

Algorithm
intervals
Results
5.1s3137×body1280valid
1.7s1828×body640valid
432.0ms711×body320valid
357.0ms1992×body80valid
135.0ms332×body160valid