Details

Time bar (total: 11.8s)

sample330.0ms

Algorithm
intervals
Results
166.0ms105×body1280valid
69.0ms63×body640valid
15.0ms25×body320valid
10.0ms56×body80valid
3.0ms7×body160valid

simplify8.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

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

localize39.0ms

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)))))))

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))))
4.0ms
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

series98.0ms

Counts
4 → 12
Calls
4 calls:
9.0ms
(* (sin theta) (sin delta))
39.0ms
(* (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))))
45.0ms
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

simplify91.0ms

Algorithm
egg-herbie
Counts
70 → 70
Iterations

Useful iterations: 2 (26.0ms)

IterNodesCost
0289930
1894837
23513835
35002835

prune187.0ms

Filtered
70 candidates to 51 candidates (27.1%)
Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New581270
Fresh000
Picked101
Done000
Total591271

Merged error: 0.1b

Counts
71 → 12

localize43.0ms

Local error

Found 4 expressions with local error:

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

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
43×pow1
17×pow-prod-down
16×add-exp-log add-cbrt-cube
10×sin-mult
8×prod-exp cbrt-unprod
6×add-log-exp
5×cos-mult
4×add-sqr-sqrt add-cube-cbrt *-un-lft-identity pow-sqr pow-prod-up
3×associate-*r/ associate-*l/ frac-sub
2×frac-times asin-acos pow-plus sub-div
1×pow2 sub-neg sqr-cos flip3-- diff-log swap-sqr associate-*r* associate-*l* associate--l+ *-commutative flip-- difference-of-squares
Counts
4 → 72
Calls
4 calls:
1.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
1.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
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))))))))
10.0ms
(* (* (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)))))))

series211.0ms

Counts
4 → 12
Calls
4 calls:
5.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
5.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
147.0ms
(- (* (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))))))))
53.0ms
(* (* (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)))))))

simplify71.0ms

Algorithm
egg-herbie
Counts
84 → 84
Iterations

Useful iterations: 2 (55.0ms)

IterNodesCost
04262117
119791741
250011711

prune173.0ms

Filtered
84 candidates to 51 candidates (39.3%)
Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New80484
Fresh6511
Picked101
Done000
Total87996

Merged error: 0.1b

Counts
96 → 9

localize41.0ms

Local error

Found 4 expressions with local error:

0.3b
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
0.4b
(- (* (cos delta) (cos delta)) (cbrt (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 6)))
0.7b
(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 6)
8.4b
(cbrt (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 6))

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt
7×pow1 add-exp-log cbrt-prod
6×add-cube-cbrt *-un-lft-identity add-log-exp
4×add-cbrt-cube
3×pow-unpow difference-of-squares sqr-pow
2×unpow-prod-down pow-pow pow-exp
1×pow-to-exp sub-neg asin-acos sqr-cos flip3-- pow1/3 diff-log pow-prod-down prod-exp associate--l+ flip--
Counts
4 → 54
Calls
4 calls:
1.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
7.0ms
(- (* (cos delta) (cos delta)) (cbrt (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 6)))
5.0ms
(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 6)
3.0ms
(cbrt (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 6))

series341.0ms

Counts
4 → 12
Calls
4 calls:
5.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
143.0ms
(- (* (cos delta) (cos delta)) (cbrt (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 6)))
141.0ms
(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 6)
51.0ms
(cbrt (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 6))

simplify54.0ms

Algorithm
egg-herbie
Counts
66 → 66
Iterations

Useful iterations: 2 (43.0ms)

IterNodesCost
03841320
115871238
250011225

prune193.0ms

Filtered
66 candidates to 52 candidates (21.2%)
Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New65166
Fresh088
Picked101
Done000
Total66975

Merged error: 0.0b

Counts
75 → 9

localize53.0ms

Local error

Found 4 expressions with local error:

0.7b
(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 6)
8.4b
(cbrt (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 6))
8.4b
(cbrt (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 6))
8.4b
(cbrt (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 6))

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
15×cbrt-prod
8×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
7×pow1 add-exp-log
4×unpow-prod-down add-cbrt-cube add-log-exp sqr-pow
3×pow-unpow pow1/3
2×pow-pow pow-exp
1×pow-to-exp pow-prod-down prod-exp
Counts
4 → 56
Calls
4 calls:
5.0ms
(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 6)
3.0ms
(cbrt (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 6))
3.0ms
(cbrt (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 6))
3.0ms
(cbrt (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 6))

series287.0ms

Counts
4 → 12
Calls
4 calls:
140.0ms
(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 6)
48.0ms
(cbrt (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 6))
50.0ms
(cbrt (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 6))
49.0ms
(cbrt (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 6))

simplify160.0ms

Algorithm
egg-herbie
Counts
68 → 68
Iterations

Useful iterations: 2 (24.0ms)

IterNodesCost
01861302
16731195
236351186
350011186

prune223.0ms

Filtered
68 candidates to 55 candidates (19.1%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New68068
Fresh088
Picked011
Done000
Total68977

Merged error: 0.0b

Counts
77 → 9

regimes591.0ms

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 (1.0ms)

IterNodesCost
04977
14977

end0.0ms

sample8.5s

Algorithm
intervals
Results
5.2s3138×body1280valid
1.9s1850×body640valid
443.0ms716×body320valid
380.0ms2023×body80valid
126.0ms273×body160valid

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