Details

Time bar (total: 12.3s)

sample289.0ms

Algorithm
intervals
Results
171.0ms94×body1280valid
59.0ms57×body640valid
16.0ms25×body320valid
12.0ms66×body80valid
6.0ms14×body160valid

simplify26.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (24.0ms)

IterNodesCost
046233
146233

prune20.0ms

Filtered
1 candidates to 1 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 → 2

localize31.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (sin delta) (* (cos phi1) (cos theta)))
0.3b
(asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta)))))
0.3b
(* (sin phi1) (sin (asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta)))))))
0.5b
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta))))))))

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
11×pow1 add-exp-log add-cbrt-cube
9×add-sqr-sqrt
7×add-cube-cbrt *-un-lft-identity
6×associate-*l* add-log-exp
4×associate-*r* pow-prod-down prod-exp cbrt-unprod
2×*-commutative
1×sub-neg asin-acos flip3-- diff-log associate-*r/ cos-mult flip-- sin-mult unswap-sqr
Counts
4 → 58
Calls
4 calls:
9.0ms
(* (sin delta) (* (cos phi1) (cos theta)))
1.0ms
(asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta)))))
5.0ms
(* (sin phi1) (sin (asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta)))))))
4.0ms
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta))))))))

series103.0ms

Counts
4 → 12
Calls
4 calls:
19.0ms
(* (sin delta) (* (cos phi1) (cos theta)))
5.0ms
(asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta)))))
34.0ms
(* (sin phi1) (sin (asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta)))))))
45.0ms
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta))))))))

simplify63.0ms

Algorithm
egg-herbie
Counts
70 → 70
Iterations

Useful iterations: 0 (55.0ms)

IterNodesCost
049211278
149211278

prune149.0ms

Filtered
48 candidates to 70 candidates (-45.8%)
Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New64670
Fresh011
Picked011
Done000
Total64872

Merged error: 0.1b

Counts
72 → 8

localize43.0ms

Local error

Found 4 expressions with local error:

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

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt
6×pow1 add-exp-log add-cube-cbrt *-un-lft-identity add-cbrt-cube add-log-exp
3×associate-*r* associate-*l*
2×asin-acos
1×sub-neg sqr-cos flip3-- diff-log pow-prod-down prod-exp associate--l+ *-commutative flip-- cbrt-unprod sin-mult unswap-sqr
Counts
4 → 48
Calls
4 calls:
1.0ms
(asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta)))))
2.0ms
(asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta)))))
5.0ms
(* (sin phi1) (sin (asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta)))))))
7.0ms
(- (* (cos delta) (cos delta)) (* (sin (asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta)))))) (* (sin (asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta)))))) (pow (sin phi1) 2))))

series191.0ms

Counts
4 → 12
Calls
4 calls:
5.0ms
(asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta)))))
5.0ms
(asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta)))))
34.0ms
(* (sin phi1) (sin (asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta)))))))
146.0ms
(- (* (cos delta) (cos delta)) (* (sin (asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta)))))) (* (sin (asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta)))))) (pow (sin phi1) 2))))

simplify48.0ms

Algorithm
egg-herbie
Counts
60 → 60
Iterations

Useful iterations: 0 (39.0ms)

IterNodesCost
049471706
149471706

prune170.0ms

Filtered
45 candidates to 60 candidates (-33.3%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New56460
Fresh246
Picked101
Done011
Total59968

Merged error: 0.0b

Counts
68 → 9

localize48.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (sin phi1) (sin (asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta)))))))
0.4b
(- (* (cos delta) (cos delta)) (* (sin (asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta)))))) (* (sin (cbrt (pow (asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta))))) 3))) (pow (sin phi1) 2))))
0.6b
(pow (asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta))))) 3)
7.7b
(cbrt (pow (asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta))))) 3))

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
12×cbrt-prod add-cube-cbrt *-un-lft-identity
7×pow1 add-exp-log add-cbrt-cube
6×unpow-prod-down cube-prod add-log-exp
3×pow-unpow associate-*r* associate-*l*
2×cube-mult unpow3 sqr-pow
1×pow-to-exp sub-neg sqr-cos flip3-- pow-pow pow1/3 diff-log pow-prod-down pow-exp prod-exp associate--l+ *-commutative flip-- rem-cbrt-cube cbrt-unprod sin-mult rem-cube-cbrt unswap-sqr
Counts
4 → 76
Calls
4 calls:
5.0ms
(* (sin phi1) (sin (asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta)))))))
7.0ms
(- (* (cos delta) (cos delta)) (* (sin (asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta)))))) (* (sin (cbrt (pow (asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta))))) 3))) (pow (sin phi1) 2))))
3.0ms
(pow (asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta))))) 3)
2.0ms
(cbrt (pow (asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta))))) 3))

series208.0ms

Counts
4 → 12
Calls
4 calls:
36.0ms
(* (sin phi1) (sin (asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta)))))))
142.0ms
(- (* (cos delta) (cos delta)) (* (sin (asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta)))))) (* (sin (cbrt (pow (asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta))))) 3))) (pow (sin phi1) 2))))
24.0ms
(pow (asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta))))) 3)
5.0ms
(cbrt (pow (asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta))))) 3))

simplify41.0ms

Algorithm
egg-herbie
Counts
88 → 88
Iterations

Useful iterations: 0 (28.0ms)

IterNodesCost
051652336

prune185.0ms

Filtered
49 candidates to 88 candidates (-79.6%)
Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New88088
Fresh077
Picked011
Done011
Total88997

Merged error: 0.0b

Counts
97 → 9

localize44.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (sin phi1) (sin (asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta)))))))
0.4b
(- (pow (cos delta) 2) (* (sin (asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta)))))) (* (sin (asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta)))))) (pow (sin phi1) 2))))
0.4b
(cbrt (pow (- (pow (cos delta) 2) (* (sin (asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta)))))) (* (sin (asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta)))))) (pow (sin phi1) 2)))) 3))
0.5b
(pow (- (pow (cos delta) 2) (* (sin (asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta)))))) (* (sin (asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta)))))) (pow (sin phi1) 2)))) 3)

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
12×cbrt-prod add-cube-cbrt *-un-lft-identity
7×pow1 add-exp-log add-cbrt-cube
6×unpow-prod-down cube-prod add-log-exp
4×cube-div
3×pow-unpow flip3-- associate-*r* associate-*l* flip--
2×cube-mult cbrt-div unpow3 sqr-pow
1×pow-to-exp sub-neg pow-pow pow1/3 diff-log pow-prod-down pow-exp prod-exp *-commutative rem-cbrt-cube cbrt-unprod sin-mult rem-cube-cbrt unswap-sqr
Counts
4 → 79
Calls
4 calls:
5.0ms
(* (sin phi1) (sin (asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta)))))))
6.0ms
(- (pow (cos delta) 2) (* (sin (asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta)))))) (* (sin (asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta)))))) (pow (sin phi1) 2))))
6.0ms
(cbrt (pow (- (pow (cos delta) 2) (* (sin (asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta)))))) (* (sin (asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta)))))) (pow (sin phi1) 2)))) 3))
8.0ms
(pow (- (pow (cos delta) 2) (* (sin (asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta)))))) (* (sin (asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta)))))) (pow (sin phi1) 2)))) 3)

series599.0ms

Counts
4 → 12
Calls
4 calls:
35.0ms
(* (sin phi1) (sin (asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta)))))))
144.0ms
(- (pow (cos delta) 2) (* (sin (asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta)))))) (* (sin (asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta)))))) (pow (sin phi1) 2))))
145.0ms
(cbrt (pow (- (pow (cos delta) 2) (* (sin (asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta)))))) (* (sin (asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta)))))) (pow (sin phi1) 2)))) 3))
275.0ms
(pow (- (pow (cos delta) 2) (* (sin (asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta)))))) (* (sin (asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta)))))) (pow (sin phi1) 2)))) 3)

simplify73.0ms

Algorithm
egg-herbie
Counts
91 → 91
Iterations

Useful iterations: 0 (53.0ms)

IterNodesCost
050004415

prune173.0ms

Filtered
56 candidates to 91 candidates (-62.5%)
Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New90191
Fresh156
Picked101
Done022
Total928100

Merged error: 0.0b

Counts
100 → 8

regimes544.0ms

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
08681
18681

end0.0ms

sample9.2s

Algorithm
intervals
Results
5.7s3170×body1280valid
1.9s1864×body640valid
470.0ms706×body320valid
373.0ms1951×body80valid
138.0ms309×body160valid

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