Details

Time bar (total: 11.2s)

sample275.0ms

Algorithm
intervals
Results
168.0ms102×body1280valid
52.0ms55×body640valid
15.0ms17×body320valid
12.0ms69×body80valid
5.0ms13×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

localize36.0ms

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:
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))))
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))
37.0ms
(* (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))))
44.0ms
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

simplify88.0ms

Algorithm
egg-herbie
Counts
70 → 70
Iterations

Useful iterations: 2 (24.0ms)

IterNodesCost
0289930
1894837
23513835
35002835

prune183.0ms

Filtered
70 candidates to 51 candidates (27.1%)
Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New591170
Fresh000
Picked101
Done000
Total601171

Merged error: 0.1b

Counts
71 → 11

localize45.0ms

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

rewrite12.0ms

Algorithm
rewrite-expression-head
Rules
8×pow1 add-exp-log add-sqr-sqrt add-cube-cbrt *-un-lft-identity add-cbrt-cube
6×pow-unpow
4×unpow-prod-down cube-prod add-log-exp
3×pow-pow pow-exp rem-cube-cbrt
2×cube-mult pow-to-exp asin-acos unpow3 sqr-pow
1×cube-div pow-prod-down prod-exp cbrt-unprod sin-mult
Counts
4 → 62
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))))
2.0ms
(pow (cos delta) 3)
5.0ms
(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)

series81.0ms

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))))
5.0ms
(pow (cos delta) 3)
66.0ms
(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)

simplify39.0ms

Algorithm
egg-herbie
Counts
74 → 74
Iterations

Useful iterations: 2 (32.0ms)

IterNodesCost
0250773
11025671
25001666

prune194.0ms

Filtered
74 candidates to 48 candidates (35.1%)
Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New71374
Fresh3710
Picked101
Done000
Total751085

Merged error: 0.1b

Counts
85 → 10

localize49.0ms

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

rewrite12.0ms

Algorithm
rewrite-expression-head
Rules
8×pow1 add-exp-log add-sqr-sqrt add-cube-cbrt *-un-lft-identity
6×pow-unpow
5×add-cbrt-cube
4×unpow-prod-down add-log-exp
3×pow-pow cube-prod pow-exp
2×pow-to-exp asin-acos sqr-pow
1×cube-mult unpow3 pow-prod-down prod-exp unpow2 rem-cube-cbrt
Counts
4 → 57
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))))
2.0ms
(pow (cos delta) 3)
6.0ms
(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 2)

series67.0ms

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))))
5.0ms
(pow (cos delta) 3)
52.0ms
(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 2)

simplify35.0ms

Algorithm
egg-herbie
Counts
69 → 69
Iterations

Useful iterations: 2 (29.0ms)

IterNodesCost
0222682
1889617
25001612

prune179.0ms

Filtered
69 candidates to 44 candidates (36.2%)
Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New68169
Fresh099
Picked101
Done000
Total691079

Merged error: 0.1b

Counts
79 → 10

localize60.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (cbrt (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (cbrt (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
0.6b
(cbrt (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))
0.6b
(cbrt (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))
0.6b
(cbrt (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))

rewrite12.0ms

Algorithm
rewrite-expression-head
Rules
25×cbrt-prod
23×add-sqr-sqrt
15×add-cube-cbrt *-un-lft-identity
11×pow1
9×pow1/3
6×add-exp-log swap-sqr associate-*r* associate-*l*
4×add-cbrt-cube add-log-exp unswap-sqr
2×pow-prod-down pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 73
Calls
4 calls:
6.0ms
(* (cbrt (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (cbrt (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
1.0ms
(cbrt (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))
1.0ms
(cbrt (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))
1.0ms
(cbrt (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))

series118.0ms

Counts
4 → 12
Calls
4 calls:
39.0ms
(* (cbrt (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (cbrt (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
28.0ms
(cbrt (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))
26.0ms
(cbrt (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))
26.0ms
(cbrt (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))

simplify85.0ms

Algorithm
egg-herbie
Counts
85 → 85
Iterations

Useful iterations: 3 (73.0ms)

IterNodesCost
01101704
13801481
225841395
350011379

prune149.0ms

Filtered
85 candidates to 56 candidates (34.1%)
Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New85085
Fresh099
Picked011
Done000
Total851095

Merged error: 0.1b

Counts
95 → 10

regimes621.0ms

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
05197
15197

end0.0ms

sample8.7s

Algorithm
intervals
Results
5.2s3144×body1280valid
2.0s1874×body640valid
443.0ms710×body320valid
369.0ms1966×body80valid
124.0ms306×body160valid

Profiling

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