Details

Time bar (total: 6.6s)

sample117.0ms

Algorithm
intervals
Results
38.0ms86×body1280valid
22.0ms71×body640valid
18.0ms249×body80valid
7.0ms30×body320valid
3.0ms20×body160valid

simplify4.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (3.0ms)

IterNodesCost
010513
110513

prune14.0ms

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: 0.6b

Counts
2 → 2

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* a1 a1) (* a2 a2))
0.2b
(* (cos th) (/ (+ (* a1 a1) (* a2 a2)) (sqrt 2.0)))
0.6b
(/ (+ (* a1 a1) (* a2 a2)) (sqrt 2.0))

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
40×add-sqr-sqrt
38×times-frac
32×add-cube-cbrt *-un-lft-identity
22×associate-*r* sqrt-prod
10×add-exp-log add-cbrt-cube
6×associate-/r*
5×pow1 add-log-exp
3×associate-*l* associate-/l* unswap-sqr
2×cbrt-undiv flip3-+ div-exp prod-exp cbrt-unprod flip-+ div-inv associate-/l/
1×+-commutative frac-2neg associate-*r/ pow-prod-down clear-num sum-log *-commutative
Counts
3 → 94
Calls
3 calls:
3.0ms
(+ (* a1 a1) (* a2 a2))
10.0ms
(* (cos th) (/ (+ (* a1 a1) (* a2 a2)) (sqrt 2.0)))
6.0ms
(/ (+ (* a1 a1) (* a2 a2)) (sqrt 2.0))

series53.0ms

Counts
3 → 9
Calls
3 calls:
5.0ms
(+ (* a1 a1) (* a2 a2))
37.0ms
(* (cos th) (/ (+ (* a1 a1) (* a2 a2)) (sqrt 2.0)))
10.0ms
(/ (+ (* a1 a1) (* a2 a2)) (sqrt 2.0))

simplify49.0ms

Algorithm
egg-herbie
Counts
103 → 103
Iterations

Useful iterations: 0 (39.0ms)

IterNodesCost
049611529
149611529

prune191.0ms

Filtered
69 candidates to 103 candidates (-49.3%)
Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New9310103
Fresh101
Picked101
Done000
Total9510105

Merged error: 0.0b

Counts
105 → 10

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (/ a1 (sqrt 2.0)) a1)
0.2b
(* (/ a2 (sqrt 2.0)) a2)
0.4b
(/ a1 (sqrt 2.0))
0.4b
(/ a2 (sqrt 2.0))

rewrite30.0ms

Algorithm
rewrite-expression-head
Rules
78×add-sqr-sqrt
76×times-frac
62×add-cube-cbrt *-un-lft-identity
44×associate-*l* sqrt-prod
18×add-exp-log add-cbrt-cube
12×associate-/r*
8×pow1
6×associate-*r* associate-/l* unswap-sqr
4×cbrt-undiv div-exp prod-exp cbrt-unprod div-inv add-log-exp
2×frac-2neg pow-prod-down associate-*l/ clear-num *-commutative
Counts
4 → 162
Calls
4 calls:
7.0ms
(* (/ a1 (sqrt 2.0)) a1)
7.0ms
(* (/ a2 (sqrt 2.0)) a2)
4.0ms
(/ a1 (sqrt 2.0))
6.0ms
(/ a2 (sqrt 2.0))

series22.0ms

Counts
4 → 12
Calls
4 calls:
6.0ms
(* (/ a1 (sqrt 2.0)) a1)
6.0ms
(* (/ a2 (sqrt 2.0)) a2)
5.0ms
(/ a1 (sqrt 2.0))
5.0ms
(/ a2 (sqrt 2.0))

simplify60.0ms

Algorithm
egg-herbie
Counts
174 → 174
Iterations

Useful iterations: 0 (48.0ms)

IterNodesCost
049861286
149861286

prune293.0ms

Filtered
116 candidates to 174 candidates (-50.0%)
Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New1713174
Fresh369
Picked101
Done000
Total1759184

Merged error: 0b

Counts
184 → 9

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (/ a2 (sqrt 2.0)) a2)
0.2b
(/ a1 (sqrt (sqrt 2.0)))
0.3b
(/ (/ a1 (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
0.4b
(/ a2 (sqrt 2.0))

rewrite65.0ms

Algorithm
rewrite-expression-head
Rules
616×sqrt-prod
614×times-frac
349×add-sqr-sqrt
341×add-cube-cbrt *-un-lft-identity
37×associate-/l*
24×associate-/r*
22×associate-*l*
18×add-exp-log add-cbrt-cube
14×div-inv
6×pow1 cbrt-undiv div-exp
4×add-log-exp
3×frac-2neg associate-*r* clear-num unswap-sqr
2×prod-exp cbrt-unprod
1×pow-prod-down associate-*l/ *-commutative associate-/l/
Counts
4 → 466
Calls
4 calls:
7.0ms
(* (/ a2 (sqrt 2.0)) a2)
5.0ms
(/ a1 (sqrt (sqrt 2.0)))
15.0ms
(/ (/ a1 (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
4.0ms
(/ a2 (sqrt 2.0))

series25.0ms

Counts
4 → 12
Calls
4 calls:
6.0ms
(* (/ a2 (sqrt 2.0)) a2)
9.0ms
(/ a1 (sqrt (sqrt 2.0)))
5.0ms
(/ (/ a1 (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
5.0ms
(/ a2 (sqrt 2.0))

simplify153.0ms

Algorithm
egg-herbie
Counts
478 → 478
Iterations

Useful iterations: 0 (100.0ms)

IterNodesCost
049776705
149776705

prune646.0ms

Filtered
187 candidates to 478 candidates (-155.6%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New4780478
Fresh088
Picked011
Done000
Total4789487

Merged error: 0b

Counts
487 → 9

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* a1 a1) (* a2 a2))
0.2b
(* (cos th) (/ (/ (+ (* a1 a1) (* a2 a2)) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (cbrt (sqrt 2.0))))
0.3b
(/ (/ (+ (* a1 a1) (* a2 a2)) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (cbrt (sqrt 2.0)))
0.4b
(/ (+ (* a1 a1) (* a2 a2)) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))

rewrite62.0ms

Algorithm
rewrite-expression-head
Rules
195×times-frac
111×add-sqr-sqrt
94×cbrt-prod
91×add-cube-cbrt *-un-lft-identity
67×associate-*r*
47×sqrt-prod
32×add-exp-log
22×div-inv
20×add-cbrt-cube
12×cbrt-undiv div-exp
10×associate-/r* associate-/l*
7×prod-exp cbrt-unprod unswap-sqr
6×pow1 add-log-exp
3×associate-*l* associate-/l/
2×frac-2neg flip3-+ clear-num flip-+
1×+-commutative associate-*r/ pow-prod-down sum-log *-commutative
Counts
4 → 225
Calls
4 calls:
4.0ms
(+ (* a1 a1) (* a2 a2))
26.0ms
(* (cos th) (/ (/ (+ (* a1 a1) (* a2 a2)) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (cbrt (sqrt 2.0))))
12.0ms
(/ (/ (+ (* a1 a1) (* a2 a2)) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (cbrt (sqrt 2.0)))
10.0ms
(/ (+ (* a1 a1) (* a2 a2)) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))

series89.0ms

Counts
4 → 12
Calls
4 calls:
5.0ms
(+ (* a1 a1) (* a2 a2))
34.0ms
(* (cos th) (/ (/ (+ (* a1 a1) (* a2 a2)) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (cbrt (sqrt 2.0))))
15.0ms
(/ (/ (+ (* a1 a1) (* a2 a2)) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (cbrt (sqrt 2.0)))
34.0ms
(/ (+ (* a1 a1) (* a2 a2)) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))

simplify93.0ms

Algorithm
egg-herbie
Counts
237 → 237
Iterations

Useful iterations: 0 (66.0ms)

IterNodesCost
049564599
149564599

prune500.0ms

Filtered
173 candidates to 237 candidates (-37.0%)
Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New2361237
Fresh167
Picked011
Done011
Total2379246

Merged error: 0b

Counts
246 → 9

regimes654.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 0.5b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01821
11821

end0.0ms

sample3.4s

Algorithm
intervals
Results
1.2s2527×body1280valid
677.0ms2102×body640valid
604.0ms7999×body80valid
245.0ms1065×body320valid
84.0ms551×body160valid

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