Details

Time bar (total: 6.4s)

sample88.0ms

Algorithm
intervals
Results
32.0ms79×body1280valid
18.0ms71×body640valid
15.0ms252×body80valid
6.0ms33×body320valid
2.0ms17×body160valid

simplify16.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0257
1507
2777
3967
41127
51277
61417
71417

prune7.0ms

Filtered
1 candidates to 1 candidates (100.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 0.4b

Counts
2 → 2

localize11.0ms

Local error

Found 2 expressions with local error:

0.3b
(* (/ (cos th) (sqrt 2.0)) (+ (* a1 a1) (* a2 a2)))
0.6b
(/ (cos th) (sqrt 2.0))

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
39×add-sqr-sqrt
38×times-frac
31×add-cube-cbrt *-un-lft-identity
22×associate-*l* sqrt-prod
9×add-exp-log add-cbrt-cube
6×associate-/r*
4×pow1
3×associate-*r* associate-/l* unswap-sqr
2×cbrt-undiv frac-times flip3-+ associate-*r/ div-exp prod-exp cbrt-unprod flip-+ div-inv add-log-exp
1×distribute-rgt-in frac-2neg distribute-lft-in pow-prod-down associate-*l/ clear-num *-commutative
Counts
2 → 87
Calls
2 calls:
10.0ms
(* (/ (cos th) (sqrt 2.0)) (+ (* a1 a1) (* a2 a2)))
4.0ms
(/ (cos th) (sqrt 2.0))

series273.0ms

Counts
2 → 6
Calls
2 calls:
210.0ms
(* (/ (cos th) (sqrt 2.0)) (+ (* a1 a1) (* a2 a2)))
62.0ms
(/ (cos th) (sqrt 2.0))

simplify55.0ms

Algorithm
egg-herbie
Counts
93 → 93
Iterations

Useful iterations: 2 (46.0ms)

IterNodesCost
0479795
12384738
25003725

prune239.0ms

Filtered
93 candidates to 63 candidates (67.7%)
Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New84993
Fresh101
Picked101
Done000
Total86995

Merged error: 0.0b

Counts
95 → 9

localize13.0ms

Local error

Found 2 expressions with local error:

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

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
39×add-sqr-sqrt
38×times-frac
31×add-cube-cbrt *-un-lft-identity
22×associate-*r* sqrt-prod
9×add-exp-log add-cbrt-cube
6×associate-/r*
4×pow1
3×associate-*l* associate-/l* unswap-sqr
2×cbrt-undiv div-exp prod-exp cbrt-unprod div-inv associate-/l/ add-log-exp
1×frac-2neg flip3-+ associate-*r/ pow-prod-down clear-num *-commutative flip-+
Counts
2 → 83
Calls
2 calls:
10.0ms
(* (cos th) (/ (+ (* a1 a1) (* a2 a2)) (sqrt 2.0)))
7.0ms
(/ (+ (* a1 a1) (* a2 a2)) (sqrt 2.0))

series303.0ms

Counts
2 → 6
Calls
2 calls:
207.0ms
(* (cos th) (/ (+ (* a1 a1) (* a2 a2)) (sqrt 2.0)))
96.0ms
(/ (+ (* a1 a1) (* a2 a2)) (sqrt 2.0))

simplify48.0ms

Algorithm
egg-herbie
Counts
89 → 89
Iterations

Useful iterations: 2 (39.0ms)

IterNodesCost
0314880
11523816
25001800

prune181.0ms

Filtered
89 candidates to 57 candidates (64.0%)
Pruning

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New87289
Fresh538
Picked101
Done000
Total93598

Merged error: 0b

Counts
98 → 5

localize12.0ms

Local error

Found 3 expressions with local error:

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

rewrite159.0ms

Algorithm
rewrite-expression-head
Rules
1137×sqrt-prod
1119×times-frac
624×add-sqr-sqrt
577×add-cube-cbrt *-un-lft-identity
283×associate-*r*
34×associate-/l*
22×div-inv
19×add-exp-log add-cbrt-cube
18×associate-/r*
13×unswap-sqr
7×cbrt-undiv div-exp
5×pow1
3×associate-*l* prod-exp cbrt-unprod associate-/l/ add-log-exp
2×frac-2neg clear-num
1×flip3-+ associate-*r/ pow-prod-down *-commutative flip-+
Counts
3 → 702
Calls
3 calls:
68.0ms
(* (cos th) (/ (/ (+ (* a1 a1) (* a2 a2)) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))))
22.0ms
(/ (/ (+ (* a1 a1) (* a2 a2)) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
8.0ms
(/ (+ (* a1 a1) (* a2 a2)) (sqrt (sqrt 2.0)))

series462.0ms

Counts
3 → 9
Calls
3 calls:
212.0ms
(* (cos th) (/ (/ (+ (* a1 a1) (* a2 a2)) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))))
100.0ms
(/ (/ (+ (* a1 a1) (* a2 a2)) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
150.0ms
(/ (+ (* a1 a1) (* a2 a2)) (sqrt (sqrt 2.0)))

simplify134.0ms

Algorithm
egg-herbie
Counts
711 → 711
Iterations

Useful iterations: 1 (42.0ms)

IterNodesCost
0153212059
1500210660

prune925.0ms

Filtered
711 candidates to 242 candidates (34.0%)
Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New7110711
Fresh044
Picked011
Done000
Total7115716

Merged error: 0b

Counts
716 → 5

localize13.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (/ (cos th) (sqrt 2.0)) (sqrt (+ (* a1 a1) (* a2 a2))))
0.6b
(/ (cos th) (sqrt 2.0))
6.1b
(sqrt (+ (* a1 a1) (* a2 a2)))
6.1b
(sqrt (+ (* a1 a1) (* a2 a2)))

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
54×add-sqr-sqrt
40×times-frac
36×add-cube-cbrt *-un-lft-identity
35×sqrt-prod
22×associate-*l*
11×add-exp-log add-cbrt-cube
8×pow1 sqrt-div
6×associate-*r* associate-/r* unswap-sqr
4×flip3-+ flip-+ add-log-exp
3×associate-/l*
2×cbrt-undiv frac-times rem-sqrt-square sqrt-pow1 pow1/2 associate-*r/ div-exp prod-exp cbrt-unprod div-inv
1×frac-2neg pow-prod-down associate-*l/ clear-num *-commutative
Counts
4 → 121
Calls
4 calls:
13.0ms
(* (/ (cos th) (sqrt 2.0)) (sqrt (+ (* a1 a1) (* a2 a2))))
4.0ms
(/ (cos th) (sqrt 2.0))
3.0ms
(sqrt (+ (* a1 a1) (* a2 a2)))
3.0ms
(sqrt (+ (* a1 a1) (* a2 a2)))

series330.0ms

Counts
4 → 12
Calls
4 calls:
193.0ms
(* (/ (cos th) (sqrt 2.0)) (sqrt (+ (* a1 a1) (* a2 a2))))
65.0ms
(/ (cos th) (sqrt 2.0))
37.0ms
(sqrt (+ (* a1 a1) (* a2 a2)))
35.0ms
(sqrt (+ (* a1 a1) (* a2 a2)))

simplify46.0ms

Algorithm
egg-herbie
Counts
133 → 133
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
03521093
112561042
250011028

prune321.0ms

Filtered
133 candidates to 96 candidates (72.2%)
Pruning

5 alts after pruning (3 fresh and 2 done)

PrunedKeptTotal
New1330133
Fresh033
Picked011
Done011
Total1335138

Merged error: 0b

Counts
138 → 5

regimes185.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 0.5b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01511
11511

end0.0ms

sample2.5s

Algorithm
intervals
Results
926.0ms2517×body1280valid
518.0ms2030×body640valid
471.0ms7931×body80valid
190.0ms1052×body320valid
74.0ms563×body160valid

Profiling

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