Details

Time bar (total: 8.9s)

sample84.0ms

Algorithm
intervals
Results
31.0ms82×body1280valid
17.0ms76×body640valid
12.0ms235×body80valid
5.0ms34×body320valid
3.0ms23×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

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
0.3b
(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
0.7b
(/ (cos th) (sqrt 2.0))
0.7b
(/ (cos th) (sqrt 2.0))

rewrite35.0ms

Algorithm
rewrite-expression-head
Rules
76×times-frac
70×add-sqr-sqrt
60×add-cube-cbrt *-un-lft-identity
44×associate-*l* sqrt-prod
32×add-exp-log add-cbrt-cube
14×pow1
12×prod-exp associate-/r* cbrt-unprod
6×cbrt-undiv div-exp pow-prod-down associate-/l* unswap-sqr
4×div-inv add-log-exp
2×frac-2neg associate-*r* associate-*l/ clear-num *-commutative
Counts
4 → 168
Calls
4 calls:
9.0ms
(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
9.0ms
(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
5.0ms
(/ (cos th) (sqrt 2.0))
5.0ms
(/ (cos th) (sqrt 2.0))

series553.0ms

Counts
4 → 12
Calls
4 calls:
114.0ms
(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
112.0ms
(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
259.0ms
(/ (cos th) (sqrt 2.0))
67.0ms
(/ (cos th) (sqrt 2.0))

simplify53.0ms

Algorithm
egg-herbie
Counts
180 → 180
Iterations

Useful iterations: 2 (41.0ms)

IterNodesCost
05041284
120091156
250021136

prune477.0ms

Filtered
180 candidates to 116 candidates (64.4%)
Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New16911180
Fresh101
Picked101
Done000
Total17111182

Merged error: 0.0b

Counts
182 → 11

localize15.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
0.6b
(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
0.6b
(/ (cos th) (sqrt (sqrt 2.0)))
0.7b
(/ (cos th) (sqrt 2.0))

rewrite75.0ms

Algorithm
rewrite-expression-head
Rules
616×sqrt-prod
614×times-frac
345×add-sqr-sqrt
340×add-cube-cbrt *-un-lft-identity
37×associate-/l*
25×add-exp-log add-cbrt-cube
24×associate-/r*
22×associate-*l*
14×div-inv
9×pow1
7×cbrt-undiv div-exp
6×prod-exp cbrt-unprod
4×add-log-exp
3×frac-2neg pow-prod-down clear-num unswap-sqr
1×associate-*r* associate-*l/ *-commutative associate-/l/
Counts
4 → 469
Calls
4 calls:
10.0ms
(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
16.0ms
(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
6.0ms
(/ (cos th) (sqrt (sqrt 2.0)))
5.0ms
(/ (cos th) (sqrt 2.0))

series344.0ms

Counts
4 → 12
Calls
4 calls:
117.0ms
(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
60.0ms
(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
100.0ms
(/ (cos th) (sqrt (sqrt 2.0)))
66.0ms
(/ (cos th) (sqrt 2.0))

simplify110.0ms

Algorithm
egg-herbie
Counts
481 → 481
Iterations

Useful iterations: 2 (62.0ms)

IterNodesCost
011156666
145695845
250025839

prune874.0ms

Filtered
481 candidates to 189 candidates (39.3%)
Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New4756481
Fresh7310
Picked101
Done000
Total4839492

Merged error: 0.0b

Counts
492 → 9

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (* a2 a2))
0.3b
(/ (pow a1 2) (sqrt 2.0))
0.6b
(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
0.6b
(/ (cos th) (sqrt (sqrt 2.0)))

rewrite155.0ms

Algorithm
rewrite-expression-head
Rules
1167×times-frac
1164×sqrt-prod
643×add-sqr-sqrt
609×add-cube-cbrt *-un-lft-identity
283×associate-*l*
42×associate-/l*
37×add-exp-log
34×add-cbrt-cube
24×associate-/r*
23×div-inv
21×unpow-prod-down
13×div-exp unswap-sqr
11×cbrt-undiv
9×pow1 prod-exp cbrt-unprod
7×unpow2 sqr-pow
4×add-log-exp
3×frac-2neg pow-prod-down clear-num
1×pow-to-exp associate-*r* associate-*l/ pow-exp *-commutative associate-/l/
Counts
4 → 781
Calls
4 calls:
50.0ms
(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (* a2 a2))
6.0ms
(/ (pow a1 2) (sqrt 2.0))
16.0ms
(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
9.0ms
(/ (cos th) (sqrt (sqrt 2.0)))

series352.0ms

Counts
4 → 12
Calls
4 calls:
123.0ms
(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (* a2 a2))
59.0ms
(/ (pow a1 2) (sqrt 2.0))
66.0ms
(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
103.0ms
(/ (cos th) (sqrt (sqrt 2.0)))

simplify113.0ms

Algorithm
egg-herbie
Counts
793 → 793
Iterations

Useful iterations: 1 (32.0ms)

IterNodesCost
0164910169
150018949

prune1.9s

Filtered
793 candidates to 365 candidates (46.0%)
Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New7903793
Fresh448
Picked101
Done000
Total7957802

Merged error: 0b

Counts
802 → 7

localize19.0ms

Local error

Found 4 expressions with local error:

0.6b
(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
0.6b
(/ (cos th) (sqrt (sqrt 2.0)))
20.0b
(sqrt (pow a1 2))
20.0b
(sqrt (pow a1 2))

rewrite62.0ms

Algorithm
rewrite-expression-head
Rules
610×sqrt-prod
576×times-frac
320×add-sqr-sqrt
316×add-cube-cbrt *-un-lft-identity
34×associate-/l*
18×associate-/r*
12×div-inv
11×add-exp-log add-cbrt-cube
8×unpow-prod-down rem-sqrt-square
4×pow1 cbrt-undiv div-exp unpow2 add-log-exp sqr-pow
2×frac-2neg sqrt-pow1 pow1/2 clear-num
1×associate-/l/
Counts
4 → 427
Calls
4 calls:
16.0ms
(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
6.0ms
(/ (cos th) (sqrt (sqrt 2.0)))
2.0ms
(sqrt (pow a1 2))
3.0ms
(sqrt (pow a1 2))

series189.0ms

Counts
4 → 12
Calls
4 calls:
68.0ms
(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
104.0ms
(/ (cos th) (sqrt (sqrt 2.0)))
9.0ms
(sqrt (pow a1 2))
9.0ms
(sqrt (pow a1 2))

simplify101.0ms

Algorithm
egg-herbie
Counts
439 → 439
Iterations

Useful iterations: 2 (49.0ms)

IterNodesCost
09196198
138025407
250025393

prune889.0ms

Filtered
439 candidates to 169 candidates (38.5%)
Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New4381439
Fresh156
Picked101
Done000
Total4406446

Merged error: 0b

Counts
446 → 6

regimes232.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02725
12725

end0.0ms

sample2.2s

Algorithm
intervals
Results
815.0ms2428×body1280valid
461.0ms2116×body640valid
413.0ms8197×body80valid
162.0ms1021×body320valid
57.0ms528×body160valid