Details

Time bar (total: 8.1s)

sample88.0ms

Algorithm
intervals
Results
28.0ms76×body1280valid
18.0ms71×body640valid
17.0ms264×body80valid
6.0ms30×body320valid
3.0ms21×body160valid

simplify16.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0257
1507
2777
3967
41127
51277
61417
71417

prune9.0ms

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: 0.5b

Counts
2 → 2

localize21.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
0.3b
(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
0.8b
(/ (cos th) (sqrt 2.0))
0.8b
(/ (cos th) (sqrt 2.0))

rewrite36.0ms

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))
10.0ms
(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
5.0ms
(/ (cos th) (sqrt 2.0))
5.0ms
(/ (cos th) (sqrt 2.0))

series351.0ms

Counts
4 → 12
Calls
4 calls:
112.0ms
(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
116.0ms
(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
57.0ms
(/ (cos th) (sqrt 2.0))
65.0ms
(/ (cos th) (sqrt 2.0))

simplify54.0ms

Algorithm
egg-herbie
Counts
180 → 180
Iterations

Useful iterations: 2 (40.0ms)

IterNodesCost
05041284
120091156
250021136

prune455.0ms

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: 0b

Counts
182 → 11

localize15.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (* a1 a1))
0.7b
(/ (cos th) (sqrt (sqrt 2.0)))
0.7b
(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
0.8b
(/ (cos th) (sqrt 2.0))

rewrite144.0ms

Algorithm
rewrite-expression-head
Rules
1149×sqrt-prod
1137×times-frac
626×add-sqr-sqrt
592×add-cube-cbrt *-un-lft-identity
283×associate-*l*
37×associate-/l*
34×add-exp-log add-cbrt-cube
24×associate-/r*
23×div-inv
13×unswap-sqr
11×cbrt-undiv div-exp
9×pow1 prod-exp cbrt-unprod
4×add-log-exp
3×frac-2neg pow-prod-down clear-num
1×associate-*r* associate-*l/ *-commutative associate-/l/
Counts
4 → 744
Calls
4 calls:
51.0ms
(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (* a1 a1))
6.0ms
(/ (cos th) (sqrt (sqrt 2.0)))
17.0ms
(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
5.0ms
(/ (cos th) (sqrt 2.0))

series343.0ms

Counts
4 → 12
Calls
4 calls:
119.0ms
(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (* a1 a1))
98.0ms
(/ (cos th) (sqrt (sqrt 2.0)))
60.0ms
(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
65.0ms
(/ (cos th) (sqrt 2.0))

simplify117.0ms

Algorithm
egg-herbie
Counts
756 → 756
Iterations

Useful iterations: 1 (35.0ms)

IterNodesCost
015449868
150018666

prune1.5s

Filtered
756 candidates to 353 candidates (46.7%)
Pruning

11 alts after pruning (10 fresh and 1 done)

PrunedKeptTotal
New7551756
Fresh1910
Picked011
Done000
Total75611767

Merged error: 0b

Counts
767 → 11

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (cos th) (* a2 a2))
0.3b
(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
0.3b
(/ (* (cos th) (* a2 a2)) (sqrt 2.0))
0.8b
(/ (cos th) (sqrt 2.0))

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
44×times-frac
43×add-sqr-sqrt
37×add-cube-cbrt *-un-lft-identity
32×add-exp-log add-cbrt-cube
28×sqrt-prod
25×associate-*l*
14×pow1
12×prod-exp associate-/r* cbrt-unprod
6×cbrt-undiv div-exp pow-prod-down
4×associate-/l* add-log-exp unswap-sqr
3×div-inv
2×frac-2neg associate-*r* clear-num *-commutative
1×associate-*l/
Counts
4 → 132
Calls
4 calls:
6.0ms
(* (cos th) (* a2 a2))
10.0ms
(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
8.0ms
(/ (* (cos th) (* a2 a2)) (sqrt 2.0))
5.0ms
(/ (cos th) (sqrt 2.0))

series336.0ms

Counts
4 → 12
Calls
4 calls:
44.0ms
(* (cos th) (* a2 a2))
116.0ms
(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
113.0ms
(/ (* (cos th) (* a2 a2)) (sqrt 2.0))
63.0ms
(/ (cos th) (sqrt 2.0))

simplify54.0ms

Algorithm
egg-herbie
Counts
144 → 144
Iterations

Useful iterations: 2 (43.0ms)

IterNodesCost
0501987
12125864
25002850

prune311.0ms

Filtered
144 candidates to 91 candidates (63.2%)
Pruning

10 alts after pruning (8 fresh and 2 done)

PrunedKeptTotal
New1413144
Fresh459
Picked011
Done011
Total14510155

Merged error: 0b

Counts
155 → 10

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (/ (* (cos th) (* a2 a2)) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
0.2b
(/ (* (cos th) (* a2 a2)) (sqrt (sqrt 2.0)))
0.3b
(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
0.8b
(/ (cos th) (sqrt 2.0))

rewrite57.0ms

Algorithm
rewrite-expression-head
Rules
256×sqrt-prod
254×times-frac
125×add-sqr-sqrt
120×add-cube-cbrt *-un-lft-identity
41×add-exp-log add-cbrt-cube
24×associate-/r*
22×associate-*l*
17×associate-/l*
14×div-inv
13×cbrt-undiv div-exp
12×prod-exp cbrt-unprod
9×pow1
4×add-log-exp
3×frac-2neg pow-prod-down clear-num unswap-sqr
1×associate-*r* associate-*l/ *-commutative associate-/l/
Counts
4 → 277
Calls
4 calls:
19.0ms
(/ (/ (* (cos th) (* a2 a2)) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
10.0ms
(/ (* (cos th) (* a2 a2)) (sqrt (sqrt 2.0)))
10.0ms
(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
5.0ms
(/ (cos th) (sqrt 2.0))

series671.0ms

Counts
4 → 12
Calls
4 calls:
318.0ms
(/ (/ (* (cos th) (* a2 a2)) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
174.0ms
(/ (* (cos th) (* a2 a2)) (sqrt (sqrt 2.0)))
120.0ms
(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
59.0ms
(/ (cos th) (sqrt 2.0))

simplify101.0ms

Algorithm
egg-herbie
Counts
289 → 289
Iterations

Useful iterations: 2 (72.0ms)

IterNodesCost
09143480
141492999
250012994

prune491.0ms

Filtered
289 candidates to 140 candidates (48.4%)
Pruning

10 alts after pruning (7 fresh and 3 done)

PrunedKeptTotal
New2890289
Fresh077
Picked011
Done022
Total28910299

Merged error: 0b

Counts
299 → 10

regimes246.0ms

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
01815
11815

end0.0ms

sample2.7s

Algorithm
intervals
Results
959.0ms2516×body1280valid
565.0ms2098×body640valid
497.0ms7930×body80valid
207.0ms1057×body320valid
71.0ms546×body160valid