Details

Time bar (total: 30.3s)

sample198.0ms

Algorithm
intervals
Results
52.0ms80×body1280valid
49.0ms260×body80valid
37.0ms78×body640valid
16.0ms46×body320valid
3.0ms15×body160valid

simplify232.0ms

Counts
1 → 1
Iterations

Useful iterations: 1 (6.0ms)

IterNodesCost
01219
12513
24913
37613
49513
511113
612613
714213
done14213

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.5b

localize35.0ms

Local error

Found 4 expressions with local error:

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

rewrite188.0ms

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:
67.0ms
(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
68.0ms
(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
19.0ms
(/ (cos th) (sqrt 2.0))
19.0ms
(/ (cos th) (sqrt 2.0))

series590.0ms

Counts
4 → 12
Calls
4 calls:
190.0ms
(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
202.0ms
(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
103.0ms
(/ (cos th) (sqrt 2.0))
96.0ms
(/ (cos th) (sqrt 2.0))

simplify2.8s

Counts
180 → 180
Iterations

Useful iterations: 2 (801.0ms)

IterNodesCost
01812118
15412012
228441832
done50011832

prune1.4s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize49.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (cos th) (pow a2 2))
0.3b
(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
0.3b
(/ (* (cos th) (pow a2 2)) (sqrt 2.0))
0.7b
(/ (cos th) (sqrt 2.0))

rewrite158.0ms

Algorithm
rewrite-expression-head
Rules
50×add-sqr-sqrt
44×times-frac
39×add-cube-cbrt *-un-lft-identity
33×add-exp-log
28×sqrt-prod
25×associate-*l* add-cbrt-cube
12×prod-exp associate-/r*
9×pow1 associate-*r*
8×cbrt-unprod
7×div-exp unswap-sqr
5×cbrt-undiv
4×unpow-prod-down associate-/l* add-log-exp
3×pow-prod-down div-inv
2×pow-to-exp frac-2neg pow-exp clear-num *-commutative unpow2 sqr-pow
1×associate-*l/
Counts
4 → 140
Calls
4 calls:
32.0ms
(* (cos th) (pow a2 2))
60.0ms
(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
29.0ms
(/ (* (cos th) (pow a2 2)) (sqrt 2.0))
27.0ms
(/ (cos th) (sqrt 2.0))

series569.0ms

Counts
4 → 12
Calls
4 calls:
79.0ms
(* (cos th) (pow a2 2))
185.0ms
(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
201.0ms
(/ (* (cos th) (pow a2 2)) (sqrt 2.0))
103.0ms
(/ (cos th) (sqrt 2.0))

simplify3.5s

Counts
152 → 152
Iterations

Useful iterations: 2 (1.2s)

IterNodesCost
02041751
15311636
232361475
done50001475

prune1.3s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0b

localize54.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (cos th) (pow a2 2))
0.1b
(* (cos th) (/ (pow a1 2) (sqrt 2.0)))
0.3b
(/ (pow a1 2) (sqrt 2.0))
0.3b
(/ (* (cos th) (pow a2 2)) (sqrt 2.0))

rewrite178.0ms

Algorithm
rewrite-expression-head
Rules
110×times-frac
101×add-sqr-sqrt
73×add-cube-cbrt *-un-lft-identity
61×sqrt-prod
60×associate-*r*
45×unpow-prod-down
34×add-exp-log
18×add-cbrt-cube
17×unpow2 sqr-pow
13×unswap-sqr
12×associate-/r*
10×div-exp prod-exp
9×associate-/l*
6×pow1 associate-*l*
4×cbrt-undiv pow-to-exp pow-exp cbrt-unprod add-log-exp
3×div-inv
2×frac-2neg clear-num *-commutative
1×associate-*r/ pow-prod-down
Counts
4 → 212
Calls
4 calls:
29.0ms
(* (cos th) (pow a2 2))
78.0ms
(* (cos th) (/ (pow a1 2) (sqrt 2.0)))
21.0ms
(/ (pow a1 2) (sqrt 2.0))
30.0ms
(/ (* (cos th) (pow a2 2)) (sqrt 2.0))

series614.0ms

Counts
4 → 12
Calls
4 calls:
83.0ms
(* (cos th) (pow a2 2))
209.0ms
(* (cos th) (/ (pow a1 2) (sqrt 2.0)))
112.0ms
(/ (pow a1 2) (sqrt 2.0))
210.0ms
(/ (* (cos th) (pow a2 2)) (sqrt 2.0))

simplify720.0ms

Counts
224 → 224
Iterations

Useful iterations: done (708.0ms)

IterNodesCost
02772813
16562493
done50012175

prune1.6s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

localize60.0ms

Local error

Found 4 expressions with local error:

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

rewrite222.0ms

Algorithm
rewrite-expression-head
Rules
105×sqrt-prod
87×times-frac
71×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
39×add-exp-log
34×add-cbrt-cube
31×associate-*r*
24×associate-/r*
13×prod-exp
11×div-exp cbrt-unprod
9×pow1 cbrt-undiv
7×associate-/l*
4×div-inv add-log-exp
3×frac-2neg associate-*r/ pow-prod-down clear-num
1×frac-times pow-to-exp associate-*l* associate-*l/ pow-exp *-commutative
Counts
4 → 188
Calls
4 calls:
18.0ms
(/ a1 (sqrt (sqrt 2.0)))
19.0ms
(/ a1 (sqrt (sqrt 2.0)))
138.0ms
(* (* (cos th) (/ a1 (sqrt (sqrt 2.0)))) (/ a1 (sqrt (sqrt 2.0))))
30.0ms
(/ (* (cos th) (pow a2 2)) (sqrt 2.0))

series814.0ms

Counts
4 → 12
Calls
4 calls:
204.0ms
(/ a1 (sqrt (sqrt 2.0)))
207.0ms
(/ a1 (sqrt (sqrt 2.0)))
203.0ms
(* (* (cos th) (/ a1 (sqrt (sqrt 2.0)))) (/ a1 (sqrt (sqrt 2.0))))
200.0ms
(/ (* (cos th) (pow a2 2)) (sqrt 2.0))

simplify4.4s

Counts
200 → 200
Iterations

Useful iterations: done (4.4s)

IterNodesCost
02122756
15902470
244662236
done50012232

prune1.5s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0b

regimes1.1s

Accuracy

0% (0.5b remaining)

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

bsearch0.0ms

simplify8.0ms

Iterations

Useful iterations: 2 (6.0ms)

IterNodesCost
01828
12526
22724
done2724

end0.0ms

sample7.9s

Algorithm
intervals
Results
3.0s2571×body1280valid
1.9s8065×body80valid
1.2s2103×body640valid
515.0ms1055×body320valid
199.0ms496×body160valid