Details

Time bar (total: 11.8s)

sample128.0ms

Algorithm
intervals
Results
46.0ms96×body1280valid
28.0ms268×body80valid
27.0ms66×body640valid
7.0ms28×body320valid
4.0ms20×body160valid

simplify16.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0257
1507
2777
3967
41127
51277
61417
71417

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.5b

localize12.0ms

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))
0.7b
(/ (cos th) (sqrt 2.0))
0.7b
(/ (cos th) (sqrt 2.0))

rewrite49.0ms

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:
15.0ms
(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
18.0ms
(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
4.0ms
(/ (cos th) (sqrt 2.0))
4.0ms
(/ (cos th) (sqrt 2.0))

series344.0ms

Counts
4 → 12
Calls
4 calls:
115.0ms
(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
109.0ms
(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
56.0ms
(/ (cos th) (sqrt 2.0))
63.0ms
(/ (cos th) (sqrt 2.0))

simplify52.0ms

Algorithm
egg-herbie
Counts
180 → 180
Iterations

Useful iterations: 2 (39.0ms)

IterNodesCost
05041284
120091156
250021136

prune472.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite191.0ms

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:
95.0ms
(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (* a1 a1))
21.0ms
(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
5.0ms
(/ (cos th) (sqrt (sqrt 2.0)))
4.0ms
(/ (cos th) (sqrt 2.0))

series337.0ms

Counts
4 → 12
Calls
4 calls:
110.0ms
(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (* a1 a1))
64.0ms
(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
97.0ms
(/ (cos th) (sqrt (sqrt 2.0)))
65.0ms
(/ (cos th) (sqrt 2.0))

simplify105.0ms

Algorithm
egg-herbie
Counts
756 → 756
Iterations

Useful iterations: 1 (30.0ms)

IterNodesCost
015449868
150028666

prune1.8s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize13.0ms

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))) (sqrt (sqrt 2.0)))
0.6b
(/ (cos th) (sqrt (sqrt 2.0)))
0.6b
(/ (cos th) (sqrt (sqrt 2.0)))

rewrite113.0ms

Algorithm
rewrite-expression-head
Rules
1188×sqrt-prod
1152×times-frac
620×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
68×associate-/l*
36×associate-/r*
24×div-inv
18×add-exp-log add-cbrt-cube
8×cbrt-undiv div-exp
4×pow1 frac-2neg clear-num add-log-exp
2×associate-/l/
Counts
4 → 770
Calls
4 calls:
17.0ms
(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
21.0ms
(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
5.0ms
(/ (cos th) (sqrt (sqrt 2.0)))
5.0ms
(/ (cos th) (sqrt (sqrt 2.0)))

series507.0ms

Counts
4 → 12
Calls
4 calls:
63.0ms
(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
64.0ms
(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
97.0ms
(/ (cos th) (sqrt (sqrt 2.0)))
283.0ms
(/ (cos th) (sqrt (sqrt 2.0)))

simplify132.0ms

Algorithm
egg-herbie
Counts
782 → 782
Iterations

Useful iterations: 2 (44.0ms)

IterNodesCost
086912144
1341910626
2500110588

prune1.3s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

localize25.0ms

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)))
1.0b
(/ (/ 1 (sqrt (sqrt 2.0))) (sqrt (cbrt (sqrt 2.0))))
1.0b
(/ 1 (sqrt (sqrt 2.0)))

rewrite131.0ms

Algorithm
rewrite-expression-head
Rules
1365×sqrt-prod
1326×times-frac
709×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
192×cbrt-prod
68×associate-/l*
39×associate-/r*
27×div-inv
24×add-exp-log
18×add-cbrt-cube
12×div-exp
8×pow1 cbrt-undiv
7×pow-flip sqrt-pow1
4×frac-2neg clear-num add-log-exp
3×pow1/2
2×rec-exp pow1/3 1-exp associate-/l/ pow-div
1×inv-pow
Counts
4 → 878
Calls
4 calls:
18.0ms
(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
5.0ms
(/ (cos th) (sqrt (sqrt 2.0)))
20.0ms
(/ (/ 1 (sqrt (sqrt 2.0))) (sqrt (cbrt (sqrt 2.0))))
5.0ms
(/ 1 (sqrt (sqrt 2.0)))

series165.0ms

Counts
4 → 8
Calls
4 calls:
64.0ms
(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
100.0ms
(/ (cos th) (sqrt (sqrt 2.0)))
0.0ms
(/ (/ 1 (sqrt (sqrt 2.0))) (sqrt (cbrt (sqrt 2.0))))
0.0ms
(/ 1 (sqrt (sqrt 2.0)))

simplify141.0ms

Algorithm
egg-herbie
Counts
886 → 886
Iterations

Useful iterations: 1 (35.0ms)

IterNodesCost
0184913905
1500212619

prune1.9s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0b

regimes278.0ms

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
02825
12825

end0.0ms

sample3.6s

Algorithm
intervals
Results
1.2s2538×body1280valid
848.0ms7998×body80valid
748.0ms2117×body640valid
283.0ms1056×body320valid
98.0ms485×body160valid