Details

Time bar (total: 9.6s)

sample113.0ms

Algorithm
intervals
Results
35.0ms67×body1280valid
28.0ms263×body80valid
22.0ms62×body640valid
9.0ms34×body320valid
3.0ms18×body160valid

simplify16.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0257
1507
2777
3967
41127
51277
61417
71417

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (/ (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))

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)) (* a1 a1))
19.0ms
(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
4.0ms
(/ (cos th) (sqrt 2.0))
4.0ms
(/ (cos th) (sqrt 2.0))

series343.0ms

Counts
4 → 12
Calls
4 calls:
107.0ms
(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
117.0ms
(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
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 (40.0ms)

IterNodesCost
05041284
120091156
250011136

prune446.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

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

rewrite45.0ms

Algorithm
rewrite-expression-head
Rules
76×times-frac
74×add-sqr-sqrt
61×add-cube-cbrt *-un-lft-identity
44×associate-*l* sqrt-prod
25×add-exp-log add-cbrt-cube
12×associate-/r*
11×pow1
8×prod-exp cbrt-unprod
6×associate-/l* unswap-sqr
5×cbrt-undiv div-exp
4×associate-*r* pow-prod-down div-inv add-log-exp
2×frac-2neg associate-*l/ clear-num *-commutative
Counts
4 → 165
Calls
4 calls:
15.0ms
(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
12.0ms
(* (/ (cos th) (sqrt 2.0)) a1)
4.0ms
(/ (cos th) (sqrt 2.0))
8.0ms
(/ (cos th) (sqrt 2.0))

series337.0ms

Counts
4 → 12
Calls
4 calls:
110.0ms
(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
106.0ms
(* (/ (cos th) (sqrt 2.0)) a1)
58.0ms
(/ (cos th) (sqrt 2.0))
63.0ms
(/ (cos th) (sqrt 2.0))

simplify50.0ms

Algorithm
egg-herbie
Counts
177 → 177
Iterations

Useful iterations: 2 (38.0ms)

IterNodesCost
04441207
118021104
250011084

prune460.0ms

Pruning

9 alts after pruning (9 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)
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
640×add-sqr-sqrt
593×add-cube-cbrt *-un-lft-identity
283×associate-*l*
37×associate-/l*
24×associate-/r*
23×div-inv
22×add-exp-log add-cbrt-cube
13×unswap-sqr
8×cbrt-undiv div-exp
6×pow1
4×add-log-exp
3×frac-2neg associate-*r* prod-exp clear-num cbrt-unprod
1×pow-prod-down associate-*l/ *-commutative associate-/l/
Counts
4 → 739
Calls
4 calls:
95.0ms
(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) a1)
22.0ms
(/ (/ (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))

series334.0ms

Counts
4 → 12
Calls
4 calls:
104.0ms
(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) a1)
65.0ms
(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
98.0ms
(/ (cos th) (sqrt (sqrt 2.0)))
67.0ms
(/ (cos th) (sqrt 2.0))

simplify145.0ms

Algorithm
egg-herbie
Counts
751 → 751
Iterations

Useful iterations: 1 (28.0ms)

IterNodesCost
013199484
149678360
250018360

prune1.9s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 4 expressions with local error:

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

rewrite218.0ms

Algorithm
rewrite-expression-head
Rules
82×sqrt-prod
81×times-frac
79×add-sqr-sqrt
68×add-exp-log add-cbrt-cube
63×associate-*l*
60×add-cube-cbrt *-un-lft-identity
29×prod-exp cbrt-unprod
17×cbrt-undiv div-exp
16×pow1
11×associate-*r*
8×unswap-sqr
7×pow-prod-down
6×associate-*l/ associate-/r*
4×div-inv add-log-exp
3×*-commutative associate-/l*
2×frac-times associate-*r/
1×frac-2neg clear-num
Counts
4 → 191
Calls
4 calls:
135.0ms
(* (* (/ (cos th) (sqrt (sqrt (sqrt 2.0)))) (/ a1 (* (sqrt (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))))) a1)
17.0ms
(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
52.0ms
(* (/ (cos th) (sqrt (sqrt (sqrt 2.0)))) (/ a1 (* (sqrt (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))))
4.0ms
(/ (cos th) (sqrt 2.0))

series394.0ms

Counts
4 → 12
Calls
4 calls:
114.0ms
(* (* (/ (cos th) (sqrt (sqrt (sqrt 2.0)))) (/ a1 (* (sqrt (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))))) a1)
110.0ms
(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
112.0ms
(* (/ (cos th) (sqrt (sqrt (sqrt 2.0)))) (/ a1 (* (sqrt (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))))
57.0ms
(/ (cos th) (sqrt 2.0))

simplify100.0ms

Algorithm
egg-herbie
Counts
203 → 203
Iterations

Useful iterations: 2 (83.0ms)

IterNodesCost
08162549
142691985
250011726

prune574.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

regimes231.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02320
12320

end0.0ms

sample3.5s

Algorithm
intervals
Results
1.2s2515×body1280valid
821.0ms7891×body80valid
731.0ms2051×body640valid
268.0ms1016×body320valid
99.0ms513×body160valid