Details

Time bar (total: 9.6s)

sample74.0ms

Algorithm
intervals
Results
24.0ms76×body1280valid
17.0ms66×body640valid
12.0ms258×body80valid
4.0ms27×body320valid
2.0ms17×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: 0.8b

localize11.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
0.4b
(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
0.7b
(/ (cos th) (sqrt 2.0))
0.7b
(/ (cos th) (sqrt 2.0))

rewrite40.0ms

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:
14.0ms
(* (/ (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))

series356.0ms

Counts
4 → 12
Calls
4 calls:
120.0ms
(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
112.0ms
(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
65.0ms
(/ (cos th) (sqrt 2.0))
59.0ms
(/ (cos th) (sqrt 2.0))

simplify53.0ms

Algorithm
egg-herbie
Counts
180 → 180
Iterations

Useful iterations: 2 (40.0ms)

IterNodesCost
05041284
120091156
250021136

prune460.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
0.4b
(* (/ (cos th) (sqrt 2.0)) a1)
0.7b
(/ (cos th) (sqrt 2.0))
0.7b
(/ (cos th) (sqrt 2.0))

rewrite33.0ms

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:
9.0ms
(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
8.0ms
(* (/ (cos th) (sqrt 2.0)) a1)
5.0ms
(/ (cos th) (sqrt 2.0))
5.0ms
(/ (cos th) (sqrt 2.0))

series343.0ms

Counts
4 → 12
Calls
4 calls:
113.0ms
(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
103.0ms
(* (/ (cos th) (sqrt 2.0)) a1)
64.0ms
(/ (cos th) (sqrt 2.0))
63.0ms
(/ (cos th) (sqrt 2.0))

simplify52.0ms

Algorithm
egg-herbie
Counts
177 → 177
Iterations

Useful iterations: 2 (40.0ms)

IterNodesCost
04441207
118021104
250011084

prune445.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) a1)
0.7b
(/ (cos th) (sqrt (sqrt 2.0)))
0.7b
(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
0.7b
(/ (cos th) (sqrt 2.0))

rewrite150.0ms

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:
53.0ms
(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) a1)
6.0ms
(/ (cos th) (sqrt (sqrt 2.0)))
20.0ms
(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
5.0ms
(/ (cos th) (sqrt 2.0))

series518.0ms

Counts
4 → 12
Calls
4 calls:
101.0ms
(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) a1)
95.0ms
(/ (cos th) (sqrt (sqrt 2.0)))
264.0ms
(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
58.0ms
(/ (cos th) (sqrt 2.0))

simplify140.0ms

Algorithm
egg-herbie
Counts
751 → 751
Iterations

Useful iterations: 1 (28.0ms)

IterNodesCost
013199484
149678360
250018360

prune1.6s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (/ (cos th) (sqrt (sqrt 2.0))) a1)
0.3b
(* (/ (/ 1 (sqrt (sqrt (sqrt 2.0)))) (sqrt (sqrt (sqrt 2.0)))) (* (/ (cos th) (sqrt (sqrt 2.0))) a1))
0.7b
(/ (cos th) (sqrt (sqrt 2.0)))
0.7b
(/ (cos th) (sqrt 2.0))

rewrite176.0ms

Algorithm
rewrite-expression-head
Rules
1446×sqrt-prod
987×times-frac
533×add-sqr-sqrt
522×add-cube-cbrt *-un-lft-identity
515×associate-*l*
73×add-exp-log
49×add-cbrt-cube
27×prod-exp
26×div-exp
17×cbrt-unprod
16×div-inv
15×cbrt-undiv associate-/r*
11×pow1
6×associate-/l*
4×associate-*r* pow-prod-down associate-*l/ add-log-exp unswap-sqr
3×rec-exp 1-exp
2×frac-2neg clear-num *-commutative
1×frac-times associate-*r/
Counts
4 → 664
Calls
4 calls:
10.0ms
(* (/ (cos th) (sqrt (sqrt 2.0))) a1)
86.0ms
(* (/ (/ 1 (sqrt (sqrt (sqrt 2.0)))) (sqrt (sqrt (sqrt 2.0)))) (* (/ (cos th) (sqrt (sqrt 2.0))) a1))
6.0ms
(/ (cos th) (sqrt (sqrt 2.0)))
5.0ms
(/ (cos th) (sqrt 2.0))

series446.0ms

Counts
4 → 12
Calls
4 calls:
171.0ms
(* (/ (cos th) (sqrt (sqrt 2.0))) a1)
110.0ms
(* (/ (/ 1 (sqrt (sqrt (sqrt 2.0)))) (sqrt (sqrt (sqrt 2.0)))) (* (/ (cos th) (sqrt (sqrt 2.0))) a1))
98.0ms
(/ (cos th) (sqrt (sqrt 2.0)))
66.0ms
(/ (cos th) (sqrt 2.0))

simplify105.0ms

Algorithm
egg-herbie
Counts
676 → 676
Iterations

Useful iterations: 1 (31.0ms)

IterNodesCost
015279366
150028228

prune2.2s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0b

regimes172.0ms

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
02625
12625

end0.0ms

sample2.2s

Algorithm
intervals
Results
798.0ms2456×body1280valid
451.0ms2105×body640valid
409.0ms8133×body80valid
160.0ms1017×body320valid
59.0ms537×body160valid