Details

Time bar (total: 11.4s)

sample97.0ms

Algorithm
intervals
Results
39.0ms104×body1280valid
15.0ms279×body80valid
14.0ms61×body640valid
6.0ms39×body320valid
1.0ms13×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

localize14.0ms

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))

rewrite94.0ms

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:
33.0ms
(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
31.0ms
(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
14.0ms
(/ (cos th) (sqrt 2.0))
10.0ms
(/ (cos th) (sqrt 2.0))

series331.0ms

Counts
4 → 12
Calls
4 calls:
106.0ms
(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
107.0ms
(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
61.0ms
(/ (cos th) (sqrt 2.0))
57.0ms
(/ (cos th) (sqrt 2.0))

simplify50.0ms

Algorithm
egg-herbie
Counts
180 → 180
Iterations

Useful iterations: 2 (38.0ms)

IterNodesCost
05041284
120091156
250021136

prune499.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite97.0ms

Algorithm
rewrite-expression-head
Rules
142×times-frac
121×add-sqr-sqrt
94×add-cube-cbrt *-un-lft-identity
77×sqrt-prod
53×associate-*r*
41×unpow-prod-down
33×add-exp-log
25×associate-*l* add-cbrt-cube
15×unpow2 sqr-pow
12×associate-/r* unswap-sqr
11×pow1 associate-/l*
10×prod-exp
9×div-exp
8×cbrt-unprod
5×cbrt-undiv
4×pow-prod-down div-inv add-log-exp
2×pow-to-exp frac-2neg pow-exp clear-num *-commutative
1×associate-*r/ associate-*l/
Counts
4 → 240
Calls
4 calls:
32.0ms
(* (cos th) (/ (pow a1 2) (sqrt 2.0)))
13.0ms
(/ (pow a1 2) (sqrt 2.0))
31.0ms
(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
10.0ms
(/ (cos th) (sqrt 2.0))

series337.0ms

Counts
4 → 12
Calls
4 calls:
107.0ms
(* (cos th) (/ (pow a1 2) (sqrt 2.0)))
64.0ms
(/ (pow a1 2) (sqrt 2.0))
107.0ms
(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
59.0ms
(/ (cos th) (sqrt 2.0))

simplify76.0ms

Algorithm
egg-herbie
Counts
252 → 252
Iterations

Useful iterations: 2 (59.0ms)

IterNodesCost
06941786
130241552
250011540

prune627.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (pow a1 2) (sqrt 2.0))
0.3b
(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (* a2 a2))
0.6b
(/ (cos th) (sqrt (sqrt 2.0)))
0.7b
(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))

rewrite246.0ms

Algorithm
rewrite-expression-head
Rules
1167×times-frac
1164×sqrt-prod
643×add-sqr-sqrt
609×add-cube-cbrt *-un-lft-identity
283×associate-*l*
42×associate-/l*
37×add-exp-log
34×add-cbrt-cube
24×associate-/r*
23×div-inv
21×unpow-prod-down
13×div-exp unswap-sqr
11×cbrt-undiv
9×pow1 prod-exp cbrt-unprod
7×unpow2 sqr-pow
4×add-log-exp
3×frac-2neg pow-prod-down clear-num
1×pow-to-exp associate-*r* associate-*l/ pow-exp *-commutative associate-/l/
Counts
4 → 781
Calls
4 calls:
10.0ms
(/ (pow a1 2) (sqrt 2.0))
124.0ms
(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (* a2 a2))
12.0ms
(/ (cos th) (sqrt (sqrt 2.0)))
29.0ms
(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))

series564.0ms

Counts
4 → 12
Calls
4 calls:
64.0ms
(/ (pow a1 2) (sqrt 2.0))
113.0ms
(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (* a2 a2))
328.0ms
(/ (cos th) (sqrt (sqrt 2.0)))
58.0ms
(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))

simplify115.0ms

Algorithm
egg-herbie
Counts
793 → 793
Iterations

Useful iterations: 1 (34.0ms)

IterNodesCost
0164910169
150028951

prune1.9s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (/ (/ 1 (sqrt (sqrt (sqrt 2.0)))) (sqrt (sqrt (sqrt 2.0)))) (* (/ (cos th) (sqrt (sqrt 2.0))) (* a2 a2)))
0.2b
(* (/ (cos th) (sqrt (sqrt 2.0))) (* a2 a2))
0.3b
(/ (pow a1 2) (sqrt 2.0))
0.6b
(/ (cos th) (sqrt (sqrt 2.0)))

rewrite399.0ms

Algorithm
rewrite-expression-head
Rules
1461×sqrt-prod
1017×times-frac
545×add-sqr-sqrt
538×add-cube-cbrt *-un-lft-identity
515×associate-*l*
138×add-exp-log
89×add-cbrt-cube
61×prod-exp
46×div-exp
39×cbrt-unprod
25×cbrt-undiv
21×unpow-prod-down
18×pow1
16×div-inv
15×associate-/r*
11×associate-/l*
9×pow-prod-down
7×unpow2 sqr-pow
5×rec-exp 1-exp
4×associate-*l/ add-log-exp unswap-sqr
2×frac-2neg associate-*r* clear-num *-commutative
1×frac-times pow-to-exp associate-*r/ pow-exp
Counts
4 → 721
Calls
4 calls:
257.0ms
(* (/ (/ 1 (sqrt (sqrt (sqrt 2.0)))) (sqrt (sqrt (sqrt 2.0)))) (* (/ (cos th) (sqrt (sqrt 2.0))) (* a2 a2)))
39.0ms
(* (/ (cos th) (sqrt (sqrt 2.0))) (* a2 a2))
14.0ms
(/ (pow a1 2) (sqrt 2.0))
15.0ms
(/ (cos th) (sqrt (sqrt 2.0)))

series441.0ms

Counts
4 → 12
Calls
4 calls:
117.0ms
(* (/ (/ 1 (sqrt (sqrt (sqrt 2.0)))) (sqrt (sqrt (sqrt 2.0)))) (* (/ (cos th) (sqrt (sqrt 2.0))) (* a2 a2)))
169.0ms
(* (/ (cos th) (sqrt (sqrt 2.0))) (* a2 a2))
58.0ms
(/ (pow a1 2) (sqrt 2.0))
98.0ms
(/ (cos th) (sqrt (sqrt 2.0)))

simplify112.0ms

Algorithm
egg-herbie
Counts
733 → 733
Iterations

Useful iterations: 1 (34.0ms)

IterNodesCost
0175310660
150029333

prune2.5s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

regimes347.0ms

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
02621
12621

end0.0ms

sample2.5s

Algorithm
intervals
Results
873.0ms2518×body1280valid
471.0ms2019×body640valid
431.0ms8000×body80valid
176.0ms1068×body320valid
63.0ms535×body160valid