Details

Time bar (total: 7.2s)

sample73.0ms

Algorithm
intervals
Results
24.0ms77×body1280valid
13.0ms60×body640valid
13.0ms264×body80valid
6.0ms31×body320valid
1.0ms14×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: 0.4b

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (/ (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))

rewrite48.0ms

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:
16.0ms
(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
16.0ms
(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
4.0ms
(/ (cos th) (sqrt 2.0))
4.0ms
(/ (cos th) (sqrt 2.0))

series358.0ms

Counts
4 → 12
Calls
4 calls:
113.0ms
(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
112.0ms
(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
67.0ms
(/ (cos th) (sqrt 2.0))
65.0ms
(/ (cos th) (sqrt 2.0))

simplify53.0ms

Algorithm
egg-herbie
Counts
180 → 180
Iterations

Useful iterations: 2 (40.0ms)

IterNodesCost
05041284
120091156
250021136

prune501.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (cos th) (* a2 a2))
0.2b
(/ (* (cos th) (* a2 a2)) (sqrt 2.0))
0.3b
(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
0.7b
(/ (cos th) (sqrt 2.0))

rewrite46.0ms

Algorithm
rewrite-expression-head
Rules
44×times-frac
43×add-sqr-sqrt
37×add-cube-cbrt *-un-lft-identity
32×add-exp-log add-cbrt-cube
28×sqrt-prod
25×associate-*l*
14×pow1
12×prod-exp associate-/r* cbrt-unprod
6×cbrt-undiv div-exp pow-prod-down
4×associate-/l* add-log-exp unswap-sqr
3×div-inv
2×frac-2neg associate-*r* clear-num *-commutative
1×associate-*l/
Counts
4 → 132
Calls
4 calls:
9.0ms
(* (cos th) (* a2 a2))
9.0ms
(/ (* (cos th) (* a2 a2)) (sqrt 2.0))
17.0ms
(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
5.0ms
(/ (cos th) (sqrt 2.0))

series351.0ms

Counts
4 → 12
Calls
4 calls:
49.0ms
(* (cos th) (* a2 a2))
117.0ms
(/ (* (cos th) (* a2 a2)) (sqrt 2.0))
119.0ms
(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
67.0ms
(/ (cos th) (sqrt 2.0))

simplify52.0ms

Algorithm
egg-herbie
Counts
144 → 144
Iterations

Useful iterations: 2 (42.0ms)

IterNodesCost
0501987
12125864
25002850

prune365.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (cos th) (/ (pow a1 2) (sqrt 2.0)))
0.2b
(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
0.3b
(/ (pow a1 2) (sqrt 2.0))
0.7b
(/ (cos th) (sqrt 2.0))

rewrite60.0ms

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:
23.0ms
(* (cos th) (/ (pow a1 2) (sqrt 2.0)))
16.0ms
(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
6.0ms
(/ (pow a1 2) (sqrt 2.0))
4.0ms
(/ (cos th) (sqrt 2.0))

series547.0ms

Counts
4 → 12
Calls
4 calls:
104.0ms
(* (cos th) (/ (pow a1 2) (sqrt 2.0)))
107.0ms
(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
275.0ms
(/ (pow a1 2) (sqrt 2.0))
61.0ms
(/ (cos th) (sqrt 2.0))

simplify79.0ms

Algorithm
egg-herbie
Counts
252 → 252
Iterations

Useful iterations: 2 (57.0ms)

IterNodesCost
06941786
130241552
250011540

prune593.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (* (cos th) a1) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))
0.2b
(* (/ (* (cos th) a1) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (/ (pow a1 (/ 2 2)) (cbrt (sqrt 2.0))))
0.2b
(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
0.7b
(/ (cos th) (sqrt 2.0))

rewrite91.0ms

Algorithm
rewrite-expression-head
Rules
112×add-exp-log times-frac
104×add-sqr-sqrt
73×add-cube-cbrt *-un-lft-identity
68×associate-*r*
54×add-cbrt-cube
48×cbrt-prod
46×prod-exp sqrt-prod
38×div-exp
30×unpow-prod-down
28×cbrt-unprod
27×associate-*l*
20×cbrt-undiv
13×unswap-sqr
12×sqr-pow
11×pow1
7×associate-/r*
5×pow-to-exp pow-exp div-inv
4×pow-prod-down associate-/l* add-log-exp
2×frac-2neg associate-*l/ clear-num *-commutative
1×frac-times associate-*r/
Counts
4 → 229
Calls
4 calls:
7.0ms
(/ (* (cos th) a1) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))
51.0ms
(* (/ (* (cos th) a1) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (/ (pow a1 (/ 2 2)) (cbrt (sqrt 2.0))))
16.0ms
(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
4.0ms
(/ (cos th) (sqrt 2.0))

series680.0ms

Counts
4 → 12
Calls
4 calls:
402.0ms
(/ (* (cos th) a1) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))
110.0ms
(* (/ (* (cos th) a1) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (/ (pow a1 (/ 2 2)) (cbrt (sqrt 2.0))))
107.0ms
(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
60.0ms
(/ (cos th) (sqrt 2.0))

simplify54.0ms

Algorithm
egg-herbie
Counts
241 → 241
Iterations

Useful iterations: 1 (25.0ms)

IterNodesCost
011452969
150012581

prune694.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0b

regimes167.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01815
11815

end0.0ms

sample2.3s

Algorithm
intervals
Results
831.0ms2527×body1280valid
455.0ms2100×body640valid
399.0ms8129×body80valid
170.0ms1049×body320valid
58.0ms522×body160valid