Details

Time bar (total: 7.9s)

sample81.0ms

Algorithm
intervals
Results
30.0ms83×body1280valid
15.0ms69×body640valid
13.0ms256×body80valid
5.0ms30×body320valid
1.0ms11×body160valid

simplify16.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0257
1507
2777
3967
41127
51277
61417
71417

prune9.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.7b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* a1 a1) (* a2 a2))
0.6b
(* (/ (cos th) (sqrt 2.0)) (+ (* a1 a1) (* a2 a2)))
0.7b
(/ (cos th) (sqrt 2.0))

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
40×add-sqr-sqrt
38×times-frac
32×add-cube-cbrt *-un-lft-identity
22×associate-*l* sqrt-prod
10×add-exp-log add-cbrt-cube
6×associate-/r*
5×pow1 add-log-exp
3×flip3-+ associate-*r* flip-+ associate-/l* unswap-sqr
2×cbrt-undiv frac-times associate-*r/ div-exp prod-exp cbrt-unprod div-inv
1×+-commutative distribute-rgt-in frac-2neg distribute-lft-in pow-prod-down associate-*l/ clear-num sum-log *-commutative
Counts
3 → 98
Calls
3 calls:
3.0ms
(+ (* a1 a1) (* a2 a2))
22.0ms
(* (/ (cos th) (sqrt 2.0)) (+ (* a1 a1) (* a2 a2)))
4.0ms
(/ (cos th) (sqrt 2.0))

series314.0ms

Counts
3 → 9
Calls
3 calls:
28.0ms
(+ (* a1 a1) (* a2 a2))
227.0ms
(* (/ (cos th) (sqrt 2.0)) (+ (* a1 a1) (* a2 a2)))
59.0ms
(/ (cos th) (sqrt 2.0))

simplify56.0ms

Algorithm
egg-herbie
Counts
107 → 107
Iterations

Useful iterations: 2 (46.0ms)

IterNodesCost
0490872
12426805
25003791

prune317.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.3b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (pow a2 2) (pow a1 2))
0.1b
(* (cos th) (/ (+ (pow a2 2) (pow a1 2)) (sqrt 2.0)))
0.6b
(/ (+ (pow a2 2) (pow a1 2)) (sqrt 2.0))

rewrite93.0ms

Algorithm
rewrite-expression-head
Rules
96×*-un-lft-identity
62×times-frac
48×add-sqr-sqrt
40×add-cube-cbrt
34×associate-*r* sqrt-prod
28×unpow-prod-down distribute-lft-out
10×add-exp-log add-cbrt-cube
6×associate-/r*
5×pow1 associate-/l* add-log-exp
3×associate-*l* unswap-sqr
2×cbrt-undiv flip3-+ div-exp prod-exp cbrt-unprod flip-+ div-inv associate-/l/
1×+-commutative frac-2neg associate-*r/ pow-prod-down clear-num sum-log *-commutative
Counts
3 → 122
Calls
3 calls:
9.0ms
(+ (pow a2 2) (pow a1 2))
45.0ms
(* (cos th) (/ (+ (pow a2 2) (pow a1 2)) (sqrt 2.0)))
32.0ms
(/ (+ (pow a2 2) (pow a1 2)) (sqrt 2.0))

series347.0ms

Counts
3 → 9
Calls
3 calls:
28.0ms
(+ (pow a2 2) (pow a1 2))
218.0ms
(* (cos th) (/ (+ (pow a2 2) (pow a1 2)) (sqrt 2.0)))
101.0ms
(/ (+ (pow a2 2) (pow a1 2)) (sqrt 2.0))

simplify50.0ms

Algorithm
egg-herbie
Counts
131 → 131
Iterations

Useful iterations: 2 (38.0ms)

IterNodesCost
03441118
115571023
250011018

prune327.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.3b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (/ (pow a1 2) (sqrt 2.0)) (/ (pow a2 2) (sqrt 2.0)))
0.1b
(* (cos th) (+ (/ (pow a1 2) (sqrt 2.0)) (/ (pow a2 2) (sqrt 2.0))))
0.3b
(/ (pow a1 2) (sqrt 2.0))
0.5b
(/ (pow a2 2) (sqrt 2.0))

rewrite591.0ms

Algorithm
rewrite-expression-head
Rules
160×times-frac
154×*-un-lft-identity
104×add-sqr-sqrt
86×add-cube-cbrt sqrt-prod
74×unpow-prod-down
34×distribute-lft-out
21×associate-*r*
16×add-exp-log associate-/l*
14×unpow2 sqr-pow
12×associate-/r*
10×add-cbrt-cube
6×pow1 div-exp div-inv add-log-exp
3×associate-*r/ associate-*l*
2×cbrt-undiv pow-to-exp distribute-rgt-out frac-2neg flip3-+ frac-add pow-exp clear-num flip-+
1×+-commutative distribute-rgt-in distribute-lft-in pow-prod-down prod-exp sum-log *-commutative cbrt-unprod unswap-sqr
Counts
4 → 223
Calls
4 calls:
118.0ms
(+ (/ (pow a1 2) (sqrt 2.0)) (/ (pow a2 2) (sqrt 2.0)))
446.0ms
(* (cos th) (+ (/ (pow a1 2) (sqrt 2.0)) (/ (pow a2 2) (sqrt 2.0))))
5.0ms
(/ (pow a1 2) (sqrt 2.0))
9.0ms
(/ (pow a2 2) (sqrt 2.0))

series523.0ms

Counts
4 → 12
Calls
4 calls:
117.0ms
(+ (/ (pow a1 2) (sqrt 2.0)) (/ (pow a2 2) (sqrt 2.0)))
277.0ms
(* (cos th) (+ (/ (pow a1 2) (sqrt 2.0)) (/ (pow a2 2) (sqrt 2.0))))
65.0ms
(/ (pow a1 2) (sqrt 2.0))
64.0ms
(/ (pow a2 2) (sqrt 2.0))

simplify73.0ms

Algorithm
egg-herbie
Counts
235 → 235
Iterations

Useful iterations: 2 (48.0ms)

IterNodesCost
05381761
120701556
250011535

prune556.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ a2 (/ (sqrt 2.0) a2))
0.1b
(* (cos th) (+ (/ (pow a1 2) (sqrt 2.0)) (/ a2 (/ (sqrt 2.0) a2))))
0.3b
(/ (pow a1 2) (sqrt 2.0))
0.4b
(/ (sqrt 2.0) a2)

rewrite615.0ms

Algorithm
rewrite-expression-head
Rules
206×times-frac
134×*-un-lft-identity
130×add-sqr-sqrt
128×add-cube-cbrt
75×sqrt-prod
31×associate-/r*
21×unpow-prod-down
18×add-exp-log
17×associate-/l*
15×add-cbrt-cube
7×div-exp div-inv unpow2 sqr-pow
6×pow1
5×cbrt-undiv associate-*r*
4×add-log-exp
3×frac-2neg associate-*r/ associate-*l* clear-num
2×distribute-lft-out
1×distribute-rgt-in pow-to-exp distribute-lft-in flip3-+ pow-prod-down frac-add pow-exp prod-exp associate-/r/ *-commutative cbrt-unprod flip-+ unswap-sqr
Counts
4 → 246
Calls
4 calls:
7.0ms
(/ a2 (/ (sqrt 2.0) a2))
584.0ms
(* (cos th) (+ (/ (pow a1 2) (sqrt 2.0)) (/ a2 (/ (sqrt 2.0) a2))))
5.0ms
(/ (pow a1 2) (sqrt 2.0))
7.0ms
(/ (sqrt 2.0) a2)

series654.0ms

Counts
4 → 12
Calls
4 calls:
62.0ms
(/ a2 (/ (sqrt 2.0) a2))
479.0ms
(* (cos th) (+ (/ (pow a1 2) (sqrt 2.0)) (/ a2 (/ (sqrt 2.0) a2))))
61.0ms
(/ (pow a1 2) (sqrt 2.0))
52.0ms
(/ (sqrt 2.0) a2)

simplify104.0ms

Algorithm
egg-herbie
Counts
258 → 258
Iterations

Useful iterations: 1 (20.0ms)

IterNodesCost
07451965
138001743
250021743

prune615.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

regimes195.0ms

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
01916
11916

end0.0ms

sample2.3s

Algorithm
intervals
Results
836.0ms2485×body1280valid
469.0ms2094×body640valid
397.0ms7973×body80valid
155.0ms1004×body320valid
54.0ms506×body160valid