Details

Time bar (total: 5.2s)

sample88.0ms

Algorithm
intervals
Results
30.0ms94×body1280valid
19.0ms74×body640valid
13.0ms262×body80valid
7.0ms47×body320valid
2.0ms22×body160valid

simplify17.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0257
1507
2777
3967
41127
51277
61417
71417

prune8.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.4b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* a1 a1) (* a2 a2))
0.4b
(* (/ (cos th) (sqrt 2.0)) (+ (* a1 a1) (* a2 a2)))
0.7b
(/ (cos th) (sqrt 2.0))

rewrite28.0ms

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:
4.0ms
(+ (* a1 a1) (* a2 a2))
15.0ms
(* (/ (cos th) (sqrt 2.0)) (+ (* a1 a1) (* a2 a2)))
5.0ms
(/ (cos th) (sqrt 2.0))

series312.0ms

Counts
3 → 9
Calls
3 calls:
27.0ms
(+ (* a1 a1) (* a2 a2))
225.0ms
(* (/ (cos th) (sqrt 2.0)) (+ (* a1 a1) (* a2 a2)))
59.0ms
(/ (cos th) (sqrt 2.0))

simplify58.0ms

Algorithm
egg-herbie
Counts
107 → 107
Iterations

Useful iterations: 2 (47.0ms)

IterNodesCost
0490872
12426805
25003791

prune289.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

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)))
0.4b
(/ (+ (pow a2 2) (pow a1 2)) (sqrt 2.0))

rewrite47.0ms

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:
8.0ms
(+ (pow a2 2) (pow a1 2))
21.0ms
(* (cos th) (/ (+ (pow a2 2) (pow a1 2)) (sqrt 2.0)))
12.0ms
(/ (+ (pow a2 2) (pow a1 2)) (sqrt 2.0))

series334.0ms

Counts
3 → 9
Calls
3 calls:
27.0ms
(+ (pow a2 2) (pow a1 2))
212.0ms
(* (cos th) (/ (+ (pow a2 2) (pow a1 2)) (sqrt 2.0)))
95.0ms
(/ (+ (pow a2 2) (pow a1 2)) (sqrt 2.0))

simplify54.0ms

Algorithm
egg-herbie
Counts
131 → 131
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
03441118
115571023
250011018

prune282.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize12.0ms

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

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
17×*-un-lft-identity
11×add-sqr-sqrt
10×add-exp-log add-cbrt-cube
9×add-cube-cbrt
6×times-frac associate-/r* sqrt-prod
5×pow1 associate-*r* add-log-exp
4×unpow-prod-down associate-*r/ distribute-lft-out
3×flip3-+ associate-*l* flip-+
2×cbrt-undiv div-exp prod-exp cbrt-unprod associate-/l/
1×+-commutative distribute-rgt-in frac-2neg distribute-lft-in pow-prod-down clear-num sum-log *-commutative div-inv associate-/l* unswap-sqr
Counts
3 → 66
Calls
3 calls:
7.0ms
(+ (pow a2 2) (pow a1 2))
11.0ms
(* (cos th) (+ (pow a2 2) (pow a1 2)))
13.0ms
(/ (* (cos th) (+ (pow a2 2) (pow a1 2))) (sqrt 2.0))

series354.0ms

Counts
3 → 9
Calls
3 calls:
27.0ms
(+ (pow a2 2) (pow a1 2))
114.0ms
(* (cos th) (+ (pow a2 2) (pow a1 2)))
213.0ms
(/ (* (cos th) (+ (pow a2 2) (pow a1 2))) (sqrt 2.0))

simplify44.0ms

Algorithm
egg-herbie
Counts
75 → 75
Iterations

Useful iterations: 2 (38.0ms)

IterNodesCost
0277562
11443488
25001484

prune201.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (pow a2 2) (pow a1 2))
0.1b
(* (cos th) (* 1 (+ (pow a2 2) (pow a1 2))))
0.3b
(/ (* (cos th) (* 1 (+ (pow a2 2) (pow a1 2)))) (sqrt 2.0))

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
22×add-exp-log
17×add-cbrt-cube
12×*-un-lft-identity
10×prod-exp
8×pow1 add-sqr-sqrt add-cube-cbrt associate-*r/
6×times-frac associate-/r* sqrt-prod cbrt-unprod
5×add-log-exp
4×distribute-rgt-in distribute-lft-in div-exp
3×cbrt-undiv flip3-+ associate-*l* pow-prod-down flip-+
2×unpow-prod-down 1-exp associate-/l/ distribute-lft-out
1×+-commutative frac-2neg associate-*r* clear-num sum-log *-commutative div-inv associate-/l*
Counts
3 → 70
Calls
3 calls:
8.0ms
(+ (pow a2 2) (pow a1 2))
12.0ms
(* (cos th) (* 1 (+ (pow a2 2) (pow a1 2))))
15.0ms
(/ (* (cos th) (* 1 (+ (pow a2 2) (pow a1 2)))) (sqrt 2.0))

series352.0ms

Counts
3 → 9
Calls
3 calls:
26.0ms
(+ (pow a2 2) (pow a1 2))
113.0ms
(* (cos th) (* 1 (+ (pow a2 2) (pow a1 2))))
212.0ms
(/ (* (cos th) (* 1 (+ (pow a2 2) (pow a1 2)))) (sqrt 2.0))

simplify49.0ms

Algorithm
egg-herbie
Counts
79 → 79
Iterations

Useful iterations: 2 (41.0ms)

IterNodesCost
0346643
11767540
25001535

prune188.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

regimes177.0ms

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
0198
1218
2218

end0.0ms

sample2.2s

Algorithm
intervals
Results
823.0ms2553×body1280valid
444.0ms2094×body640valid
393.0ms8064×body80valid
164.0ms1035×body320valid
57.0ms500×body160valid