Details

Time bar (total: 7.5s)

sample88.0ms

Algorithm
intervals
Results
31.0ms94×body1280valid
17.0ms74×body640valid
13.0ms262×body80valid
7.0ms47×body320valid
2.0ms22×body160valid

simplify19.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
0267
1576
2876
31146
41326
51516
61716
71736
81736

prune8.0ms

Filtered
1 candidates to 1 candidates (100.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.3b

localize16.0ms

Local error

Found 3 expressions with local error:

0.0b
(fma a1 a1 (* a2 a2))
0.1b
(* (cos th) (fma a1 a1 (* a2 a2)))
0.3b
(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt 2.0))

rewrite10.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt
10×add-exp-log add-cbrt-cube
9×add-cube-cbrt *-un-lft-identity
6×times-frac associate-/r* sqrt-prod
5×pow1
3×expm1-log1p-u associate-*r* associate-*l* fma-udef log1p-expm1-u add-log-exp
2×cbrt-undiv div-exp prod-exp cbrt-unprod
1×distribute-rgt-in frac-2neg distribute-lft-in pow-prod-down clear-num *-commutative div-inv associate-/l* unswap-sqr
Counts
3 → 61
Calls
3 calls:
0.0ms
(fma a1 a1 (* a2 a2))
3.0ms
(* (cos th) (fma a1 a1 (* a2 a2)))
5.0ms
(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt 2.0))

series367.0ms

Counts
3 → 9
Calls
3 calls:
40.0ms
(fma a1 a1 (* a2 a2))
108.0ms
(* (cos th) (fma a1 a1 (* a2 a2)))
219.0ms
(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt 2.0))

simplify35.0ms

Algorithm
egg-herbie
Counts
70 → 70
Iterations

Useful iterations: 2 (29.0ms)

IterNodesCost
0205467
11002399
25001393

prune383.0ms

Filtered
70 candidates to 49 candidates (70.0%)
Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize12.0ms

Local error

Found 3 expressions with local error:

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

rewrite41.0ms

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt
11×add-cube-cbrt *-un-lft-identity
10×add-exp-log add-cbrt-cube
8×fma-def
6×times-frac associate-/r* sqrt-prod
5×pow1 add-log-exp
4×associate-*r/
3×expm1-log1p-u unpow-prod-down flip3-+ associate-*r* associate-*l* flip-+ log1p-expm1-u
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* unpow2 unswap-sqr sqr-pow
Counts
3 → 76
Calls
3 calls:
7.0ms
(+ (pow a1 2) (* a2 a2))
21.0ms
(* (cos th) (+ (pow a1 2) (* a2 a2)))
11.0ms
(/ (* (cos th) (+ (pow a1 2) (* a2 a2))) (sqrt 2.0))

series337.0ms

Counts
3 → 9
Calls
3 calls:
29.0ms
(+ (pow a1 2) (* a2 a2))
102.0ms
(* (cos th) (+ (pow a1 2) (* a2 a2)))
205.0ms
(/ (* (cos th) (+ (pow a1 2) (* a2 a2))) (sqrt 2.0))

simplify44.0ms

Algorithm
egg-herbie
Counts
85 → 85
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
0299594
11613486
25001466

prune257.0ms

Filtered
85 candidates to 66 candidates (77.6%)
Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

localize12.0ms

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))

rewrite47.0ms

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×expm1-log1p-u log1p-expm1-u div-inv add-log-exp
2×frac-2neg associate-*r* associate-*l/ clear-num *-commutative
Counts
4 → 176
Calls
4 calls:
15.0ms
(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
17.0ms
(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
4.0ms
(/ (cos th) (sqrt 2.0))
4.0ms
(/ (cos th) (sqrt 2.0))

series332.0ms

Counts
4 → 12
Calls
4 calls:
107.0ms
(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
109.0ms
(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
56.0ms
(/ (cos th) (sqrt 2.0))
61.0ms
(/ (cos th) (sqrt 2.0))

simplify51.0ms

Algorithm
egg-herbie
Counts
188 → 188
Iterations

Useful iterations: 2 (39.0ms)

IterNodesCost
05101324
120211196
250021174

prune464.0ms

Filtered
188 candidates to 124 candidates (66.0%)
Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite186.0ms

Algorithm
rewrite-expression-head
Rules
1149×sqrt-prod
1137×times-frac
626×add-sqr-sqrt
592×add-cube-cbrt *-un-lft-identity
283×associate-*l*
37×associate-/l*
34×add-exp-log add-cbrt-cube
24×associate-/r*
23×div-inv
13×unswap-sqr
11×cbrt-undiv div-exp
9×pow1 prod-exp cbrt-unprod
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×frac-2neg pow-prod-down clear-num
1×associate-*r* associate-*l/ *-commutative associate-/l/
Counts
4 → 752
Calls
4 calls:
95.0ms
(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (* a1 a1))
5.0ms
(/ (cos th) (sqrt (sqrt 2.0)))
20.0ms
(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
4.0ms
(/ (cos th) (sqrt 2.0))

series329.0ms

Counts
4 → 12
Calls
4 calls:
108.0ms
(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (* a1 a1))
94.0ms
(/ (cos th) (sqrt (sqrt 2.0)))
61.0ms
(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
65.0ms
(/ (cos th) (sqrt 2.0))

simplify106.0ms

Algorithm
egg-herbie
Counts
764 → 764
Iterations

Useful iterations: 1 (30.0ms)

IterNodesCost
015529914
150028705

prune1.7s

Filtered
764 candidates to 360 candidates (47.1%)
Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0b

regimes275.0ms

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
0147
1147

end0.0ms

sample2.3s

Algorithm
intervals
Results
859.0ms2553×body1280valid
486.0ms2094×body640valid
418.0ms8064×body80valid
171.0ms1035×body320valid
58.0ms500×body160valid