Details

Time bar (total: 5.9s)

analyze1.1s

Algorithm
search
Search
TrueOtherFalseIter
0%99.9%0.1%0
0%99.9%0.1%1
0%99.9%0.1%2
0%99.9%0.1%3
0%99.9%0.1%4
0%99.9%0.1%5
0%99.9%0.1%6
12.5%87.4%0.1%7
18.7%81.1%0.1%8
26.5%72.9%0.5%9
38.2%60.7%1.1%10
41.7%54.9%3.4%11
47.6%47.4%5%12
53.4%39.4%7.2%13
54.9%34.5%10.6%14

sample65.0ms

Algorithm
intervals
Results
16.0ms188×body80valid
14.0ms30×body1280valid
8.0ms56×body80invalid
7.0ms20×body640valid
3.0ms14×body320valid
2.0ms4×body1280invalid
2.0ms7×body320invalid
1.0ms4×body160valid
0.0ms1×body640invalid
0.0ms2×body160invalid

simplify65.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (63.0ms)

IterNodesCost
0484516
1484516

prune11.0ms

Filtered
1 candidates to 1 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 23.5b

Counts
2 → 2

localize13.0ms

Local error

Found 4 expressions with local error:

0.5b
(/ (cos (* 2.0 x)) (* (pow c 2.0) (* (* x (pow s 2.0)) x)))
5.1b
(* (* x (pow s 2.0)) x)
7.0b
(* x (pow s 2.0))
16.4b
(* (pow c 2.0) (* (* x (pow s 2.0)) x))

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
122×add-exp-log
82×prod-exp
34×add-cbrt-cube
18×pow-to-exp pow-exp
17×add-sqr-sqrt
16×div-exp cbrt-unprod
12×add-cube-cbrt *-un-lft-identity
11×associate-*r* associate-*l*
7×unpow-prod-down
6×pow1
4×cbrt-undiv add-log-exp
3×times-frac *-commutative associate-/l* unswap-sqr sqr-pow
1×frac-2neg pow-prod-down clear-num associate-/r* div-inv
Counts
4 → 115
Calls
4 calls:
10.0ms
(/ (cos (* 2.0 x)) (* (pow c 2.0) (* (* x (pow s 2.0)) x)))
5.0ms
(* (* x (pow s 2.0)) x)
5.0ms
(* x (pow s 2.0))
8.0ms
(* (pow c 2.0) (* (* x (pow s 2.0)) x))

series219.0ms

Counts
4 → 12
Calls
4 calls:
76.0ms
(/ (cos (* 2.0 x)) (* (pow c 2.0) (* (* x (pow s 2.0)) x)))
30.0ms
(* (* x (pow s 2.0)) x)
31.0ms
(* x (pow s 2.0))
81.0ms
(* (pow c 2.0) (* (* x (pow s 2.0)) x))

simplify65.0ms

Algorithm
egg-herbie
Counts
127 → 127
Iterations

Useful iterations: 0 (54.0ms)

IterNodesCost
049651594
149651594

prune217.0ms

Filtered
72 candidates to 127 candidates (-76.4%)
Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New1198127
Fresh011
Picked101
Done000
Total1209129

Merged error: 11.2b

Counts
129 → 9

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* x (pow s (/ 2.0 2))) (pow s (/ 2.0 2)))
0.5b
(/ (cos (* 2.0 x)) (* (pow c 2.0) (* (* (* x (pow s (/ 2.0 2))) (pow s (/ 2.0 2))) x)))
5.1b
(* (* (* x (pow s (/ 2.0 2))) (pow s (/ 2.0 2))) x)
16.4b
(* (pow c 2.0) (* (* (* x (pow s (/ 2.0 2))) (pow s (/ 2.0 2))) x))

rewrite55.0ms

Algorithm
rewrite-expression-head
Rules
416×add-exp-log
343×prod-exp
84×pow-to-exp pow-exp
52×add-cbrt-cube
43×div-exp
29×cbrt-unprod
11×add-sqr-sqrt add-cube-cbrt *-un-lft-identity associate-*r*
9×associate-*l*
6×pow1 unpow-prod-down
5×cbrt-undiv
4×add-log-exp
3×times-frac *-commutative associate-/l*
2×sqr-pow
1×frac-2neg pow-prod-down clear-num associate-/r* div-inv
Counts
4 → 186
Calls
4 calls:
7.0ms
(* (* x (pow s (/ 2.0 2))) (pow s (/ 2.0 2)))
14.0ms
(/ (cos (* 2.0 x)) (* (pow c 2.0) (* (* (* x (pow s (/ 2.0 2))) (pow s (/ 2.0 2))) x)))
9.0ms
(* (* (* x (pow s (/ 2.0 2))) (pow s (/ 2.0 2))) x)
12.0ms
(* (pow c 2.0) (* (* (* x (pow s (/ 2.0 2))) (pow s (/ 2.0 2))) x))

series215.0ms

Counts
4 → 12
Calls
4 calls:
31.0ms
(* (* x (pow s (/ 2.0 2))) (pow s (/ 2.0 2)))
73.0ms
(/ (cos (* 2.0 x)) (* (pow c 2.0) (* (* (* x (pow s (/ 2.0 2))) (pow s (/ 2.0 2))) x)))
33.0ms
(* (* (* x (pow s (/ 2.0 2))) (pow s (/ 2.0 2))) x)
77.0ms
(* (pow c 2.0) (* (* (* x (pow s (/ 2.0 2))) (pow s (/ 2.0 2))) x))

simplify48.0ms

Algorithm
egg-herbie
Counts
198 → 198
Iterations

Useful iterations: 0 (28.0ms)

IterNodesCost
052202915

prune213.0ms

Filtered
70 candidates to 198 candidates (-182.9%)
Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New1962198
Fresh178
Picked101
Done000
Total1989207

Merged error: 9.0b

Counts
207 → 9

localize14.0ms

Local error

Found 3 expressions with local error:

0.3b
(* (* x (pow s (/ 2.0 2))) (* x (pow s (/ 2.0 2))))
0.5b
(/ (cos (* 2.0 x)) (* (pow c 2.0) (* (* x (pow s (/ 2.0 2))) (* x (pow s (/ 2.0 2))))))
16.4b
(* (pow c 2.0) (* (* x (pow s (/ 2.0 2))) (* x (pow s (/ 2.0 2)))))

rewrite50.0ms

Algorithm
rewrite-expression-head
Rules
466×add-exp-log
382×prod-exp
90×pow-to-exp pow-exp
58×add-cbrt-cube
52×div-exp
34×cbrt-unprod
10×pow1
9×add-sqr-sqrt
8×associate-*l*
7×add-cube-cbrt *-un-lft-identity
6×cbrt-undiv
4×unpow-prod-down
3×times-frac associate-/l* add-log-exp unswap-sqr
2×associate-*r* *-commutative sqr-pow
1×pow2 frac-2neg pow-plus swap-sqr pow-prod-down clear-num associate-/r* pow-sqr pow-prod-up div-inv
Counts
3 → 186
Calls
3 calls:
8.0ms
(* (* x (pow s (/ 2.0 2))) (* x (pow s (/ 2.0 2))))
14.0ms
(/ (cos (* 2.0 x)) (* (pow c 2.0) (* (* x (pow s (/ 2.0 2))) (* x (pow s (/ 2.0 2))))))
12.0ms
(* (pow c 2.0) (* (* x (pow s (/ 2.0 2))) (* x (pow s (/ 2.0 2)))))

series186.0ms

Counts
3 → 9
Calls
3 calls:
30.0ms
(* (* x (pow s (/ 2.0 2))) (* x (pow s (/ 2.0 2))))
79.0ms
(/ (cos (* 2.0 x)) (* (pow c 2.0) (* (* x (pow s (/ 2.0 2))) (* x (pow s (/ 2.0 2))))))
76.0ms
(* (pow c 2.0) (* (* x (pow s (/ 2.0 2))) (* x (pow s (/ 2.0 2)))))

simplify74.0ms

Algorithm
egg-herbie
Counts
195 → 195
Iterations

Useful iterations: 0 (50.0ms)

IterNodesCost
050103047

prune183.0ms

Filtered
56 candidates to 195 candidates (-248.2%)
Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New1905195
Fresh358
Picked101
Done000
Total19410204

Merged error: 0.3b

Counts
204 → 10

localize14.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (* x (* (pow s (/ 2.0 2)) (pow c (/ 2.0 2)))) (* x (* (pow s (/ 2.0 2)) (pow c (/ 2.0 2)))))
0.5b
(/ (cos (* 2.0 x)) (* (* x (* (pow s (/ 2.0 2)) (pow c (/ 2.0 2)))) (* x (* (pow s (/ 2.0 2)) (pow c (/ 2.0 2))))))
5.3b
(* x (* (pow s (/ 2.0 2)) (pow c (/ 2.0 2))))
5.3b
(* x (* (pow s (/ 2.0 2)) (pow c (/ 2.0 2))))

rewrite86.0ms

Algorithm
rewrite-expression-head
Rules
1229×add-exp-log
1116×prod-exp
276×pow-to-exp pow-exp
122×div-exp
97×add-cbrt-cube
60×cbrt-unprod
47×pow1
19×pow-prod-down
10×cbrt-undiv
8×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
7×associate-*l*
4×pow-sqr pow-prod-up add-log-exp
3×times-frac associate-*r* *-commutative associate-/l*
2×pow-plus
1×pow2 frac-2neg swap-sqr clear-num associate-/r* div-inv
Counts
4 → 355
Calls
4 calls:
15.0ms
(* (* x (* (pow s (/ 2.0 2)) (pow c (/ 2.0 2)))) (* x (* (pow s (/ 2.0 2)) (pow c (/ 2.0 2)))))
23.0ms
(/ (cos (* 2.0 x)) (* (* x (* (pow s (/ 2.0 2)) (pow c (/ 2.0 2)))) (* x (* (pow s (/ 2.0 2)) (pow c (/ 2.0 2))))))
7.0ms
(* x (* (pow s (/ 2.0 2)) (pow c (/ 2.0 2))))
7.0ms
(* x (* (pow s (/ 2.0 2)) (pow c (/ 2.0 2))))

series243.0ms

Counts
4 → 12
Calls
4 calls:
59.0ms
(* (* x (* (pow s (/ 2.0 2)) (pow c (/ 2.0 2)))) (* x (* (pow s (/ 2.0 2)) (pow c (/ 2.0 2)))))
75.0ms
(/ (cos (* 2.0 x)) (* (* x (* (pow s (/ 2.0 2)) (pow c (/ 2.0 2)))) (* x (* (pow s (/ 2.0 2)) (pow c (/ 2.0 2))))))
51.0ms
(* x (* (pow s (/ 2.0 2)) (pow c (/ 2.0 2))))
58.0ms
(* x (* (pow s (/ 2.0 2)) (pow c (/ 2.0 2))))

simplify72.0ms

Algorithm
egg-herbie
Counts
367 → 367
Iterations

Useful iterations: 0 (33.0ms)

IterNodesCost
055116129

prune195.0ms

Filtered
62 candidates to 367 candidates (-491.9%)
Pruning

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New3607367
Fresh369
Picked101
Done000
Total36413377

Merged error: 0.0b

Counts
377 → 13

regimes529.0ms

Accuracy

0% (2.3b remaining)

Error of 2.8b against oracle of 0.6b and baseline of 2.8b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01732
11732

end0.0ms

sample1.9s

Algorithm
intervals
Results
524.0ms5977×body80valid
331.0ms693×body1280valid
265.0ms751×body640valid
161.0ms1871×body80invalid
97.0ms359×body320valid
85.0ms255×body640invalid
64.0ms143×body1280invalid
41.0ms174×body320invalid
38.0ms220×body160valid
14.0ms91×body160invalid

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