Details

Time bar (total: 6.5s)

sample59.0ms

Algorithm
intervals
Results
23.0ms286×body80valid
11.0ms27×body1280valid
8.0ms28×body640valid
3.0ms13×body320valid
2.0ms15×body160valid

simplify39.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0278
1688
22438
312668
450018

prune3.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 26.9b

Counts
2 → 1

localize13.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
6.2b
(* (* x (pow sin 2.0)) x)
7.5b
(* x (pow sin 2.0))
16.1b
(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

rewrite34.0ms

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 expm1-log1p-u log1p-expm1-u 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 → 123
Calls
4 calls:
10.0ms
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
5.0ms
(* (* x (pow sin 2.0)) x)
5.0ms
(* x (pow sin 2.0))
9.0ms
(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

series804.0ms

Counts
4 → 12
Calls
4 calls:
284.0ms
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
142.0ms
(* (* x (pow sin 2.0)) x)
130.0ms
(* x (pow sin 2.0))
248.0ms
(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

simplify59.0ms

Algorithm
egg-herbie
Counts
135 → 135
Iterations

Useful iterations: 1 (12.0ms)

IterNodesCost
0448971
12063815
25002815

prune302.0ms

Filtered
135 candidates to 73 candidates (54.1%)
Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New12510135
Fresh000
Picked101
Done000
Total12610136

Merged error: 11.5b

Counts
136 → 10

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))
0.3b
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
6.2b
(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
16.1b
(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

rewrite54.0ms

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×expm1-log1p-u log1p-expm1-u 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 → 194
Calls
4 calls:
7.0ms
(* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))
14.0ms
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
9.0ms
(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
12.0ms
(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

series841.0ms

Counts
4 → 12
Calls
4 calls:
139.0ms
(* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))
290.0ms
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
153.0ms
(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
258.0ms
(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

simplify90.0ms

Algorithm
egg-herbie
Counts
206 → 206
Iterations

Useful iterations: 2 (69.0ms)

IterNodesCost
06032216
128211509
250021497

prune244.0ms

Filtered
206 candidates to 69 candidates (33.5%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New2024206
Fresh549
Picked101
Done000
Total2088216

Merged error: 1.2b

Counts
216 → 8

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))) (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))))
0.3b
(/ (cos (* 2.0 x)) (* (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))) (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2)))))))
4.1b
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
4.1b
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
63×add-exp-log
44×prod-exp
21×add-cbrt-cube
17×associate-*l*
16×add-sqr-sqrt
14×pow-to-exp add-cube-cbrt *-un-lft-identity pow-exp
11×pow1
8×cbrt-unprod
6×unpow-prod-down
5×associate-*r*
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×times-frac swap-sqr *-commutative associate-/l*
2×cbrt-undiv div-exp sqr-pow
1×pow2 frac-2neg pow-plus pow-prod-down clear-num associate-/r* pow-sqr pow-prod-up div-inv unswap-sqr
Counts
4 → 114
Calls
4 calls:
3.0ms
(* (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))) (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))))
5.0ms
(/ (cos (* 2.0 x)) (* (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))) (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2)))))))
8.0ms
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
8.0ms
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

series558.0ms

Counts
4 → 12
Calls
4 calls:
31.0ms
(* (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))) (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))))
103.0ms
(/ (cos (* 2.0 x)) (* (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))) (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2)))))))
214.0ms
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
210.0ms
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

simplify56.0ms

Algorithm
egg-herbie
Counts
126 → 126
Iterations

Useful iterations: 2 (36.0ms)

IterNodesCost
03251562
112441292
250011217

prune334.0ms

Filtered
126 candidates to 75 candidates (59.5%)
Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New1197126
Fresh437
Picked101
Done000
Total12410134

Merged error: 0.0b

Counts
134 → 10

localize17.0ms

Local error

Found 4 expressions with local error:

0.7b
(/ 1 (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))))
0.7b
(/ (cos (* 2.0 x)) (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))))
4.1b
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
4.1b
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
62×add-exp-log
42×prod-exp
24×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
18×times-frac add-cbrt-cube
14×pow-to-exp associate-*l* pow-exp
6×unpow-prod-down associate-/r* cbrt-unprod associate-/l*
5×pow1
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×div-exp
2×cbrt-undiv frac-2neg associate-*r* clear-num *-commutative div-inv sqr-pow
1×rec-exp pow-flip 1-exp inv-pow
Counts
4 → 126
Calls
4 calls:
3.0ms
(/ 1 (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))))
4.0ms
(/ (cos (* 2.0 x)) (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))))
8.0ms
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
8.0ms
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

series529.0ms

Counts
4 → 12
Calls
4 calls:
31.0ms
(/ 1 (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))))
71.0ms
(/ (cos (* 2.0 x)) (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))))
210.0ms
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
216.0ms
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

simplify47.0ms

Algorithm
egg-herbie
Counts
138 → 138
Iterations

Useful iterations: 2 (33.0ms)

IterNodesCost
03281475
111561327
250011313

prune318.0ms

Filtered
138 candidates to 81 candidates (58.7%)
Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New1353138
Fresh189
Picked101
Done000
Total13711148

Merged error: 0.0b

Counts
148 → 11

regimes306.0ms

Accuracy

0% (2.3b remaining)

Error of 2.5b against oracle of 0.2b and baseline of 2.5b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02420
12420

end0.0ms

sample1.7s

Algorithm
intervals
Results
660.0ms8975×body80valid
349.0ms872×body1280valid
272.0ms952×body640valid
120.0ms578×body320valid
50.0ms320×body160valid