Details

Time bar (total: 8.6s)

sample61.0ms

Algorithm
intervals
Results
21.0ms281×body80valid
9.0ms26×body1280valid
9.0ms36×body640valid
3.0ms18×body320valid
1.0ms9×body160valid

simplify42.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0278
1688
22438
312668
450018

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.2b

localize13.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
4.3b
(* (* x (pow sin 2.0)) x)
8.3b
(* x (pow sin 2.0))
16.6b
(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

rewrite162.0ms

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:
61.0ms
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
22.0ms
(* (* x (pow sin 2.0)) x)
12.0ms
(* x (pow sin 2.0))
62.0ms
(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

series759.0ms

Counts
4 → 12
Calls
4 calls:
271.0ms
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
130.0ms
(* (* x (pow sin 2.0)) x)
123.0ms
(* x (pow sin 2.0))
234.0ms
(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

simplify64.0ms

Algorithm
egg-herbie
Counts
135 → 135
Iterations

Useful iterations: 1 (11.0ms)

IterNodesCost
0448971
12063815
25002815

prune408.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 13.6b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))
0.4b
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
4.3b
(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
16.6b
(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

rewrite508.0ms

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:
28.0ms
(* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))
192.0ms
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
76.0ms
(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
200.0ms
(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

series842.0ms

Counts
4 → 12
Calls
4 calls:
133.0ms
(* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))
285.0ms
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
145.0ms
(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
279.0ms
(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

simplify89.0ms

Algorithm
egg-herbie
Counts
206 → 206
Iterations

Useful iterations: 2 (70.0ms)

IterNodesCost
06032216
128211509
250021497

prune425.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 2.6b

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))) (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))))
0.4b
(/ (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)))))))
4.2b
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
4.2b
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

rewrite85.0ms

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:
7.0ms
(* (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))) (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))))
17.0ms
(/ (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)))))))
28.0ms
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
30.0ms
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

series538.0ms

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))))))
101.0ms
(/ (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)))))))
201.0ms
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
204.0ms
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

simplify48.0ms

Algorithm
egg-herbie
Counts
126 → 126
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
03251562
112441292
250011217

prune612.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (/ (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))))))
0.6b
(/ (cos (* 2.0 x)) (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))))
4.2b
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
4.2b
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

rewrite97.0ms

Algorithm
rewrite-expression-head
Rules
84×times-frac
63×add-exp-log
58×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
42×prod-exp
21×add-cbrt-cube
16×associate-/l*
14×pow-to-exp associate-*l* pow-exp
6×unpow-prod-down associate-/r* cbrt-unprod div-inv
4×pow1 cbrt-undiv expm1-log1p-u div-exp log1p-expm1-u add-log-exp
2×frac-2neg associate-*r* clear-num *-commutative sqr-pow
1×associate-/l/
Counts
4 → 165
Calls
4 calls:
18.0ms
(/ (/ (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))))))
14.0ms
(/ (cos (* 2.0 x)) (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))))
31.0ms
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
28.0ms
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

series582.0ms

Counts
4 → 12
Calls
4 calls:
101.0ms
(/ (/ (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))))))
70.0ms
(/ (cos (* 2.0 x)) (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))))
206.0ms
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
205.0ms
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

simplify69.0ms

Algorithm
egg-herbie
Counts
177 → 177
Iterations

Useful iterations: 2 (41.0ms)

IterNodesCost
05193377
118443082
250012997

prune1.1s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

regimes363.0ms

Accuracy

2.2% (2.4b remaining)

Error of 2.5b against oracle of 0.1b and baseline of 2.6b

bsearch50.0ms

Steps
ItersRangePoint
4
1.5653319394241413e-192
2.944220213231063e-192
1.638785243186149e-192

simplify7.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03438
13438

end0.0ms

sample1.6s

Algorithm
intervals
Results
585.0ms8987×body80valid
310.0ms828×body1280valid
244.0ms932×body640valid
111.0ms574×body320valid
40.0ms304×body160valid