Details

Time bar (total: 7.1s)

sample50.0ms

Algorithm
intervals
Results
17.0ms267×body80valid
10.0ms29×body1280valid
6.0ms23×body640valid
3.0ms17×body320valid
1.0ms7×body160valid

simplify43.0ms

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

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.1b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
5.5b
(* (* x (pow sin 2.0)) x)
7.5b
(* x (pow sin 2.0))
17.4b
(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

rewrite71.0ms

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:
24.0ms
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
8.0ms
(* (* x (pow sin 2.0)) x)
6.0ms
(* x (pow sin 2.0))
28.0ms
(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

series841.0ms

Counts
4 → 12
Calls
4 calls:
302.0ms
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
144.0ms
(* (* x (pow sin 2.0)) x)
136.0ms
(* x (pow sin 2.0))
259.0ms
(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

simplify57.0ms

Algorithm
egg-herbie
Counts
135 → 135
Iterations

Useful iterations: 1 (11.0ms)

IterNodesCost
0448971
12063815
25002815

prune298.0ms

Filtered
135 candidates to 73 candidates (54.1%)
Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 14.2b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))
0.2b
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
5.5b
(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
17.4b
(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

rewrite235.0ms

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:
11.0ms
(* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))
89.0ms
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
33.0ms
(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
90.0ms
(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

series850.0ms

Counts
4 → 12
Calls
4 calls:
140.0ms
(* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))
289.0ms
(/ (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)
267.0ms
(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

simplify87.0ms

Algorithm
egg-herbie
Counts
206 → 206
Iterations

Useful iterations: 2 (67.0ms)

IterNodesCost
06032216
128211509
250021497

prune304.0ms

Filtered
206 candidates to 71 candidates (34.5%)
Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 2.0b

localize16.0ms

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)))))))
0.3b
(* (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))) (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))))
5.1b
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
5.1b
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

rewrite35.0ms

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:
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)))))))
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))))))
14.0ms
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
11.0ms
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

series543.0ms

Counts
4 → 12
Calls
4 calls:
98.0ms
(/ (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)))))))
36.0ms
(* (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))) (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))))
203.0ms
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
205.0ms
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

simplify46.0ms

Algorithm
egg-herbie
Counts
126 → 126
Iterations

Useful iterations: 2 (33.0ms)

IterNodesCost
03251562
112441292
250011217

prune366.0ms

Filtered
126 candidates to 75 candidates (59.5%)
Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize19.0ms

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))))))
0.5b
(/ (cos (* 2.0 x)) (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))))
5.1b
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
5.1b
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

rewrite37.0ms

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:
7.0ms
(/ (/ (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))))))
4.0ms
(/ (cos (* 2.0 x)) (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))))
11.0ms
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
11.0ms
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

series591.0ms

Counts
4 → 12
Calls
4 calls:
100.0ms
(/ (/ (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))))))
64.0ms
(/ (cos (* 2.0 x)) (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))))
213.0ms
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
214.0ms
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

simplify70.0ms

Algorithm
egg-herbie
Counts
177 → 177
Iterations

Useful iterations: 2 (40.0ms)

IterNodesCost
05193377
118443082
250012997

prune522.0ms

Filtered
177 candidates to 116 candidates (65.5%)
Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.0b

regimes268.0ms

Accuracy

17.6% (1.8b remaining)

Error of 2.0b against oracle of 0.2b and baseline of 2.4b

bsearch205.0ms

Steps
ItersRangePoint
7
3.6691713438147897e-150
4.9494863965455535e-148
4.181764666122331e-149
11
-6.208652502439282e-192
-4.119745624249939e-214
-9.430874193392341e-213

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04247
14247

end0.0ms

sample1.5s

Algorithm
intervals
Results
560.0ms8968×body80valid
300.0ms828×body1280valid
239.0ms954×body640valid
108.0ms598×body320valid
41.0ms327×body160valid