Details

Time bar (total: 7.6s)

sample74.0ms

Algorithm
intervals
Results
29.0ms294×body80valid
11.0ms24×body1280valid
9.0ms28×body640valid
8.0ms21×body320valid
2.0ms14×body160valid

simplify41.0ms

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: 29.4b

localize13.0ms

Local error

Found 4 expressions with local error:

0.7b
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
3.4b
(* (* x (pow sin 2.0)) x)
7.5b
(* x (pow sin 2.0))
20.0b
(* (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 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:
25.0ms
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
11.0ms
(* (* x (pow sin 2.0)) x)
5.0ms
(* x (pow sin 2.0))
25.0ms
(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

series865.0ms

Counts
4 → 12
Calls
4 calls:
308.0ms
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
153.0ms
(* (* x (pow sin 2.0)) x)
141.0ms
(* x (pow sin 2.0))
263.0ms
(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

simplify58.0ms

Algorithm
egg-herbie
Counts
127 → 127
Iterations

Useful iterations: 1 (11.0ms)

IterNodesCost
0435927
12042771
25002771

prune279.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 15.2b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))
0.7b
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
3.4b
(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
20.0b
(* (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×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:
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)))
31.0ms
(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
93.0ms
(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

series871.0ms

Counts
4 → 12
Calls
4 calls:
146.0ms
(* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))
305.0ms
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
158.0ms
(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
262.0ms
(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

simplify90.0ms

Algorithm
egg-herbie
Counts
198 → 198
Iterations

Useful iterations: 2 (71.0ms)

IterNodesCost
05862140
127921433
250021421

prune267.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 2.9b

localize15.0ms

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))))))
0.7b
(/ (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)))))))
5.4b
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
5.4b
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

rewrite32.0ms

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×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 → 106
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)))))))
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))))

series565.0ms

Counts
4 → 12
Calls
4 calls:
33.0ms
(* (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))) (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))))
105.0ms
(/ (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)))))))
212.0ms
(* (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
118 → 118
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
03161464
112291194
250021122

prune347.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.2b

localize19.0ms

Local error

Found 4 expressions with local error:

0.7b
(/ (* (cbrt (cos (* 2.0 x))) (cbrt (cos (* 2.0 x)))) (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))))
0.8b
(/ (cbrt (cos (* 2.0 x))) (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))))
5.4b
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
5.4b
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

rewrite39.0ms

Algorithm
rewrite-expression-head
Rules
63×add-exp-log
43×prod-exp
25×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
21×times-frac
18×add-cbrt-cube
14×pow-to-exp associate-*l* pow-exp
12×cbrt-prod
7×cbrt-unprod associate-/l*
6×unpow-prod-down associate-/r*
4×pow1 add-log-exp
3×cbrt-undiv div-exp
2×frac-2neg associate-*r* clear-num *-commutative div-inv sqr-pow
Counts
4 → 120
Calls
4 calls:
7.0ms
(/ (* (cbrt (cos (* 2.0 x))) (cbrt (cos (* 2.0 x)))) (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))))
3.0ms
(/ (cbrt (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))))
14.0ms
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

series708.0ms

Counts
4 → 12
Calls
4 calls:
143.0ms
(/ (* (cbrt (cos (* 2.0 x))) (cbrt (cos (* 2.0 x)))) (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))))
136.0ms
(/ (cbrt (cos (* 2.0 x))) (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))))
215.0ms
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

simplify57.0ms

Algorithm
egg-herbie
Counts
132 → 132
Iterations

Useful iterations: 2 (36.0ms)

IterNodesCost
03801765
113771576
250011547

prune453.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.2b

regimes351.0ms

Accuracy

19% (2.3b remaining)

Error of 2.4b against oracle of 0.1b and baseline of 3.0b

bsearch1.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04449
14449

end0.0ms

sample2.1s

Algorithm
intervals
Results
895.0ms9056×body80valid
368.0ms827×body1280valid
329.0ms995×body640valid
147.0ms569×body320valid
56.0ms308×body160valid