Details

Time bar (total: 17.1s)

sample68.0ms

Algorithm
intervals
Results
22.0ms291×body80valid
12.0ms28×body1280valid
8.0ms28×body640valid
3.0ms14×body320valid
3.0ms19×body160valid

simplify495.0ms

Counts
1 → 1

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.7b

localize15.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
4.2b
(* (* x (pow sin 2.0)) x)
10.2b
(* x (pow sin 2.0))
16.5b
(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

rewrite243.0ms

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:
81.0ms
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
32.0ms
(* (* x (pow sin 2.0)) x)
21.0ms
(* x (pow sin 2.0))
104.0ms
(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

series1.1s

Counts
4 → 12
Calls
4 calls:
359.0ms
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
204.0ms
(* (* x (pow sin 2.0)) x)
199.0ms
(* x (pow sin 2.0))
315.0ms
(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

simplify978.0ms

Counts
127 → 127

prune320.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 15.5b

localize21.0ms

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)))
4.2b
(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
16.5b
(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

rewrite936.0ms

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:
35.0ms
(* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))
234.0ms
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
105.0ms
(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
548.0ms
(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

series1.0s

Counts
4 → 12
Calls
4 calls:
146.0ms
(* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))
395.0ms
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
192.0ms
(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
302.0ms
(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

simplify1.2s

Counts
198 → 198

prune408.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.3b

localize31.0ms

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)))))))
4.7b
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
4.7b
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

rewrite133.0ms

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:
9.0ms
(* (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))) (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))))
29.0ms
(/ (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)))))))
51.0ms
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
40.0ms
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

series822.0ms

Counts
4 → 12
Calls
4 calls:
59.0ms
(* (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))) (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))))
144.0ms
(/ (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)))))))
313.0ms
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
305.0ms
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

simplify725.0ms

Counts
118 → 118

prune496.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize33.0ms

Local error

Found 3 expressions with local error:

0.3b
(pow (fabs (* (pow (* (pow cos 1.0) (pow sin 1.0)) 1.0) x)) 2)
0.4b
(/ (cos (* 2.0 x)) (pow (fabs (* (pow (* (pow cos 1.0) (pow sin 1.0)) 1.0) x)) 2))
3.6b
(* (pow (* (pow cos 1.0) (pow sin 1.0)) 1.0) x)

rewrite75.0ms

Algorithm
rewrite-expression-head
Rules
35×add-exp-log
27×add-sqr-sqrt
24×add-cube-cbrt *-un-lft-identity times-frac
21×prod-exp
18×pow-exp
16×unpow-prod-down
9×pow-to-exp
8×associate-/r*
7×add-cbrt-cube sqr-pow
5×associate-*l* unpow2
4×pow1
3×pow-unpow div-exp associate-*r* associate-/l* add-log-exp
2×unswap-sqr
1×cbrt-undiv pow-pow frac-2neg clear-num *-commutative cbrt-unprod div-inv
Counts
3 → 98
Calls
3 calls:
4.0ms
(pow (fabs (* (pow (* (pow cos 1.0) (pow sin 1.0)) 1.0) x)) 2)
25.0ms
(/ (cos (* 2.0 x)) (pow (fabs (* (pow (* (pow cos 1.0) (pow sin 1.0)) 1.0) x)) 2))
41.0ms
(* (pow (* (pow cos 1.0) (pow sin 1.0)) 1.0) x)

series719.0ms

Counts
3 → 9
Calls
3 calls:
46.0ms
(pow (fabs (* (pow (* (pow cos 1.0) (pow sin 1.0)) 1.0) x)) 2)
187.0ms
(/ (cos (* 2.0 x)) (pow (fabs (* (pow (* (pow cos 1.0) (pow sin 1.0)) 1.0) x)) 2))
486.0ms
(* (pow (* (pow cos 1.0) (pow sin 1.0)) 1.0) x)

simplify493.0ms

Counts
107 → 107

prune493.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

regimes432.0ms

Accuracy

0% (2.5b remaining)

Error of 2.7b against oracle of 0.1b and baseline of 2.7b

bsearch0.0ms

simplify2.2s

end0.0ms

sample3.7s

Algorithm
intervals
Results
1.2s9004×body80valid
667.0ms601×body320valid
637.0ms848×body1280valid
420.0ms935×body640valid
113.0ms309×body160valid