Details

Time bar (total: 10.8s)

sample108.0ms

Algorithm
intervals
Results
32.0ms295×body80valid
21.0ms36×body1280valid
17.0ms14×body320valid
10.0ms23×body640valid
2.0ms10×body160valid

simplify38.0ms

Counts
1 → 1

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.8b
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
5.5b
(* (* x (pow sin 2.0)) x)
9.5b
(* x (pow sin 2.0))
18.0b
(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

rewrite267.0ms

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:
106.0ms
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
42.0ms
(* (* x (pow sin 2.0)) x)
20.0ms
(* x (pow sin 2.0))
90.0ms
(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

series1.1s

Counts
4 → 12
Calls
4 calls:
399.0ms
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
210.0ms
(* (* x (pow sin 2.0)) x)
154.0ms
(* x (pow sin 2.0))
378.0ms
(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

simplify56.0ms

Counts
127 → 127

prune386.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 15.2b

localize30.0ms

Local error

Found 4 expressions with local error:

0.2b
(cos (* 2.0 x))
0.8b
(/ (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)
18.0b
(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

rewrite679.0ms

Algorithm
rewrite-expression-head
Rules
390×add-exp-log
322×prod-exp
77×pow-to-exp pow-exp
47×add-cbrt-cube
43×div-exp
26×cbrt-unprod
9×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
8×associate-*l*
6×pow1
5×cbrt-undiv
4×associate-*r* add-log-exp
3×unpow-prod-down times-frac associate-/l*
2×*-commutative
1×frac-2neg pow-prod-down clear-num associate-/r* div-inv sqr-pow
Counts
4 → 163
Calls
4 calls:
7.0ms
(cos (* 2.0 x))
257.0ms
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
109.0ms
(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
291.0ms
(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

series1.2s

Counts
4 → 12
Calls
4 calls:
18.0ms
(cos (* 2.0 x))
688.0ms
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
189.0ms
(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
349.0ms
(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

simplify85.0ms

Counts
175 → 175

prune331.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 3.3b

localize32.0ms

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))))))
0.8b
(/ (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)))))))
4.4b
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
4.4b
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

rewrite150.0ms

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:
11.0ms
(* (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))) (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))))
27.0ms
(/ (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)))))))
54.0ms
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
51.0ms
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

series697.0ms

Counts
4 → 12
Calls
4 calls:
41.0ms
(* (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))) (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))))
122.0ms
(/ (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)))))))
265.0ms
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
269.0ms
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

simplify49.0ms

Counts
118 → 118

prune523.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 0.3b

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b
(cos (* 2.0 x))
0.9b
(/ (cos (* 2.0 x)) (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))))
4.4b
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
4.4b
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

rewrite123.0ms

Algorithm
rewrite-expression-head
Rules
58×add-exp-log
42×prod-exp
16×add-sqr-sqrt add-cube-cbrt *-un-lft-identity add-cbrt-cube
14×pow-to-exp associate-*l* pow-exp
9×times-frac
6×unpow-prod-down cbrt-unprod
4×pow1 add-log-exp
3×associate-/r* associate-/l*
2×associate-*r* *-commutative sqr-pow
1×cbrt-undiv frac-2neg div-exp clear-num div-inv
Counts
4 → 94
Calls
4 calls:
11.0ms
(cos (* 2.0 x))
21.0ms
(/ (cos (* 2.0 x)) (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))))
40.0ms
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
47.0ms
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

series675.0ms

Counts
4 → 12
Calls
4 calls:
18.0ms
(cos (* 2.0 x))
87.0ms
(/ (cos (* 2.0 x)) (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))))
284.0ms
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
285.0ms
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

simplify157.0ms

Counts
106 → 106

prune414.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.2b

regimes493.0ms

Accuracy

-6.4% (2.7b remaining)

Error of 2.9b against oracle of 0.1b and baseline of 2.7b

bsearch0.0ms

simplify114.0ms

end0.0ms

sample3.0s

Algorithm
intervals
Results
1.0s9096×body80valid
756.0ms934×body640valid
464.0ms818×body1280valid
231.0ms614×body320valid
56.0ms309×body160valid