Details

Time bar (total: 8.6s)

sample72.0ms

Algorithm
intervals
Results
21.0ms289×body80valid
12.0ms28×body1280valid
9.0ms31×body640valid
8.0ms18×body320valid
2.0ms10×body160valid

simplify38.0ms

Counts
1 → 1

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.8b

localize17.0ms

Local error

Found 4 expressions with local error:

0.8b
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
3.5b
(* (* x (pow sin 2.0)) x)
9.6b
(* x (pow sin 2.0))
19.2b
(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

rewrite187.0ms

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:
65.0ms
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
25.0ms
(* (* x (pow sin 2.0)) x)
12.0ms
(* x (pow sin 2.0))
80.0ms
(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

series917.0ms

Counts
4 → 12
Calls
4 calls:
321.0ms
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
159.0ms
(* (* x (pow sin 2.0)) x)
147.0ms
(* x (pow sin 2.0))
291.0ms
(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

simplify54.0ms

Counts
127 → 127

prune274.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 13.8b

localize18.0ms

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)))
3.5b
(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
19.2b
(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

rewrite499.0ms

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:
8.0ms
(cos (* 2.0 x))
196.0ms
(/ (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)
208.0ms
(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

series778.0ms

Counts
4 → 12
Calls
4 calls:
13.0ms
(cos (* 2.0 x))
315.0ms
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
162.0ms
(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
288.0ms
(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

simplify77.0ms

Counts
175 → 175

prune237.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 2.6b

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (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)))))))
4.9b
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
4.9b
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

rewrite90.0ms

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:
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)))))))
32.0ms
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
27.0ms
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

series671.0ms

Counts
4 → 12
Calls
4 calls:
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))))))
118.0ms
(/ (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)))))))
236.0ms
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
281.0ms
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

simplify46.0ms

Counts
118 → 118

prune370.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.2b

localize26.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ 1 (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))))))
4.9b
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
4.9b
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

rewrite82.0ms

Algorithm
rewrite-expression-head
Rules
62×add-exp-log
42×prod-exp
24×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
18×times-frac add-cbrt-cube
14×pow-to-exp associate-*l* pow-exp
6×unpow-prod-down associate-/r* cbrt-unprod associate-/l*
5×pow1
4×add-log-exp
3×div-exp
2×cbrt-undiv frac-2neg associate-*r* clear-num *-commutative div-inv sqr-pow
1×rec-exp pow-flip 1-exp inv-pow
Counts
4 → 118
Calls
4 calls:
5.0ms
(/ 1 (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))))))
30.0ms
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
28.0ms
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

series586.0ms

Counts
4 → 12
Calls
4 calls:
41.0ms
(/ 1 (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))))
74.0ms
(/ (cos (* 2.0 x)) (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))))
234.0ms
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
237.0ms
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

simplify42.0ms

Counts
130 → 130

prune367.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.2b

regimes395.0ms

Accuracy

0% (2.7b remaining)

Error of 2.8b against oracle of 0.1b and baseline of 2.8b

bsearch0.0ms

simplify1.0ms

end0.0ms

sample2.7s

Algorithm
intervals
Results
1.2s8961×body80valid
382.0ms838×body1280valid
330.0ms925×body640valid
233.0ms602×body320valid
119.0ms319×body160valid