Details

Time bar (total: 11.7s)

sample53.0ms

Algorithm
intervals
Results
22.0ms308×body80valid
7.0ms28×body640valid
7.0ms19×body1280valid
3.0ms15×body320valid
1.0ms7×body160valid

simplify465.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01216
12616
26616
322716
4101316
done500116

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.7b

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)))
5.3b
(* (* x (pow sin 2.0)) x)
9.5b
(* x (pow sin 2.0))
16.1b
(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

rewrite74.0ms

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:
25.0ms
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
9.0ms
(* (* x (pow sin 2.0)) x)
5.0ms
(* x (pow sin 2.0))
29.0ms
(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

series846.0ms

Counts
4 → 12
Calls
4 calls:
302.0ms
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
143.0ms
(* (* x (pow sin 2.0)) x)
138.0ms
(* x (pow sin 2.0))
262.0ms
(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

simplify1.0s

Counts
135 → 135
Iterations

Useful iterations: 2 (167.0ms)

IterNodesCost
01792045
14511897
219311617
done50001617

prune308.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 14.7b

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b
(cos (* 2.0 x))
0.7b
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
5.3b
(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
16.1b
(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

rewrite245.0ms

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×expm1-log1p-u associate-*r* log1p-expm1-u 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 → 171
Calls
4 calls:
2.0ms
(cos (* 2.0 x))
105.0ms
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
32.0ms
(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
94.0ms
(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

series717.0ms

Counts
4 → 12
Calls
4 calls:
18.0ms
(cos (* 2.0 x))
296.0ms
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
149.0ms
(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
255.0ms
(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

simplify992.0ms

Counts
183 → 183
Iterations

Useful iterations: 2 (234.0ms)

IterNodesCost
01954656
15682788
222962382
done50002382

prune290.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 11.9b

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b
(cos (* 2.0 x))
0.3b
(* (* x (pow sin (/ 2.0 2))) (* x (pow sin (/ 2.0 2))))
0.7b
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin (/ 2.0 2))) (* x (pow sin (/ 2.0 2))))))
16.1b
(* (pow cos 2.0) (* (* x (pow sin (/ 2.0 2))) (* x (pow sin (/ 2.0 2)))))

rewrite119.0ms

Algorithm
rewrite-expression-head
Rules
467×add-exp-log
382×prod-exp
90×pow-to-exp pow-exp
59×add-cbrt-cube
52×div-exp
34×cbrt-unprod
11×pow1
10×add-sqr-sqrt
8×add-cube-cbrt *-un-lft-identity associate-*l*
6×cbrt-undiv
4×expm1-log1p-u unpow-prod-down log1p-expm1-u add-log-exp
3×times-frac associate-/l* unswap-sqr
2×associate-*r* *-commutative sqr-pow
1×pow2 frac-2neg pow-plus swap-sqr pow-prod-down clear-num associate-/r* pow-sqr pow-prod-up div-inv
Counts
4 → 201
Calls
4 calls:
2.0ms
(cos (* 2.0 x))
14.0ms
(* (* x (pow sin (/ 2.0 2))) (* x (pow sin (/ 2.0 2))))
41.0ms
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin (/ 2.0 2))) (* x (pow sin (/ 2.0 2))))))
44.0ms
(* (pow cos 2.0) (* (* x (pow sin (/ 2.0 2))) (* x (pow sin (/ 2.0 2)))))

series719.0ms

Counts
4 → 12
Calls
4 calls:
18.0ms
(cos (* 2.0 x))
146.0ms
(* (* x (pow sin (/ 2.0 2))) (* x (pow sin (/ 2.0 2))))
296.0ms
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin (/ 2.0 2))) (* x (pow sin (/ 2.0 2))))))
257.0ms
(* (pow cos 2.0) (* (* x (pow sin (/ 2.0 2))) (* x (pow sin (/ 2.0 2)))))

simplify872.0ms

Counts
213 → 213
Iterations

Useful iterations: 2 (227.0ms)

IterNodesCost
01955414
15273277
220252775
done50002775

prune304.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 2.8b

localize15.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2)))) (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2)))))
0.7b
(/ (cos (* 2.0 x)) (* (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2)))) (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))))
4.6b
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
4.6b
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

rewrite178.0ms

Algorithm
rewrite-expression-head
Rules
1631×add-exp-log
1472×prod-exp
378×pow-to-exp pow-exp
170×div-exp
97×add-cbrt-cube
60×cbrt-unprod
15×associate-*l*
11×pow1
10×cbrt-undiv add-sqr-sqrt add-cube-cbrt *-un-lft-identity
6×unpow-prod-down
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×times-frac associate-*r* *-commutative associate-/l*
2×sqr-pow
1×pow2 frac-2neg pow-plus swap-sqr pow-prod-down clear-num associate-/r* pow-sqr pow-prod-up div-inv
Counts
4 → 459
Calls
4 calls:
48.0ms
(* (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2)))) (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2)))))
55.0ms
(/ (cos (* 2.0 x)) (* (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2)))) (* (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))))

series998.0ms

Counts
4 → 12
Calls
4 calls:
271.0ms
(* (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2)))) (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2)))))
298.0ms
(/ (cos (* 2.0 x)) (* (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2)))) (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))))
211.0ms
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
218.0ms
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

simplify1.4s

Counts
471 → 471
Iterations

Useful iterations: 2 (456.0ms)

IterNodesCost
024816070
17417730
224616814
done50006814

prune292.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 2.4b

regimes268.0ms

Accuracy

0% (0.3b remaining)

Error of 2.7b against oracle of 2.4b and baseline of 2.7b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01432
11732
done1732

end0.0ms

sample1.5s

Algorithm
intervals
Results
559.0ms8983×body80valid
284.0ms795×body1280valid
233.0ms957×body640valid
107.0ms608×body320valid
37.0ms304×body160valid