Details

Time bar (total: 18.1s)

sample106.0ms

Algorithm
intervals
Results
39.0ms301×body80valid
19.0ms25×body1280valid
13.0ms23×body640valid
6.0ms13×body320valid
2.0ms9×body160valid

simplify2.0s

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01216
12616
26716
324116
4109716
done500016

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 24.8b

localize26.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
5.0b
(* (* x (pow sin 2.0)) x)
8.5b
(* x (pow sin 2.0))
15.4b
(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

rewrite279.0ms

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:
103.0ms
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
40.0ms
(* (* x (pow sin 2.0)) x)
20.0ms
(* x (pow sin 2.0))
107.0ms
(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

series1.3s

Counts
4 → 12
Calls
4 calls:
402.0ms
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
248.0ms
(* (* x (pow sin 2.0)) x)
222.0ms
(* x (pow sin 2.0))
413.0ms
(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

simplify1.0s

Counts
127 → 127
Iterations

Useful iterations: 2 (319.0ms)

IterNodesCost
01711959
14071811
214241531
done50011531

prune286.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 13.5b

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* 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)))
5.0b
(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
15.4b
(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

rewrite727.0ms

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:
45.0ms
(* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))
294.0ms
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
115.0ms
(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
252.0ms
(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

series1.1s

Counts
4 → 12
Calls
4 calls:
203.0ms
(* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))
333.0ms
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
216.0ms
(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
348.0ms
(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

simplify1.4s

Counts
198 → 198
Iterations

Useful iterations: done (1.4s)

IterNodesCost
02034993
15272927
220882483
done50002479

prune656.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 10.9b

localize20.0ms

Local error

Found 3 expressions with local error:

0.3b
(* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x))
0.4b
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x))))
15.4b
(* (pow cos 2.0) (* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x)))

rewrite361.0ms

Algorithm
rewrite-expression-head
Rules
466×add-exp-log
382×prod-exp
90×pow-to-exp pow-exp
58×add-cbrt-cube
52×div-exp
34×cbrt-unprod
8×associate-*l*
7×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
6×cbrt-undiv
5×pow1
3×unpow-prod-down times-frac associate-/l* add-log-exp
2×associate-*r* *-commutative
1×frac-2neg pow-prod-down clear-num associate-/r* div-inv sqr-pow
Counts
3 → 178
Calls
3 calls:
54.0ms
(* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x))
152.0ms
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x))))
134.0ms
(* (pow cos 2.0) (* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x)))

series947.0ms

Counts
3 → 9
Calls
3 calls:
212.0ms
(* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x))
390.0ms
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x))))
345.0ms
(* (pow cos 2.0) (* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x)))

simplify1.1s

Counts
187 → 187
Iterations

Useful iterations: 2 (381.0ms)

IterNodesCost
01825118
14613028
218472552
done50002552

prune275.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 9.5b

localize28.0ms

Local error

Found 3 expressions with local error:

0.4b
(/ (cos (* 2.0 x)) (* (* (pow cos 2.0) (* x (pow sin (/ 2.0 2)))) (* (pow sin (/ 2.0 2)) x)))
4.9b
(* (* (pow cos 2.0) (* x (pow sin (/ 2.0 2)))) (* (pow sin (/ 2.0 2)) x))
11.9b
(* (pow cos 2.0) (* x (pow sin (/ 2.0 2))))

rewrite264.0ms

Algorithm
rewrite-expression-head
Rules
455×add-exp-log
371×prod-exp
89×pow-to-exp pow-exp
58×add-cbrt-cube
53×div-exp
33×cbrt-unprod
8×associate-*l*
7×cbrt-undiv add-sqr-sqrt add-cube-cbrt *-un-lft-identity
5×pow1
3×unpow-prod-down times-frac associate-/l* add-log-exp
2×associate-*r* *-commutative
1×frac-2neg pow-prod-down clear-num associate-/r* div-inv sqr-pow
Counts
3 → 176
Calls
3 calls:
112.0ms
(/ (cos (* 2.0 x)) (* (* (pow cos 2.0) (* x (pow sin (/ 2.0 2)))) (* (pow sin (/ 2.0 2)) x)))
97.0ms
(* (* (pow cos 2.0) (* x (pow sin (/ 2.0 2)))) (* (pow sin (/ 2.0 2)) x))
42.0ms
(* (pow cos 2.0) (* x (pow sin (/ 2.0 2))))

series1.0s

Counts
3 → 9
Calls
3 calls:
404.0ms
(/ (cos (* 2.0 x)) (* (* (pow cos 2.0) (* x (pow sin (/ 2.0 2)))) (* (pow sin (/ 2.0 2)) x)))
353.0ms
(* (* (pow cos 2.0) (* x (pow sin (/ 2.0 2)))) (* (pow sin (/ 2.0 2)) x))
282.0ms
(* (pow cos 2.0) (* x (pow sin (/ 2.0 2))))

simplify1.1s

Counts
185 → 185
Iterations

Useful iterations: 2 (359.0ms)

IterNodesCost
01854968
14983206
219132672
done50012672

prune241.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 3.7b

regimes348.0ms

Accuracy

0% (1.8b remaining)

Error of 6.7b against oracle of 4.9b and baseline of 6.7b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01632
12032
done2032

end0.0ms

sample3.4s

Algorithm
intervals
Results
1.4s9132×body80valid
585.0ms804×body1280valid
469.0ms977×body640valid
234.0ms551×body320valid
54.0ms282×body160valid