Details

Time bar (total: 19.1s)

sample82.0ms

Algorithm
intervals
Results
23.0ms312×body80valid
16.0ms11×body160valid
9.0ms23×body1280valid
9.0ms32×body640valid
2.0ms11×body320valid

simplify2.1s

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: 26.8b

localize32.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
4.9b
(* (* x (pow sin 2.0)) x)
8.1b
(* x (pow sin 2.0))
15.9b
(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

rewrite214.0ms

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:
70.0ms
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
29.0ms
(* (* x (pow sin 2.0)) x)
23.0ms
(* x (pow sin 2.0))
87.0ms
(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

series1.2s

Counts
4 → 12
Calls
4 calls:
381.0ms
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
165.0ms
(* (* x (pow sin 2.0)) x)
193.0ms
(* x (pow sin 2.0))
416.0ms
(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

simplify1.2s

Counts
127 → 127
Iterations

Useful iterations: 2 (347.0ms)

IterNodesCost
01711959
14071811
214241531
done50011531

prune397.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 15.2b

localize30.0ms

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)))
4.9b
(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
15.9b
(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

rewrite666.0ms

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:
32.0ms
(* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))
231.0ms
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
84.0ms
(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
306.0ms
(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

series1.1s

Counts
4 → 12
Calls
4 calls:
171.0ms
(* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))
443.0ms
(/ (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)
342.0ms
(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

simplify1.2s

Counts
198 → 198
Iterations

Useful iterations: done (1.2s)

IterNodesCost
02034993
15272927
220882483
done50002479

prune311.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 11.6b

localize24.0ms

Local error

Found 3 expressions with local error:

0.2b
(* (* 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))))
15.9b
(* (pow cos 2.0) (* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x)))

rewrite288.0ms

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:
55.0ms
(* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x))
97.0ms
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x))))
104.0ms
(* (pow cos 2.0) (* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x)))

series1.1s

Counts
3 → 9
Calls
3 calls:
199.0ms
(* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x))
545.0ms
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x))))
399.0ms
(* (pow cos 2.0) (* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x)))

simplify970.0ms

Counts
187 → 187
Iterations

Useful iterations: 2 (291.0ms)

IterNodesCost
01825118
14613028
218472552
done50002552

prune306.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 10.4b

localize18.0ms

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)))
4.8b
(* (* (pow cos 2.0) (* x (pow sin (/ 2.0 2)))) (* (pow sin (/ 2.0 2)) x))
12.6b
(* (pow cos 2.0) (* x (pow sin (/ 2.0 2))))

rewrite286.0ms

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:
88.0ms
(/ (cos (* 2.0 x)) (* (* (pow cos 2.0) (* x (pow sin (/ 2.0 2)))) (* (pow sin (/ 2.0 2)) x)))
140.0ms
(* (* (pow cos 2.0) (* x (pow sin (/ 2.0 2)))) (* (pow sin (/ 2.0 2)) x))
33.0ms
(* (pow cos 2.0) (* x (pow sin (/ 2.0 2))))

series1.2s

Counts
3 → 9
Calls
3 calls:
422.0ms
(/ (cos (* 2.0 x)) (* (* (pow cos 2.0) (* x (pow sin (/ 2.0 2)))) (* (pow sin (/ 2.0 2)) x)))
402.0ms
(* (* (pow cos 2.0) (* x (pow sin (/ 2.0 2)))) (* (pow sin (/ 2.0 2)) x))
339.0ms
(* (pow cos 2.0) (* x (pow sin (/ 2.0 2))))

simplify1.2s

Counts
185 → 185
Iterations

Useful iterations: 2 (363.0ms)

IterNodesCost
01854968
14983206
219132672
done50012672

prune234.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 3.8b

regimes449.0ms

Accuracy

0% (1.7b remaining)

Error of 6.8b against oracle of 5.0b and baseline of 6.8b

bsearch0.0ms

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01632
12032
done2032

end0.0ms

sample4.4s

Algorithm
intervals
Results
1.5s9126×body80valid
1.3s811×body1280valid
533.0ms946×body640valid
313.0ms570×body320valid
82.0ms326×body160valid