Details

Time bar (total: 20.0s)

sample127.0ms

Algorithm
intervals
Results
57.0ms293×body80valid
17.0ms21×body1280valid
11.0ms22×body640valid
6.0ms17×body320valid
3.0ms12×body160valid

simplify2.2s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01216
12616
26716
324116
4109716
done500016

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.9b

localize21.0ms

Local error

Found 4 expressions with local error:

0.8b
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
5.7b
(* (* x (pow sin 2.0)) x)
8.2b
(* x (pow sin 2.0))
15.1b
(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

rewrite212.0ms

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:
72.0ms
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
33.0ms
(* (* x (pow sin 2.0)) x)
18.0ms
(* x (pow sin 2.0))
83.0ms
(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

series1.1s

Counts
4 → 12
Calls
4 calls:
446.0ms
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
180.0ms
(* (* x (pow sin 2.0)) x)
192.0ms
(* x (pow sin 2.0))
299.0ms
(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

simplify1.0s

Counts
135 → 135
Iterations

Useful iterations: 2 (293.0ms)

IterNodesCost
01792045
14211897
214451617
done50001617

prune488.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 13.4b

localize33.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))
0.8b
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
5.7b
(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
15.1b
(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

rewrite759.0ms

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×expm1-log1p-u log1p-expm1-u 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 → 194
Calls
4 calls:
32.0ms
(* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))
279.0ms
(/ (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)
317.0ms
(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

series1.2s

Counts
4 → 12
Calls
4 calls:
213.0ms
(* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))
408.0ms
(/ (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)
386.0ms
(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

simplify1.5s

Counts
206 → 206
Iterations

Useful iterations: done (1.4s)

IterNodesCost
02115143
15453013
221092569
done50002565

prune504.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 9.5b

localize18.0ms

Local error

Found 3 expressions with local error:

0.3b
(* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x))
0.8b
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x))))
15.1b
(* (pow cos 2.0) (* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x)))

rewrite388.0ms

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×expm1-log1p-u unpow-prod-down times-frac log1p-expm1-u 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 → 184
Calls
3 calls:
80.0ms
(* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x))
162.0ms
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x))))
124.0ms
(* (pow cos 2.0) (* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x)))

series1.1s

Counts
3 → 9
Calls
3 calls:
222.0ms
(* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x))
471.0ms
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x))))
393.0ms
(* (pow cos 2.0) (* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x)))

simplify1.4s

Counts
193 → 193
Iterations

Useful iterations: 2 (432.0ms)

IterNodesCost
01885240
14803102
218642616
done50002616

prune407.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 7.2b

localize41.0ms

Local error

Found 3 expressions with local error:

0.8b
(/ (cos (* 2.0 x)) (* (* (pow cos 2.0) (* x (pow sin (/ 2.0 2)))) (* (pow sin (/ 2.0 2)) x)))
3.5b
(* (* (pow cos 2.0) (* x (pow sin (/ 2.0 2)))) (* (pow sin (/ 2.0 2)) x))
9.6b
(* (pow cos 2.0) (* x (pow sin (/ 2.0 2))))

rewrite271.0ms

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×expm1-log1p-u unpow-prod-down times-frac log1p-expm1-u 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 → 182
Calls
3 calls:
93.0ms
(/ (cos (* 2.0 x)) (* (* (pow cos 2.0) (* x (pow sin (/ 2.0 2)))) (* (pow sin (/ 2.0 2)) x)))
123.0ms
(* (* (pow cos 2.0) (* x (pow sin (/ 2.0 2)))) (* (pow sin (/ 2.0 2)) x))
29.0ms
(* (pow cos 2.0) (* x (pow sin (/ 2.0 2))))

series1.3s

Counts
3 → 9
Calls
3 calls:
487.0ms
(/ (cos (* 2.0 x)) (* (* (pow cos 2.0) (* x (pow sin (/ 2.0 2)))) (* (pow sin (/ 2.0 2)) x)))
479.0ms
(* (* (pow cos 2.0) (* x (pow sin (/ 2.0 2)))) (* (pow sin (/ 2.0 2)) x))
313.0ms
(* (pow cos 2.0) (* x (pow sin (/ 2.0 2))))

simplify1.4s

Counts
191 → 191
Iterations

Useful iterations: 2 (477.0ms)

IterNodesCost
01915082
15103288
219102764
done50002764

prune345.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.0b

regimes464.0ms

Accuracy

0% (2.1b remaining)

Error of 6.8b against oracle of 4.8b and baseline of 6.8b

bsearch0.0ms

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01632
12032
done2032

end0.0ms

sample3.8s

Algorithm
intervals
Results
1.3s9128×body80valid
1.0s950×body640valid
518.0ms788×body1280valid
268.0ms611×body320valid
91.0ms293×body160valid