Details

Time bar (total: 24.4s)

sample113.0ms

Algorithm
intervals
Results
46.0ms285×body80valid
17.0ms29×body1280valid
11.0ms24×body640valid
7.0ms22×body320valid
3.0ms13×body160valid

simplify1.1s

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01216
12616
26716
324216
4125516
done500116

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.9b

localize36.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
4.7b
(* (* x (pow sin 2.0)) x)
9.5b
(* x (pow sin 2.0))
17.6b
(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

rewrite220.0ms

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:
85.0ms
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
35.0ms
(* (* x (pow sin 2.0)) x)
18.0ms
(* x (pow sin 2.0))
74.0ms
(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

series1.2s

Counts
4 → 12
Calls
4 calls:
431.0ms
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
219.0ms
(* (* x (pow sin 2.0)) x)
197.0ms
(* x (pow sin 2.0))
328.0ms
(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

simplify1.7s

Counts
135 → 135
Iterations

Useful iterations: 2 (444.0ms)

IterNodesCost
01792045
14571907
224141649
done50011649

prune552.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 14.4b

localize39.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))
0.3b
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
4.7b
(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
17.6b
(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

rewrite774.0ms

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:
30.0ms
(* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))
290.0ms
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
111.0ms
(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
327.0ms
(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

series1.6s

Counts
4 → 12
Calls
4 calls:
192.0ms
(* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))
786.0ms
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
226.0ms
(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
401.0ms
(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

simplify3.5s

Counts
206 → 206
Iterations

Useful iterations: 2 (740.0ms)

IterNodesCost
02115143
15973013
238522569
done50012569

prune588.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 11.4b

localize41.0ms

Local error

Found 3 expressions with local error:

0.3b
(* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x))
0.3b
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x))))
17.6b
(* (pow cos 2.0) (* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x)))

rewrite352.0ms

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:
41.0ms
(* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x))
144.0ms
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x))))
154.0ms
(* (pow cos 2.0) (* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x)))

series980.0ms

Counts
3 → 9
Calls
3 calls:
200.0ms
(* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x))
451.0ms
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x))))
328.0ms
(* (pow cos 2.0) (* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x)))

simplify1.9s

Counts
193 → 193
Iterations

Useful iterations: 2 (477.0ms)

IterNodesCost
01885240
15463102
229182616
done50012616

prune421.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 10.4b

localize38.0ms

Local error

Found 3 expressions with local error:

0.3b
(/ (cos (* 2.0 x)) (* (* (pow cos 2.0) (* x (pow sin (/ 2.0 2)))) (* (pow sin (/ 2.0 2)) x)))
5.5b
(* (* (pow cos 2.0) (* x (pow sin (/ 2.0 2)))) (* (pow sin (/ 2.0 2)) x))
12.1b
(* (pow cos 2.0) (* x (pow sin (/ 2.0 2))))

rewrite284.0ms

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:
105.0ms
(/ (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))
42.0ms
(* (pow cos 2.0) (* x (pow sin (/ 2.0 2))))

series1.3s

Counts
3 → 9
Calls
3 calls:
500.0ms
(/ (cos (* 2.0 x)) (* (* (pow cos 2.0) (* x (pow sin (/ 2.0 2)))) (* (pow sin (/ 2.0 2)) x)))
460.0ms
(* (* (pow cos 2.0) (* x (pow sin (/ 2.0 2)))) (* (pow sin (/ 2.0 2)) x))
304.0ms
(* (pow cos 2.0) (* x (pow sin (/ 2.0 2))))

simplify2.6s

Counts
191 → 191
Iterations

Useful iterations: 2 (560.0ms)

IterNodesCost
01915082
15863288
231402764
done50002764

prune452.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 4.2b

regimes917.0ms

Accuracy

0% (1.9b remaining)

Error of 6.6b against oracle of 4.7b and baseline of 6.6b

bsearch0.0ms

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01632
12032
22132
done2132

end0.0ms

sample3.9s

Algorithm
intervals
Results
1.7s9024×body80valid
597.0ms802×body1280valid
583.0ms963×body640valid
247.0ms604×body320valid
67.0ms305×body160valid