Details

Time bar (total: 29.4s)

sample140.0ms

Algorithm
intervals
Results
59.0ms288×body80valid
21.0ms28×body1280valid
20.0ms35×body640valid
7.0ms20×body320valid
3.0ms10×body160valid

simplify963.0ms

Counts
1 → 1
Iterations
IterNodes
done5000
41263
3241
267
126
012

prune13.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 24.2b

localize23.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ (cos (* 2.0 x)) (pow sin 2.0))
6.0b
(/ (/ (/ (cos (* 2.0 x)) (pow sin 2.0)) (* (pow cos 2.0) x)) x)
8.3b
(* (pow cos 2.0) x)
15.6b
(/ (/ (cos (* 2.0 x)) (pow sin 2.0)) (* (pow cos 2.0) x))

rewrite95.0ms

Algorithm
rewrite-expression-head
Rules
359×times-frac
146×add-sqr-sqrt
141×*-un-lft-identity add-cube-cbrt
128×add-exp-log
76×div-exp
70×unpow-prod-down
57×associate-/l*
38×add-cbrt-cube
27×prod-exp
24×sqr-pow
18×pow-to-exp cbrt-undiv pow-exp
13×div-inv
11×associate-/r*
7×associate-*l*
5×cbrt-unprod
4×expm1-log1p-u pow1 log1p-expm1-u add-log-exp
3×clear-num frac-2neg associate-*r* unswap-sqr
2×associate-/l/
1×*-commutative
Counts
4 → 312
Calls
4 calls:
12.0ms
(/ (cos (* 2.0 x)) (pow sin 2.0))
37.0ms
(/ (/ (/ (cos (* 2.0 x)) (pow sin 2.0)) (* (pow cos 2.0) x)) x)
9.0ms
(* (pow cos 2.0) x)
22.0ms
(/ (/ (cos (* 2.0 x)) (pow sin 2.0)) (* (pow cos 2.0) x))

series1.7s

Counts
4 → 12
Calls
4 calls:
638.0ms
(/ (cos (* 2.0 x)) (pow sin 2.0))
449.0ms
(/ (/ (/ (cos (* 2.0 x)) (pow sin 2.0)) (* (pow cos 2.0) x)) x)
269.0ms
(* (pow cos 2.0) x)
331.0ms
(/ (/ (cos (* 2.0 x)) (pow sin 2.0)) (* (pow cos 2.0) x))

simplify627.0ms

Counts
324 → 324
Iterations
IterNodes
done5001
11224
0468

prune2.1s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 11.7b

localize36.0ms

Local error

Found 4 expressions with local error:

0.2b
(cos (* 2.0 x))
4.1b
(/ (/ 1 (pow sin (/ 2.0 2))) (* (/ (pow cos 2.0) (cos (* 2.0 x))) (* x (pow sin (/ 2.0 2)))))
6.0b
(/ (/ (/ 1 (pow sin (/ 2.0 2))) (* (/ (pow cos 2.0) (cos (* 2.0 x))) (* x (pow sin (/ 2.0 2))))) x)
13.1b
(* (/ (pow cos 2.0) (cos (* 2.0 x))) (* x (pow sin (/ 2.0 2))))

rewrite324.0ms

Algorithm
rewrite-expression-head
Rules
1544×add-exp-log
967×div-exp
588×prod-exp
362×times-frac
270×pow-to-exp pow-exp
137×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
110×add-cbrt-cube
102×rec-exp 1-exp
63×unpow-prod-down
55×associate-/l*
51×cbrt-undiv
30×cbrt-unprod
25×associate-*l*
21×sqr-pow
13×div-inv
6×pow1 associate-*l/
5×associate-/r/
4×expm1-log1p-u associate-/r* log1p-expm1-u add-log-exp
2×clear-num frac-2neg associate-/l/
1×associate-*r* pow-prod-down *-commutative
Counts
4 → 630
Calls
4 calls:
11.0ms
(cos (* 2.0 x))
74.0ms
(/ (/ 1 (pow sin (/ 2.0 2))) (* (/ (pow cos 2.0) (cos (* 2.0 x))) (* x (pow sin (/ 2.0 2)))))
95.0ms
(/ (/ (/ 1 (pow sin (/ 2.0 2))) (* (/ (pow cos 2.0) (cos (* 2.0 x))) (* x (pow sin (/ 2.0 2))))) x)
77.0ms
(* (/ (pow cos 2.0) (cos (* 2.0 x))) (* x (pow sin (/ 2.0 2))))

series1.6s

Counts
4 → 12
Calls
4 calls:
15.0ms
(cos (* 2.0 x))
501.0ms
(/ (/ 1 (pow sin (/ 2.0 2))) (* (/ (pow cos 2.0) (cos (* 2.0 x))) (* x (pow sin (/ 2.0 2)))))
568.0ms
(/ (/ (/ 1 (pow sin (/ 2.0 2))) (* (/ (pow cos 2.0) (cos (* 2.0 x))) (* x (pow sin (/ 2.0 2))))) x)
471.0ms
(* (/ (pow cos 2.0) (cos (* 2.0 x))) (* x (pow sin (/ 2.0 2))))

simplify1.2s

Counts
642 → 642
Iterations
IterNodes
done5000
12070
0668

prune1.9s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 4.1b

localize42.0ms

Local error

Found 4 expressions with local error:

1.3b
(* (/ (pow cos (/ 2.0 2)) 1) (/ (* (pow cos (/ 2.0 2)) (* (pow sin (/ 2.0 2)) x)) (cos (* x 2.0))))
4.1b
(/ (/ 1 (pow sin (/ 2.0 2))) (* (/ (pow cos (/ 2.0 2)) 1) (/ (* (pow cos (/ 2.0 2)) (* (pow sin (/ 2.0 2)) x)) (cos (* x 2.0)))))
5.0b
(* (pow cos (/ 2.0 2)) (* (pow sin (/ 2.0 2)) x))
6.0b
(/ (/ (/ 1 (pow sin (/ 2.0 2))) (* (/ (pow cos (/ 2.0 2)) 1) (/ (* (pow cos (/ 2.0 2)) (* (pow sin (/ 2.0 2)) x)) (cos (* x 2.0))))) x)

rewrite845.0ms

Algorithm
rewrite-expression-head
Rules
11401×add-exp-log
7834×div-exp
5166×prod-exp
2218×pow-to-exp pow-exp
1476×1-exp
594×rec-exp
377×times-frac
247×add-cbrt-cube
158×add-sqr-sqrt
146×*-un-lft-identity
143×add-cube-cbrt
123×cbrt-undiv
73×cbrt-unprod
68×unpow-prod-down
57×associate-/l*
32×associate-*l*
24×sqr-pow
15×associate-/r/
14×div-inv
8×associate-*r*
7×unswap-sqr
6×frac-times pow1 associate-*l/ associate-*r/
4×expm1-log1p-u associate-/r* log1p-expm1-u add-log-exp
2×clear-num frac-2neg *-commutative associate-/l/
1×pow-prod-down
Counts
4 → 2420
Calls
4 calls:
64.0ms
(* (/ (pow cos (/ 2.0 2)) 1) (/ (* (pow cos (/ 2.0 2)) (* (pow sin (/ 2.0 2)) x)) (cos (* x 2.0))))
82.0ms
(/ (/ 1 (pow sin (/ 2.0 2))) (* (/ (pow cos (/ 2.0 2)) 1) (/ (* (pow cos (/ 2.0 2)) (* (pow sin (/ 2.0 2)) x)) (cos (* x 2.0)))))
34.0ms
(* (pow cos (/ 2.0 2)) (* (pow sin (/ 2.0 2)) x))
137.0ms
(/ (/ (/ 1 (pow sin (/ 2.0 2))) (* (/ (pow cos (/ 2.0 2)) 1) (/ (* (pow cos (/ 2.0 2)) (* (pow sin (/ 2.0 2)) x)) (cos (* x 2.0))))) x)

series2.2s

Counts
4 → 12
Calls
4 calls:
572.0ms
(* (/ (pow cos (/ 2.0 2)) 1) (/ (* (pow cos (/ 2.0 2)) (* (pow sin (/ 2.0 2)) x)) (cos (* x 2.0))))
495.0ms
(/ (/ 1 (pow sin (/ 2.0 2))) (* (/ (pow cos (/ 2.0 2)) 1) (/ (* (pow cos (/ 2.0 2)) (* (pow sin (/ 2.0 2)) x)) (cos (* x 2.0)))))
488.0ms
(* (pow cos (/ 2.0 2)) (* (pow sin (/ 2.0 2)) x))
668.0ms
(/ (/ (/ 1 (pow sin (/ 2.0 2))) (* (/ (pow cos (/ 2.0 2)) 1) (/ (* (pow cos (/ 2.0 2)) (* (pow sin (/ 2.0 2)) x)) (cos (* x 2.0))))) x)

simplify2.1s

Counts
2432 → 2432
Iterations
IterNodes
done5000
14665
01225

prune2.8s

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 2.3b

localize42.0ms

Local error

Found 4 expressions with local error:

0.9b
(/ (* (/ (cbrt (/ 1 (pow sin (/ 2.0 2)))) (* (* (pow cos (/ 2.0 2)) (pow sin (/ 2.0 2))) x)) (cos (* 2.0 x))) (cbrt x))
1.2b
(/ (cbrt (/ 1 (pow sin (/ 2.0 2)))) (* (* (pow cos (/ 2.0 2)) (pow sin (/ 2.0 2))) x))
2.5b
(/ (* (cbrt (/ 1 (pow sin (/ 2.0 2)))) (cbrt (/ 1 (pow sin (/ 2.0 2))))) (* (* (cbrt x) (cbrt x)) (pow cos (/ 2.0 2))))
5.7b
(* (* (pow cos (/ 2.0 2)) (pow sin (/ 2.0 2))) x)

rewrite216.0ms

Algorithm
rewrite-expression-head
Rules
173×add-exp-log
94×prod-exp
77×times-frac
56×cbrt-prod
49×div-exp
39×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
38×add-cbrt-cube
30×associate-/l*
22×pow-to-exp pow-exp cbrt-unprod
18×unpow-prod-down
17×cbrt-undiv
8×associate-/r*
6×pow1 sqr-pow
5×cbrt-div div-inv associate-/l/
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×clear-num frac-2neg associate-*r*
2×associate-*l/
1×frac-times associate-*l* pow-prod-down associate-*r/ *-commutative
Counts
4 → 193
Calls
4 calls:
104.0ms
(/ (* (/ (cbrt (/ 1 (pow sin (/ 2.0 2)))) (* (* (pow cos (/ 2.0 2)) (pow sin (/ 2.0 2))) x)) (cos (* 2.0 x))) (cbrt x))
34.0ms
(/ (cbrt (/ 1 (pow sin (/ 2.0 2)))) (* (* (pow cos (/ 2.0 2)) (pow sin (/ 2.0 2))) x))
34.0ms
(/ (* (cbrt (/ 1 (pow sin (/ 2.0 2)))) (cbrt (/ 1 (pow sin (/ 2.0 2))))) (* (* (cbrt x) (cbrt x)) (pow cos (/ 2.0 2))))
31.0ms
(* (* (pow cos (/ 2.0 2)) (pow sin (/ 2.0 2))) x)

series2.5s

Counts
4 → 12
Calls
4 calls:
714.0ms
(/ (* (/ (cbrt (/ 1 (pow sin (/ 2.0 2)))) (* (* (pow cos (/ 2.0 2)) (pow sin (/ 2.0 2))) x)) (cos (* 2.0 x))) (cbrt x))
643.0ms
(/ (cbrt (/ 1 (pow sin (/ 2.0 2)))) (* (* (pow cos (/ 2.0 2)) (pow sin (/ 2.0 2))) x))
700.0ms
(/ (* (cbrt (/ 1 (pow sin (/ 2.0 2)))) (cbrt (/ 1 (pow sin (/ 2.0 2))))) (* (* (cbrt x) (cbrt x)) (pow cos (/ 2.0 2))))
479.0ms
(* (* (pow cos (/ 2.0 2)) (pow sin (/ 2.0 2))) x)

simplify592.0ms

Counts
205 → 205
Iterations
IterNodes
done5000
11070
0425

prune1.6s

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 0.3b

regimes998.0ms

Accuracy

-11.8% (3.3b remaining)

Error of 3.4b against oracle of 0.1b and baseline of 3.1b

bsearch690.0ms

Steps
ItersRangePoint
2
5.16149553175908e+134
5.952231675750192e+134
5.8533896577513026e+134
8
1.8451777477141087e-282
1.805639974384451e-278
1.7692570139482513e-278

simplify23.0ms

Iterations
IterNodes
done73
373
271
168
051

end0.0ms

sample4.0s

Algorithm
intervals
Results
1.2s9036×body80valid
1.2s830×body1280valid
645.0ms998×body640valid
231.0ms576×body320valid
124.0ms326×body160valid