Details

Time bar (total: 33.2s)

sample83.0ms

Algorithm
intervals
Results
22.0ms26×body1280valid
21.0ms284×body80valid
10.0ms32×body640valid
4.0ms21×body320valid
2.0ms13×body160valid

simplify1.0s

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

prune14.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 26.5b

localize23.0ms

Local error

Found 4 expressions with local error:

0.6b
(/ (cos (* 2.0 x)) (pow sin 2.0))
5.8b
(/ (/ (/ (cos (* 2.0 x)) (pow sin 2.0)) (* (pow cos 2.0) x)) x)
9.0b
(* (pow cos 2.0) x)
18.8b
(/ (/ (cos (* 2.0 x)) (pow sin 2.0)) (* (pow cos 2.0) x))

rewrite172.0ms

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:
24.0ms
(/ (cos (* 2.0 x)) (pow sin 2.0))
72.0ms
(/ (/ (/ (cos (* 2.0 x)) (pow sin 2.0)) (* (pow cos 2.0) x)) x)
19.0ms
(* (pow cos 2.0) x)
27.0ms
(/ (/ (cos (* 2.0 x)) (pow sin 2.0)) (* (pow cos 2.0) x))

series1.4s

Counts
4 → 12
Calls
4 calls:
263.0ms
(/ (cos (* 2.0 x)) (pow sin 2.0))
452.0ms
(/ (/ (/ (cos (* 2.0 x)) (pow sin 2.0)) (* (pow cos 2.0) x)) x)
279.0ms
(* (pow cos 2.0) x)
369.0ms
(/ (/ (cos (* 2.0 x)) (pow sin 2.0)) (* (pow cos 2.0) x))

simplify1.0s

Counts
324 → 324
Iterations
IterNodes
done5001
11224
0468

prune2.0s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 13.5b

localize45.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (pow cos 2.0) (cos (* 2.0 x)))
5.4b
(/ (/ 1 (pow sin (/ 2.0 2))) (* (/ (pow cos 2.0) (cos (* 2.0 x))) (* x (pow sin (/ 2.0 2)))))
5.8b
(/ (/ (/ 1 (pow sin (/ 2.0 2))) (* (/ (pow cos 2.0) (cos (* 2.0 x))) (* x (pow sin (/ 2.0 2))))) x)
15.1b
(* (/ (pow cos 2.0) (cos (* 2.0 x))) (* x (pow sin (/ 2.0 2))))

rewrite339.0ms

Algorithm
rewrite-expression-head
Rules
1549×add-exp-log
970×div-exp
588×prod-exp
383×times-frac
271×pow-to-exp pow-exp
153×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
112×add-cbrt-cube
102×rec-exp 1-exp
75×unpow-prod-down
62×associate-/l*
52×cbrt-undiv
30×cbrt-unprod
25×associate-*l* sqr-pow
14×div-inv
7×associate-/r*
6×pow1 associate-*l/
5×associate-/r/
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×clear-num frac-2neg
2×associate-/l/
1×associate-*r* pow-prod-down *-commutative
Counts
4 → 668
Calls
4 calls:
10.0ms
(/ (pow cos 2.0) (cos (* 2.0 x)))
66.0ms
(/ (/ 1 (pow sin (/ 2.0 2))) (* (/ (pow cos 2.0) (cos (* 2.0 x))) (* x (pow sin (/ 2.0 2)))))
105.0ms
(/ (/ (/ 1 (pow sin (/ 2.0 2))) (* (/ (pow cos 2.0) (cos (* 2.0 x))) (* x (pow sin (/ 2.0 2))))) x)
63.0ms
(* (/ (pow cos 2.0) (cos (* 2.0 x))) (* x (pow sin (/ 2.0 2))))

series1.9s

Counts
4 → 12
Calls
4 calls:
369.0ms
(/ (pow cos 2.0) (cos (* 2.0 x)))
550.0ms
(/ (/ 1 (pow sin (/ 2.0 2))) (* (/ (pow cos 2.0) (cos (* 2.0 x))) (* x (pow sin (/ 2.0 2)))))
541.0ms
(/ (/ (/ 1 (pow sin (/ 2.0 2))) (* (/ (pow cos 2.0) (cos (* 2.0 x))) (* x (pow sin (/ 2.0 2))))) x)
434.0ms
(* (/ (pow cos 2.0) (cos (* 2.0 x))) (* x (pow sin (/ 2.0 2))))

simplify1.2s

Counts
680 → 680
Iterations
IterNodes
done5001
12145
0698

prune2.2s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.2b

localize64.0ms

Local error

Found 4 expressions with local error:

2.0b
(* (/ (pow cos (/ 2.0 2)) (* (cbrt (cos (* 2.0 x))) (cbrt (cos (* 2.0 x))))) (* (* (/ (pow cos (/ 2.0 2)) (cbrt (cos (* x 2.0)))) x) (pow sin (/ 2.0 2))))
5.4b
(/ (/ 1 (pow sin (/ 2.0 2))) (* (/ (pow cos (/ 2.0 2)) (* (cbrt (cos (* 2.0 x))) (cbrt (cos (* 2.0 x))))) (* (* (/ (pow cos (/ 2.0 2)) (cbrt (cos (* x 2.0)))) x) (pow sin (/ 2.0 2)))))
5.8b
(/ (/ (/ 1 (pow sin (/ 2.0 2))) (* (/ (pow cos (/ 2.0 2)) (* (cbrt (cos (* 2.0 x))) (cbrt (cos (* 2.0 x))))) (* (* (/ (pow cos (/ 2.0 2)) (cbrt (cos (* x 2.0)))) x) (pow sin (/ 2.0 2))))) x)
6.6b
(* (* (/ (pow cos (/ 2.0 2)) (cbrt (cos (* x 2.0)))) x) (pow sin (/ 2.0 2)))

rewrite1.5s

Algorithm
rewrite-expression-head
Rules
14631×add-exp-log
8095×div-exp
7356×prod-exp
2534×pow-to-exp pow-exp
678×rec-exp 1-exp
354×times-frac
337×add-cbrt-cube
161×cbrt-undiv
160×cbrt-unprod
130×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
60×unpow-prod-down
57×associate-/l*
32×associate-*l/
20×sqr-pow
15×associate-/r/
13×div-inv
12×associate-*l*
8×associate-*r*
6×frac-times pow1 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 → 2712
Calls
4 calls:
287.0ms
(* (/ (pow cos (/ 2.0 2)) (* (cbrt (cos (* 2.0 x))) (cbrt (cos (* 2.0 x))))) (* (* (/ (pow cos (/ 2.0 2)) (cbrt (cos (* x 2.0)))) x) (pow sin (/ 2.0 2))))
289.0ms
(/ (/ 1 (pow sin (/ 2.0 2))) (* (/ (pow cos (/ 2.0 2)) (* (cbrt (cos (* 2.0 x))) (cbrt (cos (* 2.0 x))))) (* (* (/ (pow cos (/ 2.0 2)) (cbrt (cos (* x 2.0)))) x) (pow sin (/ 2.0 2)))))
396.0ms
(/ (/ (/ 1 (pow sin (/ 2.0 2))) (* (/ (pow cos (/ 2.0 2)) (* (cbrt (cos (* 2.0 x))) (cbrt (cos (* 2.0 x))))) (* (* (/ (pow cos (/ 2.0 2)) (cbrt (cos (* x 2.0)))) x) (pow sin (/ 2.0 2))))) x)
61.0ms
(* (* (/ (pow cos (/ 2.0 2)) (cbrt (cos (* x 2.0)))) x) (pow sin (/ 2.0 2)))

series2.0s

Counts
4 → 12
Calls
4 calls:
452.0ms
(* (/ (pow cos (/ 2.0 2)) (* (cbrt (cos (* 2.0 x))) (cbrt (cos (* 2.0 x))))) (* (* (/ (pow cos (/ 2.0 2)) (cbrt (cos (* x 2.0)))) x) (pow sin (/ 2.0 2))))
600.0ms
(/ (/ 1 (pow sin (/ 2.0 2))) (* (/ (pow cos (/ 2.0 2)) (* (cbrt (cos (* 2.0 x))) (cbrt (cos (* 2.0 x))))) (* (* (/ (pow cos (/ 2.0 2)) (cbrt (cos (* x 2.0)))) x) (pow sin (/ 2.0 2)))))
521.0ms
(/ (/ (/ 1 (pow sin (/ 2.0 2))) (* (/ (pow cos (/ 2.0 2)) (* (cbrt (cos (* 2.0 x))) (cbrt (cos (* 2.0 x))))) (* (* (/ (pow cos (/ 2.0 2)) (cbrt (cos (* x 2.0)))) x) (pow sin (/ 2.0 2))))) x)
462.0ms
(* (* (/ (pow cos (/ 2.0 2)) (cbrt (cos (* x 2.0)))) x) (pow sin (/ 2.0 2)))

simplify1.0s

Counts
2724 → 2724
Iterations
IterNodes
done5000
01294

prune4.3s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 0.0b

localize86.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt sin)
1.7b
(/ (/ (sqrt 1) (pow (cbrt sin) (/ 2.0 2))) (* (cbrt x) (* (/ (pow cos (/ 2.0 2)) (cbrt (cos (* x 2.0)))) (* (pow sin (/ 2.0 2)) x))))
5.0b
(* (/ (pow cos (/ 2.0 2)) (cbrt (cos (* x 2.0)))) (* (pow sin (/ 2.0 2)) x))
5.1b
(/ (/ (sqrt 1) (pow (* (cbrt sin) (cbrt sin)) (/ 2.0 2))) (* (* (cbrt x) (cbrt x)) (/ (pow cos (/ 2.0 2)) (* (cbrt (cos (* x 2.0))) (cbrt (cos (* x 2.0)))))))

rewrite347.0ms

Algorithm
rewrite-expression-head
Rules
813×add-exp-log
381×div-exp
358×prod-exp
320×times-frac
144×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
108×pow-exp
102×unpow-prod-down
101×add-cbrt-cube
98×associate-/l*
93×pow-to-exp
90×sqrt-prod
60×cbrt-prod
53×cbrt-undiv
50×cbrt-unprod
46×associate-*l*
30×sqr-pow
7×div-inv
6×pow1
4×expm1-log1p-u log1p-expm1-u add-log-exp
2×clear-num associate-/r* frac-2neg associate-*l/ associate-*r/ associate-/r/ associate-/l/
1×pow1/3 associate-*r* pow-prod-down *-commutative
Counts
4 → 491
Calls
4 calls:
1.0ms
(cbrt sin)
102.0ms
(/ (/ (sqrt 1) (pow (cbrt sin) (/ 2.0 2))) (* (cbrt x) (* (/ (pow cos (/ 2.0 2)) (cbrt (cos (* x 2.0)))) (* (pow sin (/ 2.0 2)) x))))
81.0ms
(* (/ (pow cos (/ 2.0 2)) (cbrt (cos (* x 2.0)))) (* (pow sin (/ 2.0 2)) x))
89.0ms
(/ (/ (sqrt 1) (pow (* (cbrt sin) (cbrt sin)) (/ 2.0 2))) (* (* (cbrt x) (cbrt x)) (/ (pow cos (/ 2.0 2)) (* (cbrt (cos (* x 2.0))) (cbrt (cos (* x 2.0)))))))

series2.6s

Counts
4 → 12
Calls
4 calls:
261.0ms
(cbrt sin)
873.0ms
(/ (/ (sqrt 1) (pow (cbrt sin) (/ 2.0 2))) (* (cbrt x) (* (/ (pow cos (/ 2.0 2)) (cbrt (cos (* x 2.0)))) (* (pow sin (/ 2.0 2)) x))))
540.0ms
(* (/ (pow cos (/ 2.0 2)) (cbrt (cos (* x 2.0)))) (* (pow sin (/ 2.0 2)) x))
943.0ms
(/ (/ (sqrt 1) (pow (* (cbrt sin) (cbrt sin)) (/ 2.0 2))) (* (* (cbrt x) (cbrt x)) (/ (pow cos (/ 2.0 2)) (* (cbrt (cos (* x 2.0))) (cbrt (cos (* x 2.0)))))))

simplify1.6s

Counts
503 → 503
Iterations
IterNodes
done5000
12450
0791

prune3.5s

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 0.0b

regimes1.1s

Accuracy

20.8% (3.1b remaining)

Error of 3.2b against oracle of 0.1b and baseline of 4.0b

bsearch5.0ms

simplify14.0ms

Iterations
IterNodes
done76
176
062

end0.0ms

sample3.7s

Algorithm
intervals
Results
1.3s9119×body80valid
634.0ms784×body1280valid
613.0ms598×body320valid
499.0ms965×body640valid
91.0ms311×body160valid