Details

Time bar (total: 33.6s)

sample131.0ms

Algorithm
intervals
Results
58.0ms285×body80valid
23.0ms28×body1280valid
12.0ms25×body640valid
6.0ms17×body320valid
2.0ms10×body160valid

simplify1.0s

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

prune25.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 25.7b

localize25.0ms

Local error

Found 4 expressions with local error:

0.5b
(/ (cos (* 2.0 x)) (pow sin 2.0))
5.6b
(/ (/ (/ (cos (* 2.0 x)) (pow sin 2.0)) (* (pow cos 2.0) x)) x)
9.4b
(* (pow cos 2.0) x)
17.6b
(/ (/ (cos (* 2.0 x)) (pow sin 2.0)) (* (pow cos 2.0) x))

rewrite115.0ms

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:
21.0ms
(/ (cos (* 2.0 x)) (pow sin 2.0))
39.0ms
(/ (/ (/ (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))

series1.3s

Counts
4 → 12
Calls
4 calls:
251.0ms
(/ (cos (* 2.0 x)) (pow sin 2.0))
452.0ms
(/ (/ (/ (cos (* 2.0 x)) (pow sin 2.0)) (* (pow cos 2.0) x)) x)
210.0ms
(* (pow cos 2.0) x)
397.0ms
(/ (/ (cos (* 2.0 x)) (pow sin 2.0)) (* (pow cos 2.0) x))

simplify687.0ms

Counts
324 → 324
Iterations
IterNodes
done5001
11224
0468

prune2.0s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 11.0b

localize43.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (pow cos 2.0) (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)))))
5.6b
(/ (/ (/ 1 (pow sin (/ 2.0 2))) (* (/ (pow cos 2.0) (cos (* 2.0 x))) (* x (pow sin (/ 2.0 2))))) x)
14.6b
(* (/ (pow cos 2.0) (cos (* 2.0 x))) (* x (pow sin (/ 2.0 2))))

rewrite274.0ms

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:
16.0ms
(/ (pow cos 2.0) (cos (* 2.0 x)))
55.0ms
(/ (/ 1 (pow sin (/ 2.0 2))) (* (/ (pow cos 2.0) (cos (* 2.0 x))) (* x (pow sin (/ 2.0 2)))))
85.0ms
(/ (/ (/ 1 (pow sin (/ 2.0 2))) (* (/ (pow cos 2.0) (cos (* 2.0 x))) (* x (pow sin (/ 2.0 2))))) x)
43.0ms
(* (/ (pow cos 2.0) (cos (* 2.0 x))) (* x (pow sin (/ 2.0 2))))

series1.8s

Counts
4 → 12
Calls
4 calls:
311.0ms
(/ (pow cos 2.0) (cos (* 2.0 x)))
560.0ms
(/ (/ 1 (pow sin (/ 2.0 2))) (* (/ (pow cos 2.0) (cos (* 2.0 x))) (* x (pow sin (/ 2.0 2)))))
575.0ms
(/ (/ (/ 1 (pow sin (/ 2.0 2))) (* (/ (pow cos 2.0) (cos (* 2.0 x))) (* x (pow sin (/ 2.0 2))))) x)
404.0ms
(* (/ (pow cos 2.0) (cos (* 2.0 x))) (* x (pow sin (/ 2.0 2))))

simplify1.1s

Counts
680 → 680
Iterations
IterNodes
done5001
12145
0698

prune2.7s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 3.0b

localize54.0ms

Local error

Found 4 expressions with local error:

1.6b
(* (/ (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))))
4.1b
(/ (/ 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)))))
4.7b
(* (* (/ (pow cos (/ 2.0 2)) (cbrt (cos (* x 2.0)))) x) (pow sin (/ 2.0 2)))
5.6b
(/ (/ (/ 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)

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:
234.0ms
(* (/ (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))))
306.0ms
(/ (/ 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)))))
55.0ms
(* (* (/ (pow cos (/ 2.0 2)) (cbrt (cos (* x 2.0)))) x) (pow sin (/ 2.0 2)))
381.0ms
(/ (/ (/ 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)

series2.0s

Counts
4 → 12
Calls
4 calls:
442.0ms
(* (/ (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))))
587.0ms
(/ (/ 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)))))
500.0ms
(* (* (/ (pow cos (/ 2.0 2)) (cbrt (cos (* x 2.0)))) x) (pow sin (/ 2.0 2)))
518.0ms
(/ (/ (/ 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)

simplify981.0ms

Counts
2724 → 2724
Iterations
IterNodes
done5000
01294

prune3.7s

Pruning

19 alts after pruning (18 fresh and 1 done)

Merged error: 0.0b

localize60.0ms

Local error

Found 4 expressions with local error:

0.9b
(/ (cbrt (/ 1 (pow sin (/ 2.0 2)))) (* (/ (pow cos (/ 2.0 2)) (cbrt (cos (* 2.0 x)))) (* x (pow sin (/ 2.0 2)))))
0.9b
(/ (/ (cbrt (/ 1 (pow sin (/ 2.0 2)))) (* (/ (pow cos (/ 2.0 2)) (cbrt (cos (* 2.0 x)))) (* x (pow sin (/ 2.0 2))))) (cbrt x))
2.9b
(/ (* (cbrt (/ 1 (pow sin (/ 2.0 2)))) (cbrt (/ 1 (pow sin (/ 2.0 2))))) (* (* (cbrt x) (cbrt x)) (/ (pow cos (/ 2.0 2)) (* (cbrt (cos (* 2.0 x))) (cbrt (cos (* 2.0 x)))))))
4.6b
(* (/ (pow cos (/ 2.0 2)) (cbrt (cos (* 2.0 x)))) (* x (pow sin (/ 2.0 2))))

rewrite339.0ms

Algorithm
rewrite-expression-head
Rules
654×times-frac
348×cbrt-prod add-exp-log
241×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
153×prod-exp
142×div-exp
99×unpow-prod-down
68×add-cbrt-cube
62×associate-/l*
47×cbrt-unprod
46×associate-*l*
44×cbrt-undiv
33×sqr-pow
32×pow-to-exp pow-exp
20×div-inv
10×associate-*l/
9×associate-/r/
8×associate-/r*
6×pow1
5×cbrt-div associate-/l/
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×clear-num frac-2neg
2×associate-*r/
1×frac-times associate-*r* pow-prod-down *-commutative
Counts
4 → 509
Calls
4 calls:
71.0ms
(/ (cbrt (/ 1 (pow sin (/ 2.0 2)))) (* (/ (pow cos (/ 2.0 2)) (cbrt (cos (* 2.0 x)))) (* x (pow sin (/ 2.0 2)))))
86.0ms
(/ (/ (cbrt (/ 1 (pow sin (/ 2.0 2)))) (* (/ (pow cos (/ 2.0 2)) (cbrt (cos (* 2.0 x)))) (* x (pow sin (/ 2.0 2))))) (cbrt x))
65.0ms
(/ (* (cbrt (/ 1 (pow sin (/ 2.0 2)))) (cbrt (/ 1 (pow sin (/ 2.0 2))))) (* (* (cbrt x) (cbrt x)) (/ (pow cos (/ 2.0 2)) (* (cbrt (cos (* 2.0 x))) (cbrt (cos (* 2.0 x)))))))
60.0ms
(* (/ (pow cos (/ 2.0 2)) (cbrt (cos (* 2.0 x)))) (* x (pow sin (/ 2.0 2))))

series3.1s

Counts
4 → 12
Calls
4 calls:
969.0ms
(/ (cbrt (/ 1 (pow sin (/ 2.0 2)))) (* (/ (pow cos (/ 2.0 2)) (cbrt (cos (* 2.0 x)))) (* x (pow sin (/ 2.0 2)))))
760.0ms
(/ (/ (cbrt (/ 1 (pow sin (/ 2.0 2)))) (* (/ (pow cos (/ 2.0 2)) (cbrt (cos (* 2.0 x)))) (* x (pow sin (/ 2.0 2))))) (cbrt x))
821.0ms
(/ (* (cbrt (/ 1 (pow sin (/ 2.0 2)))) (cbrt (/ 1 (pow sin (/ 2.0 2))))) (* (* (cbrt x) (cbrt x)) (/ (pow cos (/ 2.0 2)) (* (cbrt (cos (* 2.0 x))) (cbrt (cos (* 2.0 x)))))))
509.0ms
(* (/ (pow cos (/ 2.0 2)) (cbrt (cos (* 2.0 x)))) (* x (pow sin (/ 2.0 2))))

simplify992.0ms

Counts
521 → 521
Iterations
IterNodes
done5001
12358
0879

prune4.2s

Pruning

19 alts after pruning (18 fresh and 1 done)

Merged error: 0.0b

regimes1.1s

Accuracy

24% (2.5b remaining)

Error of 2.6b against oracle of 0.1b and baseline of 3.4b

bsearch6.0ms

simplify15.0ms

Iterations
IterNodes
done58
258
157
046

end0.0ms

sample4.2s

Algorithm
intervals
Results
1.8s9053×body80valid
833.0ms900×body640valid
674.0ms825×body1280valid
227.0ms578×body320valid
133.0ms323×body160valid