Details

sample125.0ms

Algorithm

intervals

Results

39.0ms	48×	body	2560	valid
22.0ms	19×	body	160	valid
19.0ms	42×	body	1280	valid
18.0ms	52×	body	640	valid
6.0ms	27×	body	320	valid
5.0ms	68×	body	80	valid

simplify21.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	182
1	13	182
2	21	182
3	26	182
4	28	182
done	28	182

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.6b

localize15.0ms

Local error

Found 2 expressions with local error:

2.1b	(- 1.0 (cos x))
15.1b	(/ (- 1.0 (cos x)) (* x x))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt` `*-un-lft-identity`
7×	`add-cbrt-cube` `add-exp-log`
5×	`times-frac` `associate-/l*`
4×	`add-cube-cbrt` `add-log-exp`
3×	`distribute-lft-out--` `difference-of-squares`
2×	`pow1` `cbrt-undiv` `flip3--` `div-exp` `flip--` `associate-/l/`
1×	`clear-num` `associate-/r*` `sub-neg` `frac-2neg` `diff-log` `div-sub` `prod-exp` `cbrt-unprod` `div-inv`

Counts

2 → 42

Calls

2 calls:

7.0ms	(- 1.0 (cos x))
16.0ms	(/ (- 1.0 (cos x)) (* x x))

series79.0ms

Counts

2 → 6

Calls

2 calls:

19.0ms	(- 1.0 (cos x))
59.0ms	(/ (- 1.0 (cos x)) (* x x))

simplify807.0ms

Counts

48 → 48

Iterations

Useful iterations: done (803.0ms)

Iter	Nodes	Cost
0	88	12774
1	232	11197
2	1129	10866
done	5000	10826

prune200.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize13.0ms

Local error

Found 3 expressions with local error:

0.1b	(* (/ 1 x) (/ (- 1.0 (cos x)) x))
0.1b	(/ (- 1.0 (cos x)) x)
2.1b	(- 1.0 (cos x))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

62×	`add-sqr-sqrt`
47×	`*-un-lft-identity`
46×	`times-frac`
29×	`add-cube-cbrt`
27×	`add-exp-log`
19×	`associate-r`
17×	`add-cbrt-cube`
13×	`associate-l`
9×	`div-exp`
8×	`prod-exp` `distribute-lft-out--` `difference-of-squares`
6×	`unswap-sqr`
5×	`pow1` `cbrt-undiv` `associate-/l*` `add-log-exp`
4×	`cbrt-unprod`
3×	`associate-/r*` `div-inv`
2×	`rec-exp` `flip3--` `1-exp` `flip--` `associate-/l/`
1×	`frac-times` `clear-num` `sub-neg` `frac-2neg` `diff-log` `div-sub` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative`

Counts

3 → 114

Calls

3 calls:

31.0ms	(* (/ 1 x) (/ (- 1.0 (cos x)) x))
16.0ms	(/ (- 1.0 (cos x)) x)
5.0ms	(- 1.0 (cos x))

series152.0ms

Counts

3 → 9

Calls

3 calls:

65.0ms	(* (/ 1 x) (/ (- 1.0 (cos x)) x))
67.0ms	(/ (- 1.0 (cos x)) x)
20.0ms	(- 1.0 (cos x))

simplify2.0s

Counts

123 → 123

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	189	37850
1	546	32799
2	3248	31294
done	5001	31134

prune518.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize33.0ms

Local error

Found 4 expressions with local error:

0.4b	(pow (cos x) 3)
0.4b	(/ (- (pow 1.0 3) (pow (cos x) 3)) (* x (+ (* (cos x) (+ 1.0 (cos x))) (* 1.0 1.0))))
0.5b	(+ 1.0 (cos x))
1.9b	(- (pow 1.0 3) (pow (cos x) 3))

rewrite113.0ms

Algorithm

rewrite-expression-head

Rules

81×	`add-sqr-sqrt`
48×	`difference-of-squares`
41×	`*-un-lft-identity`
39×	`unpow-prod-down` `cube-prod`
25×	`times-frac` `associate-/l*` `sqr-pow`
15×	`distribute-lft-out--`
10×	`add-cbrt-cube` `add-exp-log`
9×	`add-cube-cbrt`
8×	`add-log-exp`
5×	`pow1`
3×	`difference-cubes` `pow-unpow`
2×	`cbrt-undiv` `flip3-+` `flip3--` `div-exp` `associate-*r/` `associate-/r/` `flip-+` `flip--` `associate-/l/`
1×	`cube-mult` `pow-to-exp` `+-commutative` `clear-num` `associate-/r*` `sum-log` `sub-neg` `pow-pow` `frac-2neg` `diff-log` `unpow3` `div-sub` `pow-exp` `prod-exp` `cbrt-unprod` `div-inv` `distribute-lft-out` `rem-cube-cbrt`

Counts

4 → 139

Calls

4 calls:

3.0ms	(pow (cos x) 3)
72.0ms	(/ (- (pow 1.0 3) (pow (cos x) 3)) (* x (+ (* (cos x) (+ 1.0 (cos x))) (* 1.0 1.0))))
5.0ms	(+ 1.0 (cos x))
27.0ms	(- (pow 1.0 3) (pow (cos x) 3))

series369.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(pow (cos x) 3)
245.0ms	(/ (- (pow 1.0 3) (pow (cos x) 3)) (* x (+ (* (cos x) (+ 1.0 (cos x))) (* 1.0 1.0))))
15.0ms	(+ 1.0 (cos x))
70.0ms	(- (pow 1.0 3) (pow (cos x) 3))

simplify2.9s

Counts

151 → 151

Iterations

Useful iterations: 2 (1.1s)

Iter	Nodes	Cost
0	219	115647
1	644	74037
2	3624	70557
done	5001	70557

prune748.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize81.0ms

Local error

Found 4 expressions with local error:

0.4b	(cbrt (* (* (* (* (cos x) (cos x)) (cos x)) (* (* (cos x) (cos x)) (cos x))) (* (* (cos x) (cos x)) (cos x))))
0.4b	(/ (- (pow 1.0 3) (cbrt (* (* (* (* (cos x) (cos x)) (cos x)) (* (* (cos x) (cos x)) (cos x))) (* (* (cos x) (cos x)) (cos x))))) (* x (+ (* (cos x) (+ 1.0 (cos x))) (* 1.0 1.0))))
0.5b	(+ 1.0 (cos x))
1.9b	(- (pow 1.0 3) (cbrt (* (* (* (* (cos x) (cos x)) (cos x)) (* (* (cos x) (cos x)) (cos x))) (* (* (cos x) (cos x)) (cos x)))))

rewrite786.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt`
17×	`associate-*l/`
14×	`*-un-lft-identity`
12×	`cos-mult` `difference-of-squares`
9×	`add-cbrt-cube` `add-exp-log`
8×	`times-frac` `associate-/l*` `add-log-exp`
7×	`cbrt-div`
6×	`add-cube-cbrt`
5×	`frac-times` `associate-*r/`
4×	`pow1` `pow3`
3×	`unpow-prod-down` `cube-prod` `distribute-lft-out--` `sqr-pow`
2×	`cbrt-undiv` `flip3-+` `flip3--` `div-exp` `pow-prod-down` `associate-/r/` `rem-cbrt-cube` `flip-+` `flip--` `associate-/l/`
1×	`cbrt-prod` `+-commutative` `clear-num` `associate-/r*` `sum-log` `sub-neg` `frac-2neg` `pow1/3` `diff-log` `div-sub` `prod-exp` `cbrt-unprod` `div-inv` `distribute-lft-out`

Counts

4 → 83

Calls

4 calls:

697.0ms	(cbrt (* (* (* (* (cos x) (cos x)) (cos x)) (* (* (cos x) (cos x)) (cos x))) (* (* (cos x) (cos x)) (cos x))))
66.0ms	(/ (- (pow 1.0 3) (cbrt (* (* (* (* (cos x) (cos x)) (cos x)) (* (* (cos x) (cos x)) (cos x))) (* (* (cos x) (cos x)) (cos x))))) (* x (+ (* (cos x) (+ 1.0 (cos x))) (* 1.0 1.0))))
5.0ms	(+ 1.0 (cos x))
15.0ms	(- (pow 1.0 3) (cbrt (* (* (* (* (cos x) (cos x)) (cos x)) (* (* (cos x) (cos x)) (cos x))) (* (* (cos x) (cos x)) (cos x)))))

series420.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(cbrt (* (* (* (* (cos x) (cos x)) (cos x)) (* (* (cos x) (cos x)) (cos x))) (* (* (cos x) (cos x)) (cos x))))
273.0ms	(/ (- (pow 1.0 3) (cbrt (* (* (* (* (cos x) (cos x)) (cos x)) (* (* (cos x) (cos x)) (cos x))) (* (* (cos x) (cos x)) (cos x))))) (* x (+ (* (cos x) (+ 1.0 (cos x))) (* 1.0 1.0))))
18.0ms	(+ 1.0 (cos x))
83.0ms	(- (pow 1.0 3) (cbrt (* (* (* (* (cos x) (cos x)) (cos x)) (* (* (cos x) (cos x)) (cos x))) (* (* (cos x) (cos x)) (cos x)))))

simplify2.7s

Counts

95 → 95

Iterations

Useful iterations: done (2.7s)

Iter	Nodes	Cost
0	201	64981
1	554	51389
2	3222	50589
done	5001	39029

prune490.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

regimes81.0ms

Accuracy

98.9% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 30.7b

bsearch102.0ms

Steps

Iters	Range		Point
9	5.1798647897020696e-05	160.65039477392645	0.033302914266201536
8	-0.9341403346610884	-0.003292329160956242	-0.037051728393040065

simplify20.0ms

Iterations

Useful iterations: 0 (7.0ms)

Iter	Nodes	Cost
0	38	1559
1	51	1559
done	51	1559

end0.0ms

sample3.6s

Algorithm

intervals

Results

1.8s	1623×	body	2560	valid
575.0ms	1237×	body	1280	valid
561.0ms	1505×	body	640	valid
273.0ms	923×	body	320	valid
127.0ms	2205×	body	80	valid
65.0ms	507×	body	160	valid