Details

sample101.0ms

Algorithm

intervals

Results

45.0ms	50×	body	2560	valid
15.0ms	36×	body	1280	valid
12.0ms	46×	body	640	valid
6.0ms	76×	body	80	valid
5.0ms	27×	body	320	valid
3.0ms	21×	body	160	valid

simplify31.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	13	8
2	21	8
3	26	8
4	28	8
done	28	8

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.7b

localize12.0ms

Local error

Found 2 expressions with local error:

2.3b	(- 1.0 (cos x))
13.6b	(/ (- 1.0 (cos x)) (* x x))

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt` `*-un-lft-identity`
7×	`add-exp-log` `add-cbrt-cube`
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×	`sub-neg` `frac-2neg` `diff-log` `div-sub` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

2 → 42

Calls

2 calls:

11.0ms	(- 1.0 (cos x))
49.0ms	(/ (- 1.0 (cos x)) (* x x))

series114.0ms

Counts

2 → 6

Calls

2 calls:

40.0ms	(- 1.0 (cos x))
73.0ms	(/ (- 1.0 (cos x)) (* x x))

simplify2.3s

Counts

48 → 48

Iterations

Useful iterations: 2 (176.0ms)

Iter	Nodes	Cost
0	88	507
1	212	489
2	548	441
3	1500	441
done	5000	441

prune127.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize15.0ms

Local error

Found 3 expressions with local error:

0.1b	(* (/ 1 x) (/ (- 1.0 (cos x)) x))
0.1b	(/ (- 1.0 (cos x)) x)
2.3b	(- 1.0 (cos x))

rewrite101.0ms

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` `sub-neg` `frac-2neg` `diff-log` `div-sub` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `*-commutative`

Counts

3 → 114

Calls

3 calls:

56.0ms	(* (/ 1 x) (/ (- 1.0 (cos x)) x))
26.0ms	(/ (- 1.0 (cos x)) x)
13.0ms	(- 1.0 (cos x))

series151.0ms

Counts

3 → 9

Calls

3 calls:

52.0ms	(* (/ 1 x) (/ (- 1.0 (cos x)) x))
75.0ms	(/ (- 1.0 (cos x)) x)
24.0ms	(- 1.0 (cos x))

simplify2.3s

Counts

123 → 123

Iterations

Useful iterations: done (2.3s)

Iter	Nodes	Cost
0	189	1536
1	495	1379
2	1538	1227
done	5000	1226

prune293.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- (pow 1.0 3) (pow (cos x) 3)) (+ (* (cos x) (+ 1.0 (cos x))) (* 1.0 1.0)))
0.4b	(+ 1.0 (cos x))
0.4b	(pow (cos x) 3)
2.1b	(- (pow 1.0 3) (pow (cos x) 3))

rewrite185.0ms

Algorithm

rewrite-expression-head

Rules

157×	`add-sqr-sqrt`
89×	`*-un-lft-identity`
80×	`difference-of-squares`
75×	`times-frac`
63×	`unpow-prod-down` `cube-prod`
41×	`sqr-pow`
37×	`add-cube-cbrt`
25×	`associate-/l*` `distribute-lft-out--`
8×	`add-log-exp`
7×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `difference-cubes`
3×	`pow-unpow` `associate-/r*`
2×	`flip3--` `flip3-+` `associate-/r/` `flip--` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `cube-mult` `pow-to-exp` `sub-neg` `pow-pow` `frac-2neg` `diff-log` `unpow3` `div-sub` `div-exp` `pow-exp` `clear-num` `sum-log` `div-inv` `distribute-lft-out` `rem-cube-cbrt`

Counts

4 → 189

Calls

4 calls:

103.0ms	(/ (- (pow 1.0 3) (pow (cos x) 3)) (+ (* (cos x) (+ 1.0 (cos x))) (* 1.0 1.0)))
7.0ms	(+ 1.0 (cos x))
6.0ms	(pow (cos x) 3)
53.0ms	(- (pow 1.0 3) (pow (cos x) 3))

series302.0ms

Counts

4 → 12

Calls

4 calls:

180.0ms	(/ (- (pow 1.0 3) (pow (cos x) 3)) (+ (* (cos x) (+ 1.0 (cos x))) (* 1.0 1.0)))
11.0ms	(+ 1.0 (cos x))
38.0ms	(pow (cos x) 3)
72.0ms	(- (pow 1.0 3) (pow (cos x) 3))

simplify1.4s

Counts

201 → 201

Iterations

Useful iterations: 2 (437.0ms)

Iter	Nodes	Cost
0	260	5407
1	611	5084
2	2055	4978
done	5000	4978

prune667.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.1b

localize41.0ms

Local error

Found 4 expressions with local error:

0.4b	(+ 1.0 (cos x))
0.4b	(pow (cos x) 3)
1.2b	(log (exp (pow (cos x) 3)))
2.1b	(- (pow 1.0 3) (log (exp (pow (cos x) 3))))

rewrite93.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-sqr-sqrt`
17×	`*-un-lft-identity`
14×	`log-pow`
12×	`add-cube-cbrt` `exp-prod`
7×	`pow1` `unpow-prod-down` `cube-prod` `add-log-exp`
6×	`log-prod`
5×	`add-exp-log` `add-cbrt-cube`
4×	`difference-of-squares`
3×	`pow-unpow` `associate--r+` `sqr-pow`
2×	`cube-mult` `unpow3` `distribute-lft-out--`
1×	`+-commutative` `pow-to-exp` `sub-neg` `flip3--` `pow-pow` `flip3-+` `diff-log` `rem-log-exp` `pow-exp` `sum-log` `flip--` `flip-+` `distribute-lft-out` `rem-cube-cbrt`

Counts

4 → 80

Calls

4 calls:

15.0ms	(+ 1.0 (cos x))
4.0ms	(pow (cos x) 3)
8.0ms	(log (exp (pow (cos x) 3)))
62.0ms	(- (pow 1.0 3) (log (exp (pow (cos x) 3))))

series151.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(+ 1.0 (cos x))
45.0ms	(pow (cos x) 3)
36.0ms	(log (exp (pow (cos x) 3)))
54.0ms	(- (pow 1.0 3) (log (exp (pow (cos x) 3))))

simplify849.0ms

Counts

92 → 92

Iterations

Useful iterations: 2 (161.0ms)

Iter	Nodes	Cost
0	140	922
1	294	707
2	855	660
done	5000	660

prune363.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.1b

regimes128.0ms

Accuracy

99.4% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 30.9b

bsearch113.0ms

Steps

Iters	Range		Point
9	9.85435867085541e-08	110.15968793260775	0.031416007424221945
8	-0.1517943218839364	-1.6640733670284383e-05	-0.030204237643336285

simplify14.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	47	97
1	61	97
done	61	97

end0.0ms

sample2.1s

Algorithm

intervals

Results

927.0ms	1592×	body	2560	valid
379.0ms	1298×	body	1280	valid
275.0ms	1478×	body	640	valid
133.0ms	894×	body	320	valid
103.0ms	2272×	body	80	valid
42.0ms	466×	body	160	valid