Details

sample95.0ms

Algorithm

intervals

Results

37.0ms	47×	body	2560	valid
17.0ms	40×	body	1280	valid
12.0ms	45×	body	640	valid
8.0ms	41×	body	320	valid
4.0ms	72×	body	80	valid
4.0ms	11×	body	160	valid

simplify17.0ms

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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.6b

localize11.0ms

Local error

Found 2 expressions with local error:

1.3b	(- 1.0 (cos x))
15.7b	(/ (- 1.0 (cos x)) (* x x))

rewrite61.0ms

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:

7.0ms	(- 1.0 (cos x))
51.0ms	(/ (- 1.0 (cos x)) (* x x))

series91.0ms

Counts

2 → 6

Calls

2 calls:

24.0ms	(- 1.0 (cos x))
66.0ms	(/ (- 1.0 (cos x)) (* x x))

simplify891.0ms

Counts

48 → 48

Iterations

Useful iterations: 2 (267.0ms)

Iter	Nodes	Cost
0	88	507
1	232	489
2	1094	441
done	5001	441

prune213.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize11.0ms

Local error

Found 3 expressions with local error:

0.1b	(* (/ 1 x) (/ (- 1.0 (cos x)) x))
0.1b	(/ (- 1.0 (cos x)) x)
1.3b	(- 1.0 (cos x))

rewrite103.0ms

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:

67.0ms	(* (/ 1 x) (/ (- 1.0 (cos x)) x))
19.0ms	(/ (- 1.0 (cos x)) x)
7.0ms	(- 1.0 (cos x))

series158.0ms

Counts

3 → 9

Calls

3 calls:

56.0ms	(* (/ 1 x) (/ (- 1.0 (cos x)) x))
64.0ms	(/ (- 1.0 (cos x)) x)
37.0ms	(- 1.0 (cos x))

simplify2.9s

Counts

123 → 123

Iterations

Useful iterations: done (2.9s)

Iter	Nodes	Cost
0	189	1536
1	546	1395
2	3228	1245
done	5000	1237

prune357.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize30.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos x) (+ 1.0 (cos x)))
0.4b	(pow (cos x) 3)
0.5b	(+ 1.0 (cos x))
1.1b	(- (pow 1.0 3) (pow (cos x) 3))

rewrite90.0ms

Algorithm

rewrite-expression-head

Rules

35×	`add-sqr-sqrt`
23×	`*-un-lft-identity`
16×	`difference-of-squares`
15×	`unpow-prod-down` `cube-prod`
9×	`add-cube-cbrt` `sqr-pow`
8×	`add-log-exp`
7×	`pow1` `add-exp-log` `add-cbrt-cube`
5×	`distribute-lft-out--`
4×	`associate-r`
3×	`pow-unpow` `associate-l`
2×	`flip3-+` `associate-*r/` `flip-+` `distribute-lft-out`
1×	`difference-cubes` `+-commutative` `distribute-rgt-in` `cube-mult` `pow-to-exp` `sub-neg` `flip3--` `pow-pow` `distribute-lft-in` `diff-log` `unpow3` `pow-prod-down` `pow-exp` `prod-exp` `sum-log` `*-commutative` `flip--` `cbrt-unprod` `rem-cube-cbrt` `unswap-sqr`

Counts

4 → 92

Calls

4 calls:

31.0ms	(* (cos x) (+ 1.0 (cos x)))
4.0ms	(pow (cos x) 3)
13.0ms	(+ 1.0 (cos x))
36.0ms	(- (pow 1.0 3) (pow (cos x) 3))

series171.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(* (cos x) (+ 1.0 (cos x)))
50.0ms	(pow (cos x) 3)
18.0ms	(+ 1.0 (cos x))
69.0ms	(- (pow 1.0 3) (pow (cos x) 3))

simplify2.9s

Counts

104 → 104

Iterations

Useful iterations: done (2.9s)

Iter	Nodes	Cost
0	145	1155
1	412	1045
2	2423	990
done	5000	988

prune443.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

localize39.0ms

Local error

Found 4 expressions with local error:

0.4b	(pow (cos x) 3)
0.5b	(+ 1.0 (cos x))
1.1b	(- (pow 1.0 3) (pow (cos x) 3))
1.2b	(log (exp (- (pow 1.0 3) (pow (cos x) 3))))

rewrite188.0ms

Algorithm

rewrite-expression-head

Rules

57×	`add-sqr-sqrt`
32×	`difference-of-squares`
31×	`*-un-lft-identity`
27×	`unpow-prod-down` `cube-prod`
26×	`log-pow`
25×	`exp-prod`
17×	`sqr-pow`
10×	`distribute-lft-out--`
9×	`add-cube-cbrt`
8×	`add-log-exp`
6×	`pow1`
5×	`add-exp-log` `log-prod` `add-cbrt-cube`
3×	`pow-unpow`
2×	`difference-cubes` `sub-neg` `exp-sum`
1×	`+-commutative` `cube-mult` `pow-to-exp` `log-div` `flip3--` `pow-pow` `flip3-+` `exp-diff` `diff-log` `unpow3` `rem-log-exp` `pow-exp` `sum-log` `flip--` `flip-+` `distribute-lft-out` `rem-cube-cbrt`

Counts

4 → 109

Calls

4 calls:

4.0ms	(pow (cos x) 3)
7.0ms	(+ 1.0 (cos x))
40.0ms	(- (pow 1.0 3) (pow (cos x) 3))
128.0ms	(log (exp (- (pow 1.0 3) (pow (cos x) 3))))

series224.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(pow (cos x) 3)
16.0ms	(+ 1.0 (cos x))
81.0ms	(- (pow 1.0 3) (pow (cos x) 3))
77.0ms	(log (exp (- (pow 1.0 3) (pow (cos x) 3))))

simplify1.1s

Counts

121 → 121

Iterations

Useful iterations: 2 (339.0ms)

Iter	Nodes	Cost
0	165	1422
1	396	1207
2	1507	1152
done	5000	1152

prune462.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.1b

regimes71.0ms

Accuracy

99.5% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 31.1b

bsearch107.0ms

Steps

Iters	Range		Point
9	5.2366538615162886e-09	1.4124627081995123	0.03201386298905525
7	-3.309911606533295	-0.03117879455470207	-0.033546375590763663

simplify7.0ms

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	35	77
1	48	50
done	48	50

end0.0ms

sample3.3s

Algorithm

intervals

Results

1.6s	1611×	body	2560	valid
561.0ms	1257×	body	1280	valid
493.0ms	1464×	body	640	valid
203.0ms	937×	body	320	valid
150.0ms	2255×	body	80	valid
54.0ms	476×	body	160	valid