Details

sample128.0ms

Algorithm

intervals

Results

52.0ms	57×	body	2560	valid
26.0ms	45×	body	640	valid
17.0ms	37×	body	1280	valid
11.0ms	38×	body	320	valid
4.0ms	66×	body	80	valid
2.0ms	13×	body	160	valid

simplify29.0ms

Counts

1 → 1

Iterations

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

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.3b

localize20.0ms

Local error

Found 2 expressions with local error:

1.3b	(- 1.0 (cos x))
16.9b	(/ (- 1.0 (cos x)) (* x x))

rewrite45.0ms

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:

10.0ms	(- 1.0 (cos x))
33.0ms	(/ (- 1.0 (cos x)) (* x x))

series106.0ms

Counts

2 → 6

Calls

2 calls:

28.0ms	(- 1.0 (cos x))
78.0ms	(/ (- 1.0 (cos x)) (* x x))

simplify1.6s

Counts

48 → 48

Iterations

Iter	Nodes
done	5074
3	2415
2	651
1	217
0	88

prune222.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize25.0ms

Local error

Found 3 expressions with local error:

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

rewrite77.0ms

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:

25.0ms	(/ (- 1.0 (cos x)) x)
40.0ms	(* (/ 1 x) (/ (- 1.0 (cos x)) x))
5.0ms	(- 1.0 (cos x))

series167.0ms

Counts

3 → 9

Calls

3 calls:

55.0ms	(/ (- 1.0 (cos x)) x)
77.0ms	(* (/ 1 x) (/ (- 1.0 (cos x)) x))
34.0ms	(- 1.0 (cos x))

simplify1.7s

Counts

123 → 123

Iterations

Iter	Nodes
done	5000
2	1520
1	524
0	189

prune447.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 3 expressions with local error:

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

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 147

Calls

3 calls:

28.0ms	(/ (/ (- 1.0 (cos x)) x) x)
20.0ms	(/ (- 1.0 (cos x)) x)
5.0ms	(- 1.0 (cos x))

series191.0ms

Counts

3 → 9

Calls

3 calls:

83.0ms	(/ (/ (- 1.0 (cos x)) x) x)
78.0ms	(/ (- 1.0 (cos x)) x)
30.0ms	(- 1.0 (cos x))

simplify1.6s

Counts

156 → 156

Iterations

Iter	Nodes
done	5001
2	1389
1	530
0	229

prune628.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (cos x) x)
0.1b	(* (/ 1 x) (- (/ 1.0 x) (/ (cos x) x)))
1.5b	(- (/ 1.0 x) (/ (cos x) x))

rewrite143.0ms

Algorithm

rewrite-expression-head

Rules

54×	`add-sqr-sqrt`
40×	`*-un-lft-identity` `times-frac`
23×	`add-cube-cbrt`
14×	`add-exp-log`
13×	`associate-l`
12×	`associate-r`
10×	`add-cbrt-cube`
8×	`distribute-lft-out--` `difference-of-squares`
6×	`div-inv`
5×	`pow1` `add-log-exp`
4×	`frac-times` `prod-exp` `associate-*r/`
3×	`associate-/r` `sub-neg` `flip3--` `div-exp` `frac-sub` `flip--` `associate-/l` `sub-div` `unswap-sqr`
2×	`distribute-rgt-in` `cbrt-undiv` `distribute-lft-in` `distribute-rgt-out--` `cbrt-unprod`
1×	`rec-exp` `clear-num` `frac-2neg` `diff-log` `1-exp` `pow-prod-down` `associate-l/` `-commutative`

Counts

3 → 106

Calls

3 calls:

12.0ms	(/ (cos x) x)
96.0ms	(* (/ 1 x) (- (/ 1.0 x) (/ (cos x) x)))
29.0ms	(- (/ 1.0 x) (/ (cos x) x))

series324.0ms

Counts

3 → 9

Calls

3 calls:

45.0ms	(/ (cos x) x)
173.0ms	(* (/ 1 x) (- (/ 1.0 x) (/ (cos x) x)))
106.0ms	(- (/ 1.0 x) (/ (cos x) x))

simplify2.3s

Counts

115 → 115

Iterations

Iter	Nodes
done	5011
3	4530
2	1475
1	504
0	193

prune376.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 0.0b

regimes158.0ms

Accuracy

99.6% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 31.2b

bsearch101.0ms

Steps

Iters	Range		Point
11	3.4817375791661903e-26	573579.0075499975	0.027390056951785625
10	-84463.33967257517	-3.2432757514909933e-09	-0.03115379972147734

simplify5.0ms

Iterations

Iter	Nodes
done	26
1	26
0	20

end0.0ms

sample3.6s

Algorithm

intervals

Results

1.3s	1285×	body	1280	valid
1.1s	1647×	body	2560	valid
626.0ms	1515×	body	640	valid
208.0ms	927×	body	320	valid
125.0ms	2168×	body	80	valid
56.0ms	458×	body	160	valid