Details

sample108.0ms

Algorithm

intervals

Results

40.0ms	57×	body	2560	valid
26.0ms	45×	body	640	valid
14.0ms	37×	body	1280	valid
8.0ms	38×	body	320	valid
3.0ms	66×	body	80	valid
2.0ms	13×	body	160	valid

simplify25.0ms

Counts

1 → 1

Iterations

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

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.3b

localize17.0ms

Local error

Found 2 expressions with local error:

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

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt` `*-un-lft-identity`
11×	`add-cube-cbrt`
9×	`prod-diff`
7×	`add-cbrt-cube` `add-exp-log`
5×	`times-frac` `associate-/l*`
4×	`add-log-exp`
3×	`fma-neg` `distribute-lft-out--` `difference-of-squares`
2×	`expm1-log1p-u` `pow1` `cbrt-undiv` `flip3--` `div-exp` `log1p-expm1-u` `flip--` `associate-/l/`
1×	`clear-num` `associate-/r*` `sub-neg` `frac-2neg` `diff-log` `div-sub` `prod-exp` `cbrt-unprod` `div-inv`

Counts

2 → 58

Calls

2 calls:

6.0ms	(- 1.0 (cos x))
21.0ms	(/ (- 1.0 (cos x)) (* x x))

series130.0ms

Counts

2 → 6

Calls

2 calls:

35.0ms	(- 1.0 (cos x))
95.0ms	(/ (- 1.0 (cos x)) (* x x))

simplify2.7s

Counts

64 → 64

Iterations

Iter	Nodes
done	5000
3	4103
2	936
1	290
0	116

prune284.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize18.0ms

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))

rewrite68.0ms

Algorithm

rewrite-expression-head

Rules

69×	`add-sqr-sqrt`
54×	`*-un-lft-identity`
46×	`times-frac`
36×	`add-cube-cbrt`
27×	`add-exp-log`
19×	`associate-r`
17×	`add-cbrt-cube`
13×	`associate-l`
9×	`div-exp` `prod-diff`
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×	`expm1-log1p-u` `associate-/r*` `fma-neg` `log1p-expm1-u` `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 → 132

Calls

3 calls:

14.0ms	(/ (- 1.0 (cos x)) x)
44.0ms	(* (/ 1 x) (/ (- 1.0 (cos x)) x))
6.0ms	(- 1.0 (cos x))

series152.0ms

Counts

3 → 9

Calls

3 calls:

59.0ms	(/ (- 1.0 (cos x)) x)
69.0ms	(* (/ 1 x) (/ (- 1.0 (cos x)) x))
23.0ms	(- 1.0 (cos x))

simplify1.6s

Counts

141 → 141

Iterations

Iter	Nodes
done	5000
2	1785
1	590
0	219

prune478.0ms

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))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

132×	`times-frac`
110×	`add-sqr-sqrt` `*-un-lft-identity`
76×	`add-cube-cbrt`
24×	`associate-/l*`
17×	`distribute-lft-out--` `difference-of-squares`
10×	`add-cbrt-cube` `add-exp-log`
9×	`prod-diff`
6×	`associate-/r*` `div-inv`
5×	`add-log-exp`
4×	`cbrt-undiv` `div-exp`
3×	`expm1-log1p-u` `pow1` `fma-neg` `div-sub` `log1p-expm1-u` `associate-/l/`
2×	`clear-num` `frac-2neg` `flip3--` `flip--`
1×	`sub-neg` `diff-log`

Counts

3 → 165

Calls

3 calls:

17.0ms	(/ (/ (- 1.0 (cos x)) x) x)
14.0ms	(/ (- 1.0 (cos x)) x)
6.0ms	(- 1.0 (cos x))

series171.0ms

Counts

3 → 9

Calls

3 calls:

84.0ms	(/ (/ (- 1.0 (cos x)) x) x)
60.0ms	(/ (- 1.0 (cos x)) x)
26.0ms	(- 1.0 (cos x))

simplify1.7s

Counts

174 → 174

Iterations

Iter	Nodes
done	5003
2	1582
1	604
0	259

prune731.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.0b

localize31.0ms

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))

rewrite266.0ms

Algorithm

rewrite-expression-head

Rules

751×	`times-frac`
607×	`add-sqr-sqrt`
593×	`*-un-lft-identity`
576×	`add-cube-cbrt`
507×	`prod-diff`
171×	`distribute-rgt-in` `distribute-lft-in`
85×	`div-inv`
14×	`add-exp-log`
13×	`fma-neg` `associate-l`
12×	`associate-r`
10×	`add-cbrt-cube`
8×	`distribute-lft-out--` `difference-of-squares`
5×	`pow1` `add-log-exp`
4×	`frac-times` `prod-exp` `associate-*r/`
3×	`expm1-log1p-u` `associate-/r` `sub-neg` `flip3--` `div-exp` `frac-sub` `log1p-expm1-u` `flip--` `associate-/l` `sub-div` `unswap-sqr`
2×	`cbrt-undiv` `distribute-rgt-out--` `cbrt-unprod`
1×	`rec-exp` `clear-num` `frac-2neg` `diff-log` `1-exp` `pow-prod-down` `associate-l/` `-commutative`

Counts

3 → 632

Calls

3 calls:

10.0ms	(/ (cos x) x)
145.0ms	(* (/ 1 x) (- (/ 1.0 x) (/ (cos x) x)))
60.0ms	(- (/ 1.0 x) (/ (cos x) x))

series289.0ms

Counts

3 → 9

Calls

3 calls:

50.0ms	(/ (cos x) x)
158.0ms	(* (/ 1 x) (- (/ 1.0 x) (/ (cos x) x)))
81.0ms	(- (/ 1.0 x) (/ (cos x) x))

simplify2.9s

Counts

641 → 641

Iterations

Iter	Nodes
done	5000
1	2378
0	796

prune3.2s

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 0.0b

regimes180.0ms

Accuracy

99.7% (0.1b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 31.2b

bsearch146.0ms

Steps

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

simplify6.0ms

Iterations

Iter	Nodes
done	22
1	22
0	19

end0.0ms

sample3.8s

Algorithm

intervals

Results

1.5s	1647×	body	2560	valid
645.0ms	927×	body	320	valid
632.0ms	1285×	body	1280	valid
480.0ms	1515×	body	640	valid
229.0ms	2168×	body	80	valid
61.0ms	458×	body	160	valid