Details

sample62.0ms

Algorithm

intervals

Results

23.0ms	58×	body	1280	valid
11.0ms	37×	body	640	valid
11.0ms	126×	body	80	valid
6.0ms	25×	body	320	valid
2.0ms	10×	body	160	valid

simplify264.0ms

Counts

1 → 1

Iterations

Iter	Nodes
17	206
16	206
15	204
14	192
13	143
12	112
11	99
10	90
9	68
8	51
7	40
6	30
5	24
4	21
3	20
2	17
1	13
0	7

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.4b

localize26.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (+ x 1) (- x 1))
0.0b	(/ x (+ x 1))
3.1b	(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))

rewrite111.0ms

Algorithm

rewrite-expression-head

Rules

110×	`*-un-lft-identity`
60×	`times-frac`
57×	`add-sqr-sqrt`
25×	`add-cube-cbrt`
20×	`distribute-lft-out`
18×	`distribute-lft-out--`
14×	`difference-of-squares`
11×	`associate-/r*`
7×	`add-cbrt-cube` `add-exp-log` `associate-/l*`
5×	`difference-of-sqr-1` `add-log-exp`
4×	`associate-/r/`
3×	`pow1` `insert-posit16`
2×	`cbrt-undiv` `clear-num` `frac-2neg` `flip3-+` `flip3--` `div-exp` `flip-+` `div-inv` `flip--` `associate-/l/`
1×	`sub-neg` `diff-log` `frac-sub`

Counts

3 → 117

Calls

3 calls:

37.0ms	(/ (+ x 1) (- x 1))
16.0ms	(/ x (+ x 1))
55.0ms	(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))

series157.0ms

Counts

3 → 9

Calls

3 calls:

27.0ms	(/ (+ x 1) (- x 1))
33.0ms	(/ x (+ x 1))
96.0ms	(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))

simplify1.8s

Counts

126 → 126

Iterations

Iter	Nodes
3	3095
2	992
1	383
0	180

prune882.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize30.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (+ 1 x) (- x 1))
0.0b	(/ x (+ 1 x))
3.1b	(log (exp (- (/ x (+ 1 x)) (/ (+ 1 x) (- x 1)))))
3.1b	(- (/ x (+ 1 x)) (/ (+ 1 x) (- x 1)))

rewrite233.0ms

Algorithm

rewrite-expression-head

Rules

159×	`*-un-lft-identity`
80×	`times-frac`
72×	`add-sqr-sqrt`
31×	`distribute-lft-out--`
28×	`add-cube-cbrt` `distribute-lft-out`
18×	`difference-of-squares`
17×	`log-pow`
16×	`exp-prod`
11×	`associate-/r*`
8×	`add-cbrt-cube` `add-exp-log`
7×	`associate-/l*`
6×	`add-log-exp`
5×	`pow1` `log-prod` `difference-of-sqr-1`
4×	`associate-/r/` `insert-posit16`
2×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `flip3-+` `flip3--` `div-exp` `exp-sum` `flip-+` `div-inv` `flip--` `associate-/l/`
1×	`log-div` `exp-diff` `diff-log` `rem-log-exp` `frac-sub`

Counts

4 → 149

Calls

4 calls:

29.0ms	(/ (+ 1 x) (- x 1))
11.0ms	(/ x (+ 1 x))
134.0ms	(log (exp (- (/ x (+ 1 x)) (/ (+ 1 x) (- x 1)))))
54.0ms	(- (/ x (+ 1 x)) (/ (+ 1 x) (- x 1)))

series225.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(/ (+ 1 x) (- x 1))
23.0ms	(/ x (+ 1 x))
78.0ms	(log (exp (- (/ x (+ 1 x)) (/ (+ 1 x) (- x 1)))))
98.0ms	(- (/ x (+ 1 x)) (/ (+ 1 x) (- x 1)))

simplify1.6s

Counts

161 → 161

Iterations

Iter	Nodes
3	3083
2	1156
1	459
0	219

prune1.1s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ -1 (* x x)) (/ 3 x))
0.1b	(/ (/ 3 x) (* x x))
0.2b	(/ -1 (* x x))
5.0b	(- (- (/ -1 (* x x)) (/ 3 x)) (/ (/ 3 x) (* x x)))

rewrite218.0ms

Algorithm

rewrite-expression-head

Rules

41×	`times-frac`
37×	`add-sqr-sqrt`
27×	`*-un-lft-identity`
21×	`add-cbrt-cube` `add-exp-log`
20×	`add-cube-cbrt`
16×	`associate-/l*`
11×	`add-log-exp`
8×	`cbrt-undiv` `div-exp`
7×	`difference-of-squares`
5×	`frac-sub`
4×	`pow1` `diff-log` `insert-posit16` `div-inv` `distribute-lft-out--`
3×	`sub-neg` `flip3--` `prod-exp` `cbrt-unprod` `flip--`
2×	`clear-num` `associate-/r*` `frac-2neg` `associate--l+`
1×	`associate--l-` `associate-/l/`

Counts

4 → 113

Calls

4 calls:

34.0ms	(- (/ -1 (* x x)) (/ 3 x))
16.0ms	(/ (/ 3 x) (* x x))
6.0ms	(/ -1 (* x x))
159.0ms	(- (- (/ -1 (* x x)) (/ 3 x)) (/ (/ 3 x) (* x x)))

series203.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(- (/ -1 (* x x)) (/ 3 x))
48.0ms	(/ (/ 3 x) (* x x))
38.0ms	(/ -1 (* x x))
40.0ms	(- (- (/ -1 (* x x)) (/ 3 x)) (/ (/ 3 x) (* x x)))

simplify15.4s

Counts

125 → 125

Iterations

Iter	Nodes
3	11891
2	1873
1	540
0	210

prune815.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize39.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (+ x 1) (- x 1))
0.1b	(* (/ x (- (* x x) 1)) (- x 1))
6.7b	(- (* (/ x (- (* x x) 1)) (- x 1)) (/ (+ x 1) (- x 1)))
15.3b	(/ x (- (* x x) 1))

rewrite116.0ms

Algorithm

rewrite-expression-head

Rules

80×	`*-un-lft-identity`
75×	`add-sqr-sqrt`
65×	`times-frac`
39×	`add-cube-cbrt`
26×	`difference-of-squares`
24×	`associate-l`
13×	`associate-/r*` `add-cbrt-cube` `difference-of-sqr-1` `add-exp-log`
8×	`flip3--` `flip--` `distribute-lft-out`
7×	`associate-r` `associate-/l*`
6×	`pow1` `associate-/r/` `distribute-lft-out--` `add-log-exp`
5×	`sub-neg` `frac-sub`
4×	`distribute-rgt-in` `frac-times` `distribute-lft-in` `associate--l+` `associate-*r/` `insert-posit16`
3×	`cbrt-undiv` `div-exp` `div-inv`
2×	`clear-num` `frac-2neg` `associate-*l/` `prod-exp` `cbrt-unprod` `unswap-sqr` `associate-/l/`
1×	`flip3-+` `diff-log` `pow-prod-down` `*-commutative` `flip-+`

Counts

4 → 176

Calls

4 calls:

17.0ms	(/ (+ x 1) (- x 1))
38.0ms	(* (/ x (- (* x x) 1)) (- x 1))
40.0ms	(- (* (/ x (- (* x x) 1)) (- x 1)) (/ (+ x 1) (- x 1)))
18.0ms	(/ x (- (* x x) 1))

series224.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(/ (+ x 1) (- x 1))
43.0ms	(* (/ x (- (* x x) 1)) (- x 1))
109.0ms	(- (* (/ x (- (* x x) 1)) (- x 1)) (/ (+ x 1) (- x 1)))
48.0ms	(/ x (- (* x x) 1))

simplify1.3s

Counts

188 → 188

Iterations

Iter	Nodes
2	2679
1	714
0	281

prune1.2s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

regimes53.0ms

Accuracy

99.2% (0.2b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 29.6b

bsearch494.0ms

Steps

Iters	Range		Point
9	3862.7483140020904	127843612219.27428	10055.66846222333
10	-1231591086050.0088	-0.0006858147917088189	-11471.638860480614

simplify6.0ms

Iterations

Iter	Nodes
2	35
1	35
0	29

end0.0ms

sample1.8s

Algorithm

intervals

Results

675.0ms	1686×	body	1280	valid
438.0ms	1276×	body	640	valid
302.0ms	4134×	body	80	valid
186.0ms	601×	body	320	valid
41.0ms	303×	body	160	valid

Iter	Nodes
17	206
16	206
15	204
14	192
13	143
12	112
11	99
10	90
9	68
8	51
7	40
6	30
5	24
4	21
3	20
2	17
1	13
0	7

Iter	Nodes
17	206
16	206
15	204
14	192
13	143
12	112
11	99
10	90
9	68
8	51
7	40
6	30
5	24
4	21
3	20
2	17
1	13
0	7

Iter	Nodes
17	206
16	206
15	204
14	192
13	143
12	112
11	99
10	90
9	68
8	51
7	40
6	30
5	24
4	21
3	20
2	17
1	13
0	7