Details

sample47.0ms

Algorithm

intervals

Results

19.0ms	64×	body	1280	valid
9.0ms	40×	body	640	valid
7.0ms	124×	body	80	valid
4.0ms	22×	body	320	valid
1.0ms	6×	body	160	valid

simplify143.0ms

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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.2b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (+ x 1) (- x 1))
0.0b	(/ x (+ x 1))
2.3b	(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))

rewrite66.0ms

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`
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 → 114

Calls

3 calls:

18.0ms	(/ (+ x 1) (- x 1))
7.0ms	(/ x (+ x 1))
39.0ms	(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))

series155.0ms

Counts

3 → 9

Calls

3 calls:

32.0ms	(/ (+ x 1) (- x 1))
29.0ms	(/ x (+ x 1))
94.0ms	(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))

simplify1.7s

Counts

123 → 123

Iterations

Iter	Nodes
3	3064
2	989
1	380
0	177

prune711.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.1b	(* x (* x x))
0.5b	(/ 3 (* x (* x x)))
0.8b	(/ -1 (* x x))
5.8b	(- (- (/ -1 (* x x)) (/ 3 x)) (/ 3 (* x (* x x))))

rewrite178.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-cbrt-cube` `add-exp-log`
18×	`pow1`
14×	`*-un-lft-identity`
12×	`add-sqr-sqrt`
9×	`add-cube-cbrt` `add-log-exp`
7×	`prod-exp` `cbrt-unprod`
6×	`times-frac` `associate-/l*`
5×	`cbrt-undiv` `div-exp` `pow-prod-up`
4×	`frac-sub`
3×	`diff-log` `associate-l` `pow-prod-down` `distribute-lft-out--`
2×	`clear-num` `associate-/r*` `sub-neg` `frac-2neg` `flip3--` `associate--l+` `div-inv` `flip--`
1×	`associate--l-` `pow2` `pow-plus` `cube-unmult` `associate-r` `pow-sqr` `*-commutative` `difference-of-squares` `unswap-sqr`

Counts

4 → 90

Calls

4 calls:

11.0ms	(* x (* x x))
11.0ms	(/ 3 (* x (* x x)))
5.0ms	(/ -1 (* x x))
150.0ms	(- (- (/ -1 (* x x)) (/ 3 x)) (/ 3 (* x (* x x))))

series159.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(* x (* x x))
48.0ms	(/ 3 (* x (* x x)))
39.0ms	(/ -1 (* x x))
29.0ms	(- (- (/ -1 (* x x)) (/ 3 x)) (/ 3 (* x (* x x))))

simplify10.4s

Counts

102 → 102

Iterations

Iter	Nodes
3	9209
2	1490
1	403
0	161

prune646.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize31.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (- x 1))
0.0b	(/ x (+ x 1))
0.1b	(* (+ x 1) (/ 1 (- x 1)))
9.6b	(- (/ x (+ x 1)) (* (+ x 1) (/ 1 (- x 1))))

rewrite109.0ms

Algorithm

rewrite-expression-head

Rules

72×	`add-sqr-sqrt`
69×	`*-un-lft-identity`
56×	`times-frac`
37×	`add-cube-cbrt`
27×	`associate-r`
19×	`add-exp-log`
14×	`difference-of-squares`
13×	`add-cbrt-cube`
11×	`associate-/r*`
7×	`pow1` `difference-of-sqr-1` `distribute-lft-out--`
6×	`associate-/r/` `frac-sub` `associate-/l*` `add-log-exp`
5×	`flip3-+` `div-exp` `flip-+` `distribute-lft-out`
4×	`frac-times` `associate-l` `associate-*l/` `prod-exp`
3×	`cbrt-undiv` `flip3--` `div-inv` `flip--` `unswap-sqr`
2×	`rec-exp` `clear-num` `frac-2neg` `1-exp` `associate-*r/` `un-div-inv` `cbrt-unprod`
1×	`sub-neg` `diff-log` `pow-prod-down` `*-commutative` `pow-flip` `inv-pow`

Counts

4 → 155

Calls

4 calls:

9.0ms	(/ 1 (- x 1))
7.0ms	(/ x (+ x 1))
31.0ms	(* (+ x 1) (/ 1 (- x 1)))
60.0ms	(- (/ x (+ x 1)) (* (+ x 1) (/ 1 (- x 1))))

series221.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(/ 1 (- x 1))
37.0ms	(/ x (+ x 1))
40.0ms	(* (+ x 1) (/ 1 (- x 1)))
128.0ms	(- (/ x (+ x 1)) (* (+ x 1) (/ 1 (- x 1))))

simplify2.6s

Counts

167 → 167

Iterations

Iter	Nodes
2	2109
1	586
0	234

prune1.0s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize67.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (- 1 (- x (* x x))) (* x (- x 1)))
8.4b	(/ (- (* (- 1 (- x (* x x))) (* x (- x 1))) (+ (+ 1 (* x (* x x))) (* x (+ 1 (* x (* x x)))))) (* (- 1 (- x (* x x))) (* (- x 1) (+ 1 x))))
10.0b	(+ (+ 1 (* x (* x x))) (* x (+ 1 (* x (* x x)))))
28.4b	(- (* (- 1 (- x (* x x))) (* x (- x 1))) (+ (+ 1 (* x (* x x))) (* x (+ 1 (* x (* x x))))))

rewrite420.0ms

Algorithm

rewrite-expression-head

Rules

186×	`associate-*r/`
98×	`flip3--` `flip--`
96×	`frac-sub`
94×	`flip3-+` `flip-+`
80×	`frac-times`
68×	`frac-add`
50×	`associate-/l/`
34×	`associate-*l/`
26×	`associate-/r/`
18×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
17×	`distribute-rgt-in` `distribute-lft-in`
11×	`*-un-lft-identity`
10×	`add-sqr-sqrt`
9×	`pow1` `sub-neg`
8×	`associate--l+`
7×	`add-cube-cbrt`
6×	`sum-log` `associate-l` `prod-exp` `cbrt-unprod`
3×	`cbrt-undiv` `times-frac` `diff-log` `div-exp` `pow-prod-down` `associate-/l*`
2×	`associate-+r+` `difference-of-squares`
1×	`+-commutative` `associate-+l+` `clear-num` `associate-/r` `frac-2neg` `distribute-rgt-out` `div-sub` `associate-r` `distribute-rgt1-in` `-commutative` `div-inv` `associate--r+` `distribute-lft-out--`

Counts

4 → 229

Calls

4 calls:

77.0ms	(* (- 1 (- x (* x x))) (* x (- x 1)))
235.0ms	(/ (- (* (- 1 (- x (* x x))) (* x (- x 1))) (+ (+ 1 (* x (* x x))) (* x (+ 1 (* x (* x x)))))) (* (- 1 (- x (* x x))) (* (- x 1) (+ 1 x))))
17.0ms	(+ (+ 1 (* x (* x x))) (* x (+ 1 (* x (* x x)))))
82.0ms	(- (* (- 1 (- x (* x x))) (* x (- x 1))) (+ (+ 1 (* x (* x x))) (* x (+ 1 (* x (* x x))))))

series263.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(* (- 1 (- x (* x x))) (* x (- x 1)))
113.0ms	(/ (- (* (- 1 (- x (* x x))) (* x (- x 1))) (+ (+ 1 (* x (* x x))) (* x (+ 1 (* x (* x x)))))) (* (- 1 (- x (* x x))) (* (- x 1) (+ 1 x))))
60.0ms	(+ (+ 1 (* x (* x x))) (* x (+ 1 (* x (* x x)))))
40.0ms	(- (* (- 1 (- x (* x x))) (* x (- x 1))) (+ (+ 1 (* x (* x x))) (* x (+ 1 (* x (* x x))))))

simplify1.3s

Counts

241 → 241

Iterations

Iter	Nodes
1	2273
0	549

prune3.7s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

regimes41.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 30.8b

bsearch216.0ms

Steps

Iters	Range		Point
8	0.9676876931049737	32461.898498684495	9738.110188373239
8	-426929.41805624013	-102.89153151738607	-14872.906038072784

simplify17.0ms

Iterations

Iter	Nodes
2	53
1	53
0	38

end0.0ms

sample2.5s

Algorithm

intervals

Results

1.3s	1752×	body	1280	valid
419.0ms	1260×	body	640	valid
404.0ms	4033×	body	80	valid
184.0ms	648×	body	320	valid
50.0ms	307×	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