Details

sample63.0ms

Algorithm

intervals

Results

23.0ms	60×	body	640	valid
13.0ms	140×	body	80	valid
7.0ms	26×	body	320	valid
7.0ms	14×	body	1280	valid
3.0ms	16×	body	160	valid

simplify555.0ms

Counts

1 → 1

Iterations

Iter	Nodes
11	157
10	157
9	154
8	144
7	128
6	108
5	97
4	93
3	84
2	62
1	41
0	10

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 8.2b

localize35.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (+ x 1))
0.0b	(- (/ 1 (+ x 1)) (/ 2 x))
0.0b	(/ 1 (- x 1))
3.2b	(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))

rewrite299.0ms

Algorithm

rewrite-expression-head

Rules

98×	`*-un-lft-identity`
58×	`add-sqr-sqrt`
56×	`times-frac`
25×	`add-cube-cbrt`
18×	`distribute-lft-out--`
17×	`distribute-lft-out`
14×	`difference-of-squares`
12×	`add-exp-log`
11×	`associate-/r*` `add-log-exp`
8×	`add-cbrt-cube` `div-inv`
6×	`pow1` `associate-/l*`
4×	`difference-of-sqr-1` `div-exp` `associate-/r/` `insert-posit16`
3×	`flip3--` `frac-add` `flip--`
2×	`cbrt-undiv` `rec-exp` `associate-+l+` `clear-num` `sum-log` `sub-neg` `frac-2neg` `flip3-+` `diff-log` `1-exp` `frac-sub` `flip-+` `pow-flip` `inv-pow`
1×	`+-commutative` `associate-+l-`

Counts

4 → 141

Calls

4 calls:

9.0ms	(/ 1 (+ x 1))
31.0ms	(- (/ 1 (+ x 1)) (/ 2 x))
10.0ms	(/ 1 (- x 1))
247.0ms	(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))

series186.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(/ 1 (+ x 1))
39.0ms	(- (/ 1 (+ x 1)) (/ 2 x))
29.0ms	(/ 1 (- x 1))
103.0ms	(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))

simplify1.8s

Counts

153 → 153

Iterations

Iter	Nodes
3	4835
2	1897
1	869
0	219

prune1.4s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.1b

localize45.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (/ 2 (pow x 5)) (/ (/ 2 x) (* x x)))
0.0b	(/ 2 (pow x 7))
0.1b	(/ 2 (pow x 5))
0.1b	(/ (/ 2 x) (* x x))

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

73×	`times-frac`
52×	`*-un-lft-identity`
50×	`add-sqr-sqrt` `add-cube-cbrt`
26×	`add-exp-log`
24×	`unpow-prod-down`
20×	`add-cbrt-cube`
19×	`associate-/l*`
15×	`associate-/r*`
12×	`div-exp`
8×	`cbrt-undiv` `sqr-pow`
6×	`add-log-exp`
5×	`div-inv`
4×	`pow1` `insert-posit16`
3×	`clear-num` `frac-2neg`
2×	`pow-to-exp` `pow-exp` `prod-exp` `cbrt-unprod`
1×	`+-commutative` `sum-log` `flip3-+` `frac-add` `flip-+` `distribute-lft-out` `associate-/l/`

Counts

4 → 153

Calls

4 calls:

33.0ms	(+ (/ 2 (pow x 5)) (/ (/ 2 x) (* x x)))
5.0ms	(/ 2 (pow x 7))
5.0ms	(/ 2 (pow x 5))
16.0ms	(/ (/ 2 x) (* x x))

series416.0ms

Counts

4 → 12

Calls

4 calls:

182.0ms	(+ (/ 2 (pow x 5)) (/ (/ 2 x) (* x x)))
96.0ms	(/ 2 (pow x 7))
90.0ms	(/ 2 (pow x 5))
48.0ms	(/ (/ 2 x) (* x x))

simplify653.0ms

Counts

165 → 165

Iterations

Iter	Nodes
2	2399
1	1014
0	264

prune1.4s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize31.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 2 (pow x 7))
0.1b	(/ (/ (/ 2 x) x) x)
0.1b	(/ 2 (pow x 5))
0.1b	(/ (/ 2 x) x)

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

510×	`times-frac`
262×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
62×	`associate-/l*`
28×	`add-exp-log`
24×	`unpow-prod-down` `div-inv`
22×	`add-cbrt-cube`
20×	`associate-/r*`
15×	`div-exp`
11×	`cbrt-undiv`
8×	`sqr-pow`
4×	`pow1` `clear-num` `frac-2neg` `insert-posit16` `add-log-exp`
2×	`pow-to-exp` `pow-exp` `associate-/l/`

Counts

4 → 356

Calls

4 calls:

6.0ms	(/ 2 (pow x 7))
11.0ms	(/ (/ (/ 2 x) x) x)
5.0ms	(/ 2 (pow x 5))
7.0ms	(/ (/ 2 x) x)

series205.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(/ 2 (pow x 7))
45.0ms	(/ (/ (/ 2 x) x) x)
57.0ms	(/ 2 (pow x 5))
33.0ms	(/ (/ 2 x) x)

simplify1.3s

Counts

368 → 368

Iterations

Iter	Nodes
2	3707
1	1969
0	557

prune3.6s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

localize29.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 2 (pow x 7))
0.1b	(/ 2 (pow x 5))
0.1b	(* (/ 1 x) (/ 2 (* x x)))
0.5b	(/ 2 (* x x))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

64×	`times-frac`
61×	`add-sqr-sqrt`
58×	`add-exp-log`
49×	`*-un-lft-identity`
47×	`add-cube-cbrt`
34×	`add-cbrt-cube`
24×	`unpow-prod-down`
22×	`div-exp`
17×	`prod-exp`
15×	`associate-/r*`
13×	`associate-l`
11×	`cbrt-undiv`
9×	`cbrt-unprod` `associate-/l*`
8×	`sqr-pow`
7×	`associate-r`
6×	`pow1` `unswap-sqr`
5×	`div-inv`
4×	`insert-posit16` `add-log-exp`
3×	`rec-exp` `clear-num` `frac-2neg` `1-exp`
2×	`pow-to-exp` `pow-exp`
1×	`frac-times` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative`

Counts

4 → 171

Calls

4 calls:

5.0ms	(/ 2 (pow x 7))
5.0ms	(/ 2 (pow x 5))
31.0ms	(* (/ 1 x) (/ 2 (* x x)))
6.0ms	(/ 2 (* x x))

series226.0ms

Counts

4 → 12

Calls

4 calls:

84.0ms	(/ 2 (pow x 7))
65.0ms	(/ 2 (pow x 5))
47.0ms	(* (/ 1 x) (/ 2 (* x x)))
30.0ms	(/ 2 (* x x))

simplify625.0ms

Counts

183 → 183

Iterations

Iter	Nodes
2	2423
1	1013
0	262

prune1.9s

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0b

regimes110.0ms

Accuracy

99.5% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 9.7b

bsearch188.0ms

Steps

Iters	Range		Point
9	0.8715059566266286	7213346.136357025	124.52448790004959
9	-2698469.12756182	-0.2100461492707554	-105.47328403477972

simplify5.0ms

Iterations

Iter	Nodes
2	35
1	35
0	26

end0.0ms

sample2.7s

Algorithm

intervals

Results

1.2s	1872×	body	640	valid
554.0ms	4214×	body	80	valid
356.0ms	931×	body	320	valid
318.0ms	562×	body	1280	valid
78.0ms	423×	body	160	valid