Details

sample53.0ms

Algorithm

intervals

Results

21.0ms	60×	body	640	valid
9.0ms	124×	body	80	valid
7.0ms	34×	body	320	valid
6.0ms	18×	body	1280	valid
3.0ms	20×	body	160	valid

simplify213.0ms

Counts

1 → 1

Iterations

Iter	Nodes
11	214
10	214
9	204
8	139
7	97
6	86
5	78
4	65
3	45
2	35
1	21
0	10

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 9.9b

localize39.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (- x 1))
0.0b	(/ 1 (+ x 1))
0.0b	(- (/ 1 (+ x 1)) (/ 2 x))
3.4b	(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))

rewrite330.0ms

Algorithm

rewrite-expression-head

Rules

743×	`*-un-lft-identity`
715×	`times-frac`
544×	`add-sqr-sqrt`
494×	`add-cube-cbrt`
468×	`prod-diff`
236×	`associate-+l+`
99×	`distribute-lft-out`
72×	`div-inv`
58×	`associate-/r/`
29×	`flip3-+` `flip-+`
22×	`distribute-lft-out--`
20×	`difference-of-squares`
18×	`fma-neg`
13×	`fma-def`
12×	`add-exp-log`
11×	`associate-/r*` `add-log-exp`
8×	`add-cbrt-cube`
6×	`pow1` `associate-/l*`
4×	`expm1-log1p-u` `difference-of-sqr-1` `div-exp` `insert-posit16` `log1p-expm1-u`
3×	`flip3--` `frac-add` `flip--`
2×	`cbrt-undiv` `rec-exp` `clear-num` `sum-log` `sub-neg` `frac-2neg` `diff-log` `1-exp` `frac-sub` `pow-flip` `inv-pow`
1×	`+-commutative` `associate-+l-`

Counts

4 → 648

Calls

4 calls:

14.0ms	(/ 1 (- x 1))
9.0ms	(/ 1 (+ x 1))
54.0ms	(- (/ 1 (+ x 1)) (/ 2 x))
232.0ms	(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))

series183.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(/ 1 (- x 1))
14.0ms	(/ 1 (+ x 1))
31.0ms	(- (/ 1 (+ x 1)) (/ 2 x))
111.0ms	(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))

simplify1.4s

Counts

660 → 660

Iterations

Iter	Nodes
2	2694
1	1123
0	495

prune6.4s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize44.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (- x 1))
0.0b	(/ 1 (+ x 1))
0.0b	(- (/ 1 (+ x 1)) (/ 2 x))
3.4b	(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))

rewrite279.0ms

Algorithm

rewrite-expression-head

Rules

743×	`*-un-lft-identity`
715×	`times-frac`
544×	`add-sqr-sqrt`
494×	`add-cube-cbrt`
468×	`prod-diff`
236×	`associate-+l+`
99×	`distribute-lft-out`
72×	`div-inv`
58×	`associate-/r/`
29×	`flip3-+` `flip-+`
22×	`distribute-lft-out--`
20×	`difference-of-squares`
18×	`fma-neg`
13×	`fma-def`
12×	`add-exp-log`
11×	`associate-/r*` `add-log-exp`
8×	`add-cbrt-cube`
6×	`pow1` `associate-/l*`
4×	`expm1-log1p-u` `difference-of-sqr-1` `div-exp` `insert-posit16` `log1p-expm1-u`
3×	`flip3--` `frac-add` `flip--`
2×	`cbrt-undiv` `rec-exp` `clear-num` `sum-log` `sub-neg` `frac-2neg` `diff-log` `1-exp` `frac-sub` `pow-flip` `inv-pow`
1×	`+-commutative` `associate-+l-`

Counts

4 → 648

Calls

4 calls:

15.0ms	(/ 1 (- x 1))
8.0ms	(/ 1 (+ x 1))
39.0ms	(- (/ 1 (+ x 1)) (/ 2 x))
190.0ms	(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))

series201.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(/ 1 (- x 1))
26.0ms	(/ 1 (+ x 1))
38.0ms	(- (/ 1 (+ x 1)) (/ 2 x))
112.0ms	(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))

simplify1.2s

Counts

660 → 660

Iterations

Iter	Nodes
2	2694
1	1123
0	495

prune6.5s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

localize50.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ 1 (- x 1)) (/ 1 (- x 1)))
0.3b	(* (- (/ 1 (+ x 1)) (/ 2 x)) (- (/ 1 (+ x 1)) (/ 2 x)))
3.4b	(- (* (- (/ 1 (+ x 1)) (/ 2 x)) (- (/ 1 (+ x 1)) (/ 2 x))) (* (/ 1 (- x 1)) (/ 1 (- x 1))))
11.4b	(/ (- (* (- (/ 1 (+ x 1)) (/ 2 x)) (- (/ 1 (+ x 1)) (/ 2 x))) (* (/ 1 (- x 1)) (/ 1 (- x 1)))) (- (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1))))

rewrite971.0ms

Algorithm

rewrite-expression-head

Rules

1672×	`*-un-lft-identity`
1578×	`times-frac`
1191×	`add-sqr-sqrt`
1002×	`add-cube-cbrt`
937×	`prod-diff`
472×	`distribute-rgt-in` `distribute-lft-in` `associate--l+`
196×	`frac-sub`
172×	`distribute-lft-out`
164×	`div-inv`
146×	`distribute-lft-out--`
117×	`associate-/r/`
112×	`frac-times`
87×	`difference-of-squares`
80×	`flip3--` `flip--`
62×	`swap-sqr` `associate-/l/`
58×	`associate-l/` `associate-r/`
52×	`flip3-+` `flip-+`
48×	`add-exp-log`
40×	`associate-r` `associate-l`
31×	`un-div-inv`
26×	`pow1`
20×	`add-cbrt-cube`
18×	`difference-of-sqr-1`
17×	`div-exp` `prod-exp`
16×	`associate-/r*`
10×	`unswap-sqr`
8×	`rec-exp` `1-exp` `pow-flip` `inv-pow`
6×	`pow-prod-up` `add-log-exp`
5×	`cbrt-undiv` `sub-neg` `cbrt-unprod`
4×	`expm1-log1p-u` `pow-prod-down` `pow-sqr` `insert-posit16` `log1p-expm1-u` `associate-/l*`
2×	`pow2` `pow-plus` `*-commutative`
1×	`clear-num` `frac-2neg` `fma-neg` `diff-log` `div-sub`

Counts

4 → 1422

Calls

4 calls:

60.0ms	(* (/ 1 (- x 1)) (/ 1 (- x 1)))
294.0ms	(* (- (/ 1 (+ x 1)) (/ 2 x)) (- (/ 1 (+ x 1)) (/ 2 x)))
108.0ms	(- (* (- (/ 1 (+ x 1)) (/ 2 x)) (- (/ 1 (+ x 1)) (/ 2 x))) (* (/ 1 (- x 1)) (/ 1 (- x 1))))
443.0ms	(/ (- (* (- (/ 1 (+ x 1)) (/ 2 x)) (- (/ 1 (+ x 1)) (/ 2 x))) (* (/ 1 (- x 1)) (/ 1 (- x 1)))) (- (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1))))

series659.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(* (/ 1 (- x 1)) (/ 1 (- x 1)))
58.0ms	(* (- (/ 1 (+ x 1)) (/ 2 x)) (- (/ 1 (+ x 1)) (/ 2 x)))
148.0ms	(- (* (- (/ 1 (+ x 1)) (/ 2 x)) (- (/ 1 (+ x 1)) (/ 2 x))) (* (/ 1 (- x 1)) (/ 1 (- x 1))))
434.0ms	(/ (- (* (- (/ 1 (+ x 1)) (/ 2 x)) (- (/ 1 (+ x 1)) (/ 2 x))) (* (/ 1 (- x 1)) (/ 1 (- x 1)))) (- (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1))))

simplify2.7s

Counts

1434 → 1434

Iterations

Iter	Nodes
1	3689
0	1359

prune20.1s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.2b

localize44.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* x x) x)
0.1b	(/ 2 (pow x 7))
0.3b	(/ 2 (* (* x x) x))
0.3b	(/ 2 (pow x 5))

rewrite82.0ms

Algorithm

rewrite-expression-head

Rules

45×	`times-frac`
40×	`add-sqr-sqrt`
39×	`*-un-lft-identity` `add-cube-cbrt`
28×	`add-exp-log`
24×	`unpow-prod-down`
23×	`pow1`
22×	`add-cbrt-cube`
15×	`associate-/r*`
9×	`div-exp` `associate-/l*`
8×	`sqr-pow`
6×	`pow-plus` `prod-exp` `pow-prod-up` `cbrt-unprod`
5×	`cbrt-undiv`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`clear-num` `frac-2neg` `associate-r` `pow-prod-down` `div-inv`
2×	`pow2` `pow-to-exp` `pow-exp` `pow-sqr`
1×	`associate-l` `pow3` `*-commutative` `unswap-sqr`

Counts

4 → 153

Calls

4 calls:

29.0ms	(* (* x x) x)
10.0ms	(/ 2 (pow x 7))
28.0ms	(/ 2 (* (* x x) x))
10.0ms	(/ 2 (pow x 5))

series315.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(* (* x x) x)
123.0ms	(/ 2 (pow x 7))
54.0ms	(/ 2 (* (* x x) x))
80.0ms	(/ 2 (pow x 5))

simplify1.6s

Counts

165 → 165

Iterations

Iter	Nodes
3	3494
2	1204
1	411
0	215

prune1.7s

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0.0b

regimes168.0ms

Accuracy

98.6% (0.1b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 9.7b

bsearch186.0ms

Steps

Iters	Range		Point
10	1.6697130628152668	4649870806659.843	109.57651104194328
8	-174.255226838109	-0.11981472621416538	-118.48907173078551

simplify12.0ms

Iterations

Iter	Nodes
2	39
1	39
0	31

end0.0ms

sample2.8s

Algorithm

intervals

Results

916.0ms	1890×	body	640	valid
788.0ms	537×	body	1280	valid
533.0ms	4160×	body	80	valid
323.0ms	926×	body	320	valid
143.0ms	490×	body	160	valid