Details

sample89.0ms

Algorithm

intervals

Results

33.0ms	63×	body	640	valid
18.0ms	138×	body	80	valid
13.0ms	19×	body	1280	valid
11.0ms	28×	body	320	valid
2.0ms	8×	body	160	valid

simplify211.0ms

Counts

1 → 1

Iterations

Iter	Nodes
11	195
10	195
9	187
8	132
7	94
6	83
5	75
4	63
3	43
2	33
1	19
0	10

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 8.1b

localize17.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 1 (+ x 1))
0.0b	(- (/ 1 (+ x 1)) (/ 2 x))
1.6b	(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))

rewrite326.0ms

Algorithm

rewrite-expression-head

Rules

718×	`*-un-lft-identity`
694×	`times-frac`
515×	`add-sqr-sqrt`
481×	`add-cube-cbrt`
468×	`prod-diff`
236×	`associate-+l+`
99×	`distribute-lft-out`
71×	`div-inv`
56×	`associate-/r/`
29×	`flip3-+` `flip-+`
18×	`fma-neg` `distribute-lft-out--`
13×	`fma-def`
12×	`difference-of-squares`
10×	`add-log-exp`
7×	`add-exp-log`
5×	`add-cbrt-cube`
4×	`pow1` `associate-/r*`
3×	`expm1-log1p-u` `frac-add` `insert-posit16` `log1p-expm1-u` `associate-/l*`
2×	`sum-log` `sub-neg` `flip3--` `diff-log` `div-exp` `frac-sub` `flip--`
1×	`cbrt-undiv` `+-commutative` `rec-exp` `clear-num` `frac-2neg` `1-exp` `associate-+l-` `pow-flip` `inv-pow`

Counts

3 → 596

Calls

3 calls:

8.0ms	(/ 1 (+ x 1))
55.0ms	(- (/ 1 (+ x 1)) (/ 2 x))
230.0ms	(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))

series208.0ms

Counts

3 → 9

Calls

3 calls:

23.0ms	(/ 1 (+ x 1))
42.0ms	(- (/ 1 (+ x 1)) (/ 2 x))
143.0ms	(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))

simplify1.7s

Counts

605 → 605

Iterations

Iter	Nodes
2	2483
1	1022
0	440

prune6.3s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.2b

localize37.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 1 (+ x 1))
0.0b	(- (/ 1 (+ x 1)) (/ 2 x))
1.6b	(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))

rewrite351.0ms

Algorithm

rewrite-expression-head

Rules

718×	`*-un-lft-identity`
694×	`times-frac`
515×	`add-sqr-sqrt`
481×	`add-cube-cbrt`
468×	`prod-diff`
236×	`associate-+l+`
99×	`distribute-lft-out`
71×	`div-inv`
56×	`associate-/r/`
29×	`flip3-+` `flip-+`
18×	`fma-neg` `distribute-lft-out--`
13×	`fma-def`
12×	`difference-of-squares`
10×	`add-log-exp`
7×	`add-exp-log`
5×	`add-cbrt-cube`
4×	`pow1` `associate-/r*`
3×	`expm1-log1p-u` `frac-add` `insert-posit16` `log1p-expm1-u` `associate-/l*`
2×	`sum-log` `sub-neg` `flip3--` `diff-log` `div-exp` `frac-sub` `flip--`
1×	`cbrt-undiv` `+-commutative` `rec-exp` `clear-num` `frac-2neg` `1-exp` `associate-+l-` `pow-flip` `inv-pow`

Counts

3 → 596

Calls

3 calls:

16.0ms	(/ 1 (+ x 1))
48.0ms	(- (/ 1 (+ x 1)) (/ 2 x))
256.0ms	(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))

series174.0ms

Counts

3 → 9

Calls

3 calls:

15.0ms	(/ 1 (+ x 1))
35.0ms	(- (/ 1 (+ x 1)) (/ 2 x))
124.0ms	(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))

simplify1.6s

Counts

605 → 605

Iterations

Iter	Nodes
2	2483
1	1022
0	440

prune5.9s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.2b

localize31.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ 1 (- x 1)) (/ 1 (- x 1)))
0.2b	(* (- (/ 1 (+ x 1)) (/ 2 x)) (- (/ 1 (+ x 1)) (/ 2 x)))
1.6b	(- (* (- (/ 1 (+ x 1)) (/ 2 x)) (- (/ 1 (+ x 1)) (/ 2 x))) (* (/ 1 (- x 1)) (/ 1 (- x 1))))
16.3b	(/ (- (* (- (/ 1 (+ x 1)) (/ 2 x)) (- (/ 1 (+ x 1)) (/ 2 x))) (* (/ 1 (- x 1)) (/ 1 (- x 1)))) (- (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1))))

rewrite1.0s

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:

32.0ms	(* (/ 1 (- x 1)) (/ 1 (- x 1)))
292.0ms	(* (- (/ 1 (+ x 1)) (/ 2 x)) (- (/ 1 (+ x 1)) (/ 2 x)))
134.0ms	(- (* (- (/ 1 (+ x 1)) (/ 2 x)) (- (/ 1 (+ x 1)) (/ 2 x))) (* (/ 1 (- x 1)) (/ 1 (- x 1))))
480.0ms	(/ (- (* (- (/ 1 (+ x 1)) (/ 2 x)) (- (/ 1 (+ x 1)) (/ 2 x))) (* (/ 1 (- x 1)) (/ 1 (- x 1)))) (- (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1))))

series645.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(* (/ 1 (- x 1)) (/ 1 (- x 1)))
46.0ms	(* (- (/ 1 (+ x 1)) (/ 2 x)) (- (/ 1 (+ x 1)) (/ 2 x)))
145.0ms	(- (* (- (/ 1 (+ x 1)) (/ 2 x)) (- (/ 1 (+ x 1)) (/ 2 x))) (* (/ 1 (- x 1)) (/ 1 (- x 1))))
422.0ms	(/ (- (* (- (/ 1 (+ x 1)) (/ 2 x)) (- (/ 1 (+ x 1)) (/ 2 x))) (* (/ 1 (- x 1)) (/ 1 (- x 1)))) (- (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1))))

simplify3.6s

Counts

1434 → 1434

Iterations

Iter	Nodes
1	3689
0	1359

prune20.6s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.2b

localize44.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (/ 1 (+ x 1)) (/ 2 x)) (- (/ 1 (+ x 1)) (/ 2 x)))
1.6b	(- (/ (* (- (/ 1 (+ x 1)) (/ 2 x)) (- (/ 1 (+ x 1)) (/ 2 x))) (- (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))) (/ (* (/ 1 (- x 1)) (/ 1 (- x 1))) (- (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))))
16.3b	(/ (* (/ 1 (- x 1)) (/ 1 (- x 1))) (- (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1))))
32.5b	(/ (* (- (/ 1 (+ x 1)) (/ 2 x)) (- (/ 1 (+ x 1)) (/ 2 x))) (- (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1))))

rewrite2.9s

Algorithm

rewrite-expression-head

Rules

3022×	`*-un-lft-identity`
2310×	`times-frac`
1129×	`distribute-lft-out--`
1093×	`prod-diff`
1037×	`add-sqr-sqrt`
574×	`add-cube-cbrt`
400×	`div-inv`
327×	`associate-/r/`
237×	`frac-sub`
236×	`distribute-rgt-in` `distribute-lft-in`
194×	`distribute-lft-out`
193×	`difference-of-squares`
127×	`flip3--` `flip--`
69×	`add-exp-log`
35×	`div-exp`
32×	`associate-/r*`
29×	`add-cbrt-cube`
26×	`flip3-+` `flip-+`
25×	`fma-neg`
21×	`swap-sqr`
19×	`frac-times` `associate-/l/`
18×	`prod-exp`
13×	`associate-r` `associate-l`
11×	`pow1` `cbrt-undiv`
8×	`rec-exp` `1-exp`
7×	`associate-l/` `associate-r/`
6×	`distribute-rgt-out--` `cbrt-unprod` `add-log-exp`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`sub-neg`
2×	`clear-num` `frac-2neg` `associate-/l*`
1×	`pow2` `pow-plus` `diff-log` `pow-prod-down` `pow-sqr` `un-div-inv` `*-commutative` `pow-prod-up` `sub-div` `unswap-sqr`

Counts

4 → 1378

Calls

4 calls:

228.0ms	(* (- (/ 1 (+ x 1)) (/ 2 x)) (- (/ 1 (+ x 1)) (/ 2 x)))
1.9s	(- (/ (* (- (/ 1 (+ x 1)) (/ 2 x)) (- (/ 1 (+ x 1)) (/ 2 x))) (- (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))) (/ (* (/ 1 (- x 1)) (/ 1 (- x 1))) (- (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))))
238.0ms	(/ (* (/ 1 (- x 1)) (/ 1 (- x 1))) (- (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1))))
424.0ms	(/ (* (- (/ 1 (+ x 1)) (/ 2 x)) (- (/ 1 (+ x 1)) (/ 2 x))) (- (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1))))

series1.3s

Counts

4 → 12

Calls

4 calls:

54.0ms	(* (- (/ 1 (+ x 1)) (/ 2 x)) (- (/ 1 (+ x 1)) (/ 2 x)))
990.0ms	(- (/ (* (- (/ 1 (+ x 1)) (/ 2 x)) (- (/ 1 (+ x 1)) (/ 2 x))) (- (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))) (/ (* (/ 1 (- x 1)) (/ 1 (- x 1))) (- (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))))
94.0ms	(/ (* (/ 1 (- x 1)) (/ 1 (- x 1))) (- (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1))))
130.0ms	(/ (* (- (/ 1 (+ x 1)) (/ 2 x)) (- (/ 1 (+ x 1)) (/ 2 x))) (- (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1))))

simplify2.9s

Counts

1390 → 1390

Iterations

Iter	Nodes
1	3397
0	1394

prune14.6s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.2b

regimes66.0ms

Accuracy

90.8% (0.8b remaining)

Error of 1.1b against oracle of 0.3b and baseline of 9.4b

bsearch1.0ms

simplify5.0ms

Iterations

Iter	Nodes
2	35
1	35
0	27

end0.0ms

sample1.8s

Algorithm

intervals

Results

557.0ms	1853×	body	640	valid
491.0ms	901×	body	320	valid
369.0ms	4191×	body	80	valid
220.0ms	622×	body	1280	valid
78.0ms	436×	body	160	valid