Details

sample49.0ms

Algorithm

intervals

Results

14.0ms	51×	body	1280	valid
8.0ms	39×	body	640	valid
7.0ms	130×	body	80	valid
3.0ms	21×	body	320	valid
2.0ms	15×	body	160	valid

simplify148.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	13
1	12	13
2	16	13
3	19	13
4	21	13
5	27	13
6	39	13
7	58	13
8	77	13
9	99	13
10	113	13
11	119	13
12	123	13
done	123	13

prune1.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.4b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ x (+ x 1.0))
0.0b	(/ (+ x 1.0) (- x 1.0))
4.5b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite330.0ms

Algorithm

rewrite-expression-head

Rules

981×	`*-un-lft-identity`
736×	`times-frac`
585×	`add-sqr-sqrt`
468×	`prod-diff`
419×	`add-cube-cbrt`
189×	`distribute-lft-out`
94×	`associate-/r/`
90×	`distribute-lft-out--`
81×	`difference-of-squares`
47×	`div-inv`
29×	`flip3-+` `flip-+`
20×	`flip3--` `flip--`
18×	`fma-neg`
9×	`associate-/r*`
7×	`add-exp-log` `add-cbrt-cube` `associate-/l*`
5×	`add-log-exp`
3×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
2×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `associate-/l/`
1×	`sub-neg` `diff-log` `frac-sub`

Counts

3 → 596

Calls

3 calls:

13.0ms	(/ x (+ x 1.0))
32.0ms	(/ (+ x 1.0) (- x 1.0))
210.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series237.0ms

Counts

3 → 9

Calls

3 calls:

37.0ms	(/ x (+ x 1.0))
54.0ms	(/ (+ x 1.0) (- x 1.0))
147.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify3.4s

Counts

605 → 605

Iterations

Useful iterations: done (3.3s)

Iter	Nodes	Cost
0	523	34216
1	1199	30851
2	2823	22735
done	5000	16848

prune686.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- x 1.0) (+ x 1.0))
0.0b	(/ x (+ x 1.0))
0.0b	(/ 1 (/ (- x 1.0) (+ x 1.0)))
4.5b	(- (/ x (+ x 1.0)) (/ 1 (/ (- x 1.0) (+ x 1.0))))

rewrite820.0ms

Algorithm

rewrite-expression-head

Rules

3703×	`times-frac`
3383×	`*-un-lft-identity`
2296×	`add-sqr-sqrt`
1789×	`add-cube-cbrt`
1494×	`prod-diff`
553×	`distribute-lft-out`
307×	`associate-/r/`
247×	`difference-of-squares`
241×	`distribute-lft-out--`
164×	`div-inv`
144×	`flip3-+` `flip-+`
34×	`associate-/r*`
19×	`add-exp-log`
18×	`fma-neg`
13×	`add-cbrt-cube`
11×	`associate-/l*`
9×	`div-exp`
6×	`add-log-exp`
5×	`pow1` `cbrt-undiv`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`frac-2neg` `clear-num`
2×	`rec-exp` `flip3--` `1-exp` `flip--` `associate-/l/`
1×	`sub-neg` `pow-flip` `diff-log` `div-sub` `frac-sub` `inv-pow`

Counts

4 → 1754

Calls

4 calls:

49.0ms	(/ (- x 1.0) (+ x 1.0))
23.0ms	(/ x (+ x 1.0))
41.0ms	(/ 1 (/ (- x 1.0) (+ x 1.0)))
281.0ms	(- (/ x (+ x 1.0)) (/ 1 (/ (- x 1.0) (+ x 1.0))))

series336.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(/ (- x 1.0) (+ x 1.0))
38.0ms	(/ x (+ x 1.0))
45.0ms	(/ 1 (/ (- x 1.0) (+ x 1.0)))
206.0ms	(- (/ x (+ x 1.0)) (/ 1 (/ (- x 1.0) (+ x 1.0))))

simplify2.0s

Counts

1766 → 1766

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	1421	134449
1	3236	105662
done	5000	82921

prune1.8s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize35.0ms

Local error

Found 4 expressions with local error:

12.9b	(/ x (- (* x x) (* 1.0 1.0)))
13.0b	(/ (/ -1 (fma x x (* 1.0 (- 1.0 x)))) (/ (- x 1.0) (+ (pow x 3) (pow 1.0 3))))
13.6b	(* (/ 1 (/ (- x 1.0) (+ (pow x 3) (pow 1.0 3)))) (+ (/ -1 (fma x x (* 1.0 (- 1.0 x)))) (/ 1 (fma x x (* 1.0 (- 1.0 x))))))
29.7b	(fma (/ x (- (* x x) (* 1.0 1.0))) (- x 1.0) (/ (/ -1 (fma x x (* 1.0 (- 1.0 x)))) (/ (- x 1.0) (+ (pow x 3) (pow 1.0 3)))))

rewrite638.0ms

Algorithm

rewrite-expression-head

Rules

2074×	`times-frac`
1857×	`*-un-lft-identity`
1007×	`add-sqr-sqrt`
687×	`add-cube-cbrt`
430×	`distribute-lft-out`
340×	`unpow-prod-down` `cube-prod`
158×	`associate-l`
157×	`difference-of-squares`
153×	`distribute-lft-out--`
85×	`sum-cubes`
78×	`div-inv`
55×	`associate-/r*`
38×	`associate-/r/`
37×	`add-exp-log`
27×	`add-cbrt-cube`
19×	`flip3-+` `flip-+`
16×	`div-exp` `associate-/l*`
12×	`cbrt-undiv` `associate-r`
7×	`prod-exp`
6×	`pow1`
5×	`unswap-sqr`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`frac-times` `distribute-rgt-out` `associate-*r/` `cbrt-unprod`
2×	`rec-exp` `frac-2neg` `1-exp` `frac-add` `clear-num`
1×	`distribute-rgt-in` `flip3--` `distribute-lft-in` `distribute-lft1-in` `pow-prod-down` `associate-l/` `-commutative` `flip--` `fma-udef` `associate-/l/`

Counts

4 → 999

Calls

4 calls:

30.0ms	(/ x (- (* x x) (* 1.0 1.0)))
101.0ms	(/ (/ -1 (fma x x (* 1.0 (- 1.0 x)))) (/ (- x 1.0) (+ (pow x 3) (pow 1.0 3))))
313.0ms	(* (/ 1 (/ (- x 1.0) (+ (pow x 3) (pow 1.0 3)))) (+ (/ -1 (fma x x (* 1.0 (- 1.0 x)))) (/ 1 (fma x x (* 1.0 (- 1.0 x))))))
0.0ms	(fma (/ x (- (* x x) (* 1.0 1.0))) (- x 1.0) (/ (/ -1 (fma x x (* 1.0 (- 1.0 x)))) (/ (- x 1.0) (+ (pow x 3) (pow 1.0 3)))))

series419.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(/ x (- (* x x) (* 1.0 1.0)))
105.0ms	(/ (/ -1 (fma x x (* 1.0 (- 1.0 x)))) (/ (- x 1.0) (+ (pow x 3) (pow 1.0 3))))
5.0ms	(* (/ 1 (/ (- x 1.0) (+ (pow x 3) (pow 1.0 3)))) (+ (/ -1 (fma x x (* 1.0 (- 1.0 x)))) (/ 1 (fma x x (* 1.0 (- 1.0 x))))))
229.0ms	(fma (/ x (- (* x x) (* 1.0 1.0))) (- x 1.0) (/ (/ -1 (fma x x (* 1.0 (- 1.0 x)))) (/ (- x 1.0) (+ (pow x 3) (pow 1.0 3)))))

simplify2.3s

Counts

1011 → 1011

Iterations

Useful iterations: done (2.3s)

Iter	Nodes	Cost
0	1091	42735
1	3352	39372
done	5001	38530

prune4.9s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (/ 1.0 (* x x)) (/ 3.0 x))
0.1b	(/ 3.0 (pow x 3))
0.4b	(/ 1.0 (* x x))
7.8b	(+ (+ (/ 1.0 (* x x)) (/ 3.0 x)) (/ 3.0 (pow x 3)))

rewrite346.0ms

Algorithm

rewrite-expression-head

Rules

43×	`*-un-lft-identity`
42×	`times-frac`
34×	`add-sqr-sqrt` `add-cube-cbrt`
14×	`add-exp-log`
13×	`associate-/r*`
12×	`unpow-prod-down` `cube-prod`
11×	`fma-def` `add-cbrt-cube` `add-log-exp`
6×	`associate-/l*`
5×	`div-exp` `frac-add` `distribute-lft-out`
4×	`pow1` `expm1-log1p-u` `cube-mult` `unpow3` `sum-log` `log1p-expm1-u` `sqr-pow`
3×	`cbrt-undiv` `flip3-+` `flip-+` `div-inv`
2×	`+-commutative` `frac-2neg` `clear-num`
1×	`pow-to-exp` `associate-+l+` `pow-exp` `prod-exp` `cbrt-unprod`

Counts

4 → 136

Calls

4 calls:

33.0ms	(+ (/ 1.0 (* x x)) (/ 3.0 x))
13.0ms	(/ 3.0 (pow x 3))
18.0ms	(/ 1.0 (* x x))
276.0ms	(+ (+ (/ 1.0 (* x x)) (/ 3.0 x)) (/ 3.0 (pow x 3)))

series205.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(+ (/ 1.0 (* x x)) (/ 3.0 x))
50.0ms	(/ 3.0 (pow x 3))
39.0ms	(/ 1.0 (* x x))
49.0ms	(+ (+ (/ 1.0 (* x x)) (/ 3.0 x)) (/ 3.0 (pow x 3)))

simplify1.1s

Counts

148 → 148

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	202	1801
1	455	1547
2	1624	1460
done	5000	1457

prune446.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

regimes61.0ms

Accuracy

99.1% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 29.2b

bsearch190.0ms

Steps

Iters	Range		Point
8	100426.34546533476	68030889.75935516	116203.31990693379
10	-4418200179179808.0	-1501.2167507114543	-254622.29660434803

simplify41.0ms

Iterations

Useful iterations: 1 (22.0ms)

Iter	Nodes	Cost
0	40	115
1	55	98
2	62	98
3	63	98
done	63	98

end0.0ms

sample1.4s

Algorithm

intervals

Results

449.0ms	1741×	body	1280	valid
288.0ms	1222×	body	640	valid
270.0ms	4107×	body	80	valid
124.0ms	614×	body	320	valid
27.0ms	316×	body	160	valid