Details

sample20.0ms

Algorithm

intervals

Results

5.0ms	51×	body	1280	valid
3.0ms	43×	body	640	valid
3.0ms	134×	body	80	valid
1.0ms	20×	body	320	valid
0.0ms	8×	body	160	valid

simplify119.0ms

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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.9b

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ x (+ x 1.0))
0.0b	(/ (+ x 1.0) (- x 1.0))
2.7b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite210.0ms

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:

11.0ms	(/ x (+ x 1.0))
25.0ms	(/ (+ x 1.0) (- x 1.0))
117.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series198.0ms

Counts

3 → 9

Calls

3 calls:

33.0ms	(/ x (+ x 1.0))
40.0ms	(/ (+ x 1.0) (- x 1.0))
125.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify2.2s

Counts

605 → 605

Iterations

Useful iterations: done (2.2s)

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

prune411.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (+ x 1.0) (- x 1.0))
0.0b	(* (sqrt (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))) (sqrt (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))))
2.7b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))
2.7b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite881.0ms

Algorithm

rewrite-expression-head

Rules

2707×	`*-un-lft-identity`
1732×	`times-frac`
1197×	`add-sqr-sqrt`
936×	`prod-diff`
815×	`add-cube-cbrt`
508×	`distribute-lft-out`
397×	`distribute-lft-out--`
186×	`sqrt-prod`
182×	`associate-/r/`
173×	`difference-of-squares`
91×	`div-inv`
79×	`swap-sqr`
55×	`flip3-+` `flip-+`
47×	`flip3--` `flip--`
36×	`fma-neg`
24×	`sqrt-div`
19×	`pow1` `associate-r` `associate-l`
10×	`frac-sub`
9×	`frac-times`
8×	`add-exp-log` `sqrt-pow1` `pow1/2` `add-cbrt-cube` `add-log-exp`
5×	`associate-/r*` `pow-prod-up`
4×	`expm1-log1p-u` `log1p-expm1-u` `associate-/l*` `unswap-sqr`
3×	`associate-r/` `pow-prod-down` `associate-l/` `pow-sqr`
2×	`sub-neg` `diff-log` `associate-/l/`
1×	`cbrt-undiv` `pow2` `frac-2neg` `pow-plus` `sqrt-unprod` `div-exp` `prod-exp` `clear-num` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 1238

Calls

4 calls:

23.0ms	(/ (+ x 1.0) (- x 1.0))
495.0ms	(* (sqrt (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))) (sqrt (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))))
112.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))
114.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series421.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(/ (+ x 1.0) (- x 1.0))
126.0ms	(* (sqrt (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))) (sqrt (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))))
123.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))
135.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify1.7s

Counts

1250 → 1250

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	603	73295
1	1290	63839
2	3068	47517
done	5000	41564

prune1.2s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 4 expressions with local error:

4.9b	(/ (+ x 1.0) (- (pow x 3) (pow 1.0 3)))
4.9b	(/ (+ x 1.0) (- (pow x 3) (pow 1.0 3)))
15.8b	(+ (- (fma x x (* 1.0 (+ x 1.0)))) (fma x x (* 1.0 (+ x 1.0))))
29.4b	(fma (fma x x (* 1.0 (+ x 1.0))) (- (/ (+ x 1.0) (- (pow x 3) (pow 1.0 3)))) (/ (/ x (cbrt (+ x 1.0))) (* (cbrt (+ 1.0 x)) (cbrt (+ 1.0 x)))))

rewrite141.0ms

Algorithm

rewrite-expression-head

Rules

313×	`add-sqr-sqrt`
281×	`*-un-lft-identity`
200×	`times-frac`
160×	`difference-of-squares`
120×	`unpow-prod-down` `cube-prod`
80×	`sqr-pow`
73×	`add-cube-cbrt`
56×	`distribute-lft-out`
50×	`associate-/r*` `distribute-lft-out--`
10×	`difference-cubes` `fma-def`
8×	`add-exp-log` `add-cbrt-cube` `associate-/l*` `add-log-exp`
7×	`distribute-lft-neg-in`
6×	`distribute-rgt-neg-in`
4×	`pow1` `expm1-log1p-u` `distribute-rgt-out` `associate-/r/` `log1p-expm1-u` `associate-/l/`
3×	`neg-mul-1` `flip3-+` `flip-+` `fma-udef`
2×	`cbrt-undiv` `flip3--` `frac-2neg` `distribute-lft1-in` `div-exp` `clear-num` `sum-log` `flip--` `div-inv`
1×	`+-commutative` `neg-sub0` `associate-+l-` `associate-+l+` `associate-+r+` `distribute-neg-in` `neg-log`

Counts

4 → 341

Calls

4 calls:

51.0ms	(/ (+ x 1.0) (- (pow x 3) (pow 1.0 3)))
52.0ms	(/ (+ x 1.0) (- (pow x 3) (pow 1.0 3)))
12.0ms	(+ (- (fma x x (* 1.0 (+ x 1.0)))) (fma x x (* 1.0 (+ x 1.0))))
0.0ms	(fma (fma x x (* 1.0 (+ x 1.0))) (- (/ (+ x 1.0) (- (pow x 3) (pow 1.0 3)))) (/ (/ x (cbrt (+ x 1.0))) (* (cbrt (+ 1.0 x)) (cbrt (+ 1.0 x)))))

series273.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(/ (+ x 1.0) (- (pow x 3) (pow 1.0 3)))
58.0ms	(/ (+ x 1.0) (- (pow x 3) (pow 1.0 3)))
1.0ms	(+ (- (fma x x (* 1.0 (+ x 1.0)))) (fma x x (* 1.0 (+ x 1.0))))
158.0ms	(fma (fma x x (* 1.0 (+ x 1.0))) (- (/ (+ x 1.0) (- (pow x 3) (pow 1.0 3)))) (/ (/ x (cbrt (+ x 1.0))) (* (cbrt (+ 1.0 x)) (cbrt (+ 1.0 x)))))

simplify870.0ms

Counts

353 → 353

Iterations

Useful iterations: done (857.0ms)

Iter	Nodes	Cost
0	268	7673
1	559	6771
2	1562	6420
done	5001	6218

prune1.1s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (/ 3.0 x) (+ (/ 3.0 (pow x 3)) (/ 1.0 (* x x))))
0.4b	(/ 3.0 (pow x 3))
0.4b	(/ 1.0 (* x x))
8.6b	(+ (/ 3.0 (pow x 3)) (/ 1.0 (* x x)))

rewrite206.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 179

Calls

4 calls:

131.0ms	(+ (/ 3.0 x) (+ (/ 3.0 (pow x 3)) (/ 1.0 (* x x))))
8.0ms	(/ 3.0 (pow x 3))
7.0ms	(/ 1.0 (* x x))
54.0ms	(+ (/ 3.0 (pow x 3)) (/ 1.0 (* x x)))

series182.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(+ (/ 3.0 x) (+ (/ 3.0 (pow x 3)) (/ 1.0 (* x x))))
41.0ms	(/ 3.0 (pow x 3))
25.0ms	(/ 1.0 (* x x))
87.0ms	(+ (/ 3.0 (pow x 3)) (/ 1.0 (* x x)))

simplify837.0ms

Counts

191 → 191

Iterations

Useful iterations: done (833.0ms)

Iter	Nodes	Cost
0	204	1878
1	490	1612
2	1724	1521
done	5000	1520

prune379.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0b

regimes58.0ms

Accuracy

99.7% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 29.3b

bsearch1.0ms

simplify9.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	37	100
1	48	100
2	59	100
3	61	100
done	61	100

end0.0ms

sample546.0ms

Algorithm

intervals

Results

173.0ms	1661×	body	1280	valid
106.0ms	1234×	body	640	valid
94.0ms	4166×	body	80	valid
37.0ms	600×	body	320	valid
14.0ms	339×	body	160	valid