Details

sample21.0ms

Algorithm

intervals

Results

6.0ms	54×	body	1280	valid
4.0ms	49×	body	640	valid
3.0ms	123×	body	80	valid
2.0ms	27×	body	320	valid
0.0ms	3×	body	160	valid

simplify86.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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	76	13
9	97	13
10	127	13
11	143	13
12	151	13
done	151	13

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.5b

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ x (+ x 1.0))
0.0b	(/ (+ x 1.0) (- x 1.0))
1.3b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite187.0ms

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:

5.0ms	(/ x (+ x 1.0))
11.0ms	(/ (+ x 1.0) (- x 1.0))
118.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series211.0ms

Counts

3 → 9

Calls

3 calls:

38.0ms	(/ x (+ x 1.0))
37.0ms	(/ (+ x 1.0) (- x 1.0))
136.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify1.0s

Counts

605 → 605

Iterations

Useful iterations: done (984.0ms)

Iter	Nodes	Cost
0	523	34216
1	1157	30851
2	3053	22683
done	5000	22489

prune698.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (/ 3.0 x) (/ 3.0 (pow x 3)))
0.2b	(/ 1.0 (* x x))
0.3b	(/ 3.0 (pow x 3))
6.4b	(- (- (/ 1.0 (* x x))) (+ (/ 3.0 x) (/ 3.0 (pow x 3))))

rewrite240.0ms

Algorithm

rewrite-expression-head

Rules

478×	`*-un-lft-identity`
398×	`times-frac`
234×	`prod-diff`
204×	`add-sqr-sqrt`
202×	`add-cube-cbrt`
100×	`distribute-rgt-neg-in`
99×	`unpow3`
98×	`distribute-lft-neg-in`
97×	`distribute-lft-out`
76×	`distribute-rgt-out`
69×	`div-inv`
19×	`distribute-rgt1-in`
18×	`fma-neg`
16×	`add-log-exp`
14×	`add-exp-log` `neg-mul-1`
13×	`fma-def` `associate-/r*`
12×	`unpow-prod-down` `cube-prod`
11×	`add-cbrt-cube`
6×	`associate-/l*`
5×	`div-exp`
4×	`pow1` `expm1-log1p-u` `cube-mult` `diff-log` `log1p-expm1-u` `distribute-lft-out--` `sqr-pow`
3×	`cbrt-undiv` `sum-log` `frac-sub` `distribute-neg-frac`
2×	`frac-2neg` `flip3-+` `neg-log` `frac-add` `clear-num` `flip-+`
1×	`+-commutative` `associate--l-` `neg-sub0` `pow-to-exp` `sub-neg` `flip3--` `pow-exp` `prod-exp` `flip--` `cbrt-unprod` `associate--r+` `difference-of-squares`

Counts

4 → 406

Calls

4 calls:

34.0ms	(+ (/ 3.0 x) (/ 3.0 (pow x 3)))
3.0ms	(/ 1.0 (* x x))
4.0ms	(/ 3.0 (pow x 3))
165.0ms	(- (- (/ 1.0 (* x x))) (+ (/ 3.0 x) (/ 3.0 (pow x 3))))

series179.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(+ (/ 3.0 x) (/ 3.0 (pow x 3)))
24.0ms	(/ 1.0 (* x x))
42.0ms	(/ 3.0 (pow x 3))
32.0ms	(- (- (/ 1.0 (* x x))) (+ (/ 3.0 x) (/ 3.0 (pow x 3))))

simplify1.5s

Counts

418 → 418

Iterations

Useful iterations: 2 (490.0ms)

Iter	Nodes	Cost
0	486	16711
1	1060	13690
2	3755	10588
done	5000	10588

prune459.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ x (+ x 1.0))
0.0b	(cbrt (pow (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))) 3))
0.0b	(pow (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))) 3)
1.3b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite320.0ms

Algorithm

rewrite-expression-head

Rules

1139×	`*-un-lft-identity`
796×	`times-frac`
619×	`add-sqr-sqrt`
468×	`prod-diff`
415×	`add-cube-cbrt`
215×	`distribute-lft-out`
137×	`distribute-lft-out--`
92×	`associate-/r/` `difference-of-squares`
46×	`div-inv`
38×	`cbrt-prod`
32×	`unpow-prod-down` `cube-prod`
28×	`flip3-+` `flip-+`
21×	`flip3--` `flip--`
18×	`fma-neg`
7×	`add-exp-log` `add-cbrt-cube`
6×	`cube-div` `add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `associate-/r*` `log1p-expm1-u`
3×	`pow-unpow` `cbrt-div` `frac-sub` `associate-/l*`
2×	`cube-mult` `unpow3` `sqr-pow`
1×	`cbrt-undiv` `pow-to-exp` `sub-neg` `pow-pow` `frac-2neg` `pow1/3` `diff-log` `div-exp` `pow-exp` `clear-num` `rem-cbrt-cube` `rem-cube-cbrt`

Counts

4 → 655

Calls

4 calls:

5.0ms	(/ x (+ x 1.0))
87.0ms	(cbrt (pow (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))) 3))
88.0ms	(pow (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))) 3)
78.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series474.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(/ x (+ x 1.0))
126.0ms	(cbrt (pow (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))) 3))
172.0ms	(pow (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))) 3)
138.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify1.2s

Counts

667 → 667

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	587	36483
1	1320	32660
2	3705	24364
done	5000	24170

prune814.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (/ x (+ x 1.0)))
0.3b	(cbrt (/ x (+ x 1.0)))
0.4b	(cbrt (pow (+ (fma (* (cbrt (/ x (+ x 1.0))) (cbrt (/ x (+ x 1.0)))) (cbrt (/ x (+ x 1.0))) (/ (- (/ (+ x 1.0) (cbrt (- x 1.0)))) (* (cbrt (- x 1.0)) (cbrt (- x 1.0))))) (* (/ 1 (* (cbrt (- x 1.0)) (cbrt (- x 1.0)))) (+ (- (/ (+ x 1.0) (cbrt (- x 1.0)))) (/ (+ x 1.0) (cbrt (- x 1.0)))))) 3))
21.9b	(fma (* (cbrt (/ x (+ x 1.0))) (cbrt (/ x (+ x 1.0)))) (cbrt (/ x (+ x 1.0))) (/ (- (/ (+ x 1.0) (cbrt (- x 1.0)))) (* (cbrt (- x 1.0)) (cbrt (- x 1.0)))))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

48×	`cbrt-prod`
35×	`*-un-lft-identity`
24×	`times-frac`
23×	`add-sqr-sqrt` `add-cube-cbrt`
6×	`distribute-lft-out`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `cbrt-div` `associate-/r/` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`unpow-prod-down` `flip3-+` `pow1/3` `cube-prod` `flip-+`
2×	`cube-div` `div-inv`
1×	`cube-mult` `unpow3` `rem-cbrt-cube` `fma-udef` `sqr-pow`

Counts

4 → 93

Calls

4 calls:

4.0ms	(cbrt (/ x (+ x 1.0)))
3.0ms	(cbrt (/ x (+ x 1.0)))
4.0ms	(cbrt (pow (+ (fma (* (cbrt (/ x (+ x 1.0))) (cbrt (/ x (+ x 1.0)))) (cbrt (/ x (+ x 1.0))) (/ (- (/ (+ x 1.0) (cbrt (- x 1.0)))) (* (cbrt (- x 1.0)) (cbrt (- x 1.0))))) (* (/ 1 (* (cbrt (- x 1.0)) (cbrt (- x 1.0)))) (+ (- (/ (+ x 1.0) (cbrt (- x 1.0)))) (/ (+ x 1.0) (cbrt (- x 1.0)))))) 3))
0.0ms	(fma (* (cbrt (/ x (+ x 1.0))) (cbrt (/ x (+ x 1.0)))) (cbrt (/ x (+ x 1.0))) (/ (- (/ (+ x 1.0) (cbrt (- x 1.0)))) (* (cbrt (- x 1.0)) (cbrt (- x 1.0)))))

series1.6s

Counts

4 → 12

Calls

4 calls:

155.0ms	(cbrt (/ x (+ x 1.0)))
147.0ms	(cbrt (/ x (+ x 1.0)))
632.0ms	(cbrt (pow (+ (fma (* (cbrt (/ x (+ x 1.0))) (cbrt (/ x (+ x 1.0)))) (cbrt (/ x (+ x 1.0))) (/ (- (/ (+ x 1.0) (cbrt (- x 1.0)))) (* (cbrt (- x 1.0)) (cbrt (- x 1.0))))) (* (/ 1 (* (cbrt (- x 1.0)) (cbrt (- x 1.0)))) (+ (- (/ (+ x 1.0) (cbrt (- x 1.0)))) (/ (+ x 1.0) (cbrt (- x 1.0)))))) 3))
628.0ms	(fma (* (cbrt (/ x (+ x 1.0))) (cbrt (/ x (+ x 1.0)))) (cbrt (/ x (+ x 1.0))) (/ (- (/ (+ x 1.0) (cbrt (- x 1.0)))) (* (cbrt (- x 1.0)) (cbrt (- x 1.0)))))

simplify643.0ms

Counts

105 → 105

Iterations

Useful iterations: 2 (208.0ms)

Iter	Nodes	Cost
0	226	5096
1	549	4648
2	2038	3468
done	5000	3468

prune431.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.0b

regimes47.0ms

Accuracy

99.4% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 31.7b

bsearch2.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	48
1	26	48
done	26	48

end0.0ms

sample538.0ms

Algorithm

intervals

Results

182.0ms	1731×	body	1280	valid
105.0ms	1265×	body	640	valid
104.0ms	4084×	body	80	valid
42.0ms	618×	body	320	valid
13.0ms	302×	body	160	valid