Details

sample20.0ms

Algorithm

intervals

Results

6.0ms	57×	body	1280	valid
3.0ms	39×	body	640	valid
3.0ms	133×	body	80	valid
1.0ms	18×	body	320	valid
0.0ms	9×	body	160	valid

simplify99.0ms

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	137	13
12	141	13
13	143	13
done	143	13

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.5b

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)))

rewrite156.0ms

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))
79.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series212.0ms

Counts

3 → 9

Calls

3 calls:

37.0ms	(/ x (+ x 1.0))
38.0ms	(/ (+ x 1.0) (- x 1.0))
137.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify1.1s

Counts

605 → 605

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	523	34216
1	1157	30851
2	2971	22735
done	5000	22021

prune629.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ x (+ x 1.0))
0.1b	(pow (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))) 3)
0.1b	(cbrt (pow (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))) 3))
2.7b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite327.0ms

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:

6.0ms	(/ x (+ x 1.0))
90.0ms	(pow (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))) 3)
88.0ms	(cbrt (pow (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))) 3))
79.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series485.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(/ x (+ x 1.0))
180.0ms	(pow (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))) 3)
133.0ms	(cbrt (pow (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))) 3))
138.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify1.3s

Counts

667 → 667

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	587	36483
1	1320	32660
2	3473	24416
done	5000	23858

prune799.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(cbrt (pow (* (cbrt (pow (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))) 2)) (cbrt (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))))) 3))
0.1b	(cbrt (- (/ 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)))

rewrite329.0ms

Algorithm

rewrite-expression-head

Rules

1908×	`*-un-lft-identity`
1428×	`times-frac`
1122×	`add-sqr-sqrt`
936×	`prod-diff`
798×	`add-cube-cbrt`
366×	`distribute-lft-out`
183×	`distribute-lft-out--`
180×	`associate-/r/`
156×	`difference-of-squares`
90×	`div-inv`
54×	`flip3-+` `flip-+`
40×	`flip3--` `flip--`
36×	`fma-neg`
24×	`cbrt-prod`
9×	`cbrt-div`
8×	`add-log-exp`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `frac-sub` `add-cbrt-cube` `log1p-expm1-u`
3×	`cube-div` `associate-*r/`
2×	`sub-neg` `pow1/3` `diff-log`
1×	`cube-mult` `unpow-prod-down` `unpow3` `cube-prod` `rem-cbrt-cube` `sqr-pow`

Counts

4 → 1079

Calls

4 calls:

3.0ms	(cbrt (pow (* (cbrt (pow (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))) 2)) (cbrt (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))))) 3))
42.0ms	(cbrt (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))))
81.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))
79.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series706.0ms

Counts

4 → 12

Calls

4 calls:

140.0ms	(cbrt (pow (* (cbrt (pow (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))) 2)) (cbrt (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))))) 3))
287.0ms	(cbrt (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))))
139.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))
140.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify1.3s

Counts

1091 → 1091

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	597	68457
1	1319	61583
2	3504	45093
done	5000	44497

prune2.2s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))) 2)
0.1b	(pow (/ (+ x 1.0) (- x 1.0)) 3)
2.6b	(- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ x 1.0) (- x 1.0)) 3))
2.7b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite888.0ms

Algorithm

rewrite-expression-head

Rules

5328×	`*-un-lft-identity`
3948×	`times-frac`
3248×	`add-sqr-sqrt`
2904×	`prod-diff`
2308×	`add-cube-cbrt`
2256×	`unpow-prod-down`
2240×	`cube-prod`
1003×	`distribute-lft-out`
498×	`associate-/r/`
495×	`distribute-lft-out--`
460×	`difference-of-squares`
249×	`div-inv`
145×	`flip3-+` `flip-+`
115×	`sqr-pow`
106×	`flip3--` `flip--`
102×	`cube-mult` `unpow3`
60×	`fma-neg`
8×	`add-exp-log` `add-log-exp`
7×	`add-cbrt-cube`
6×	`pow1` `pow-unpow`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`cube-div` `pow-exp`
2×	`pow-to-exp` `sub-neg` `pow-pow` `diff-log` `frac-sub` `rem-cube-cbrt`
1×	`difference-cubes` `cbrt-undiv` `div-exp` `unpow2`

Counts

4 → 3188

Calls

4 calls:

91.0ms	(pow (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))) 2)
13.0ms	(pow (/ (+ x 1.0) (- x 1.0)) 3)
275.0ms	(- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ x 1.0) (- x 1.0)) 3))
82.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series685.0ms

Counts

4 → 12

Calls

4 calls:

170.0ms	(pow (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))) 2)
61.0ms	(pow (/ (+ x 1.0) (- x 1.0)) 3)
311.0ms	(- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ x 1.0) (- x 1.0)) 3))
143.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify1.4s

Counts

3200 → 3200

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	1273	246253
1	2668	203740
done	5000	201553

prune4.1s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

regimes70.0ms

Accuracy

99.9% (0.0b remaining)

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

bsearch92.0ms

Steps

Iters	Range		Point
6	2942.2625356967415	22276.40736340321	9789.556568540302
10	-155084744.97222546	-0.0009113054925467739	-10645.547231578275

simplify6.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	32	72
1	45	57
2	52	57
3	55	57
done	55	57

end0.0ms

sample542.0ms

Algorithm

intervals

Results

177.0ms	1656×	body	1280	valid
105.0ms	4102×	body	80	valid
105.0ms	1212×	body	640	valid
43.0ms	663×	body	320	valid
16.0ms	367×	body	160	valid