Details

sample23.0ms

Algorithm

intervals

Results

7.0ms	67×	body	1280	valid
5.0ms	130×	body	80	valid
3.0ms	32×	body	640	valid
1.0ms	20×	body	320	valid
0.0ms	7×	body	160	valid

simplify20.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	12	6
1	16	6
2	19	6
3	21	6
4	27	6
5	39	6
6	58	6
7	79	6
8	107	6
9	160	6
10	277	6
11	303	6
12	303	6
done	303	6

prune1.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.7b

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ x (+ x 1.0))
0.0b	(/ (+ x 1.0) (- x 1.0))
1.6b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite199.0ms

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:

10.0ms	(/ x (+ x 1.0))
23.0ms	(/ (+ x 1.0) (- x 1.0))
112.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series207.0ms

Counts

3 → 9

Calls

3 calls:

37.0ms	(/ x (+ x 1.0))
36.0ms	(/ (+ x 1.0) (- x 1.0))
134.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify181.0ms

Counts

605 → 605

Iterations

Useful iterations: 2 (71.0ms)

Iter	Nodes	Cost
0	1208	18366
1	3687	13388
2	5001	13292
done	5001	13292

prune704.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.2b

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 1 (+ x 1.0))
0.0b	(/ (+ x 1.0) (- x 1.0))
30.4b	(fma x (/ 1 (+ x 1.0)) (- (/ (+ x 1.0) (- x 1.0))))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

53×	`*-un-lft-identity`
33×	`add-sqr-sqrt`
32×	`times-frac`
23×	`add-cube-cbrt`
10×	`distribute-lft-out`
9×	`add-exp-log` `associate-/r*`
7×	`add-cbrt-cube` `associate-/l*`
5×	`distribute-lft-out--` `difference-of-squares`
4×	`pow1` `associate-/r/`
3×	`expm1-log1p-u` `div-exp` `log1p-expm1-u` `add-log-exp`
2×	`cbrt-undiv` `frac-2neg` `flip3-+` `clear-num` `flip-+` `div-inv` `associate-/l/`
1×	`rec-exp` `flip3--` `pow-flip` `1-exp` `flip--` `fma-udef` `inv-pow`

Counts

3 → 96

Calls

3 calls:

11.0ms	(/ 1 (+ x 1.0))
27.0ms	(/ (+ x 1.0) (- x 1.0))
0.0ms	(fma x (/ 1 (+ x 1.0)) (- (/ (+ x 1.0) (- x 1.0))))

series201.0ms

Counts

3 → 9

Calls

3 calls:

23.0ms	(/ 1 (+ x 1.0))
38.0ms	(/ (+ x 1.0) (- x 1.0))
141.0ms	(fma x (/ 1 (+ x 1.0)) (- (/ (+ x 1.0) (- x 1.0))))

simplify39.0ms

Counts

105 → 105

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	352	622
1	1229	566
2	5001	540
done	5001	540

prune171.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.2b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (pow x 3))
0.2b	(fma 3.0 (/ 1 x) (* 3.0 (/ 1 (pow x 3))))
0.5b	(/ (- 1.0) (pow x 2))
8.4b	(- (/ (- 1.0) (pow x 2)) (fma 3.0 (/ 1 x) (* 3.0 (/ 1 (pow x 3)))))

rewrite149.0ms

Algorithm

rewrite-expression-head

Rules

440×	`times-frac`
354×	`add-sqr-sqrt`
344×	`*-un-lft-identity`
342×	`add-cube-cbrt`
252×	`prod-diff`
166×	`unpow-prod-down`
123×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
84×	`fma-neg`
56×	`sqr-pow`
52×	`unpow2`
41×	`neg-mul-1`
20×	`associate-/r*`
18×	`add-exp-log`
13×	`associate-/l*`
12×	`cube-prod`
9×	`div-exp`
8×	`add-cbrt-cube`
6×	`div-inv` `add-log-exp`
5×	`difference-of-squares`
4×	`pow1` `expm1-log1p-u` `cube-mult` `pow-to-exp` `unpow3` `pow-exp` `log1p-expm1-u`
3×	`rec-exp` `1-exp`
2×	`cbrt-undiv` `neg-sub0` `frac-2neg` `div-sub` `clear-num` `fma-udef`
1×	`associate--l-` `sub-neg` `flip3--` `pow-flip` `diff-log` `distribute-frac-neg` `flip--` `associate--r+` `distribute-lft-out--` `inv-pow`

Counts

4 → 559

Calls

4 calls:

9.0ms	(/ 1 (pow x 3))
0.0ms	(fma 3.0 (/ 1 x) (* 3.0 (/ 1 (pow x 3))))
11.0ms	(/ (- 1.0) (pow x 2))
95.0ms	(- (/ (- 1.0) (pow x 2)) (fma 3.0 (/ 1 x) (* 3.0 (/ 1 (pow x 3)))))

series196.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(/ 1 (pow x 3))
88.0ms	(fma 3.0 (/ 1 x) (* 3.0 (/ 1 (pow x 3))))
26.0ms	(/ (- 1.0) (pow x 2))
44.0ms	(- (/ (- 1.0) (pow x 2)) (fma 3.0 (/ 1 x) (* 3.0 (/ 1 (pow x 3)))))

simplify173.0ms

Counts

571 → 571

Iterations

Useful iterations: 2 (79.0ms)

Iter	Nodes	Cost
0	1159	12779
1	4167	7106
2	5001	7094
done	5001	7094

prune756.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(* 3.0 (/ 1 (pow x 3)))
0.1b	(/ (/ 1.0 x) x)
0.2b	(/ 1 (pow x 3))
8.4b	(- (fma -1 (/ (/ 1.0 x) x) (/ (- 3.0) x)) (* 3.0 (/ 1 (pow x 3))))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

155×	`times-frac`
116×	`add-sqr-sqrt`
100×	`*-un-lft-identity`
96×	`add-cube-cbrt`
40×	`associate-r`
38×	`add-exp-log`
23×	`unpow-prod-down` `cube-prod`
16×	`add-cbrt-cube` `associate-/l*`
15×	`div-exp` `associate-/r*`
10×	`prod-exp`
9×	`unswap-sqr` `sqr-pow`
7×	`cube-mult` `unpow3` `div-inv`
6×	`pow1` `pow-to-exp` `rec-exp` `1-exp` `pow-exp` `add-log-exp`
5×	`cbrt-undiv`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`fma-neg` `associate-l` `prod-diff`
2×	`frac-2neg` `clear-num` `cbrt-unprod`
1×	`sub-neg` `flip3--` `pow-flip` `diff-log` `associate-r/` `pow-prod-down` `associate--l+` `un-div-inv` `-commutative` `flip--` `fma-udef` `associate-/l/` `inv-pow`

Counts

4 → 245

Calls

4 calls:

29.0ms	(* 3.0 (/ 1 (pow x 3)))
11.0ms	(/ (/ 1.0 x) x)
9.0ms	(/ 1 (pow x 3))
6.0ms	(- (fma -1 (/ (/ 1.0 x) x) (/ (- 3.0) x)) (* 3.0 (/ 1 (pow x 3))))

series140.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(* 3.0 (/ 1 (pow x 3)))
27.0ms	(/ (/ 1.0 x) x)
39.0ms	(/ 1 (pow x 3))
37.0ms	(- (fma -1 (/ (/ 1.0 x) x) (/ (- 3.0) x)) (* 3.0 (/ 1 (pow x 3))))

simplify100.0ms

Counts

257 → 257

Iterations

Useful iterations: 2 (78.0ms)

Iter	Nodes	Cost
0	760	1440
1	3953	1147
2	5002	1133
done	5002	1133

prune445.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

regimes31.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 30.0b

bsearch82.0ms

Steps

Iters	Range		Point
9	7.055123656280252	892369.0132880388	12009.419676004025
10	-1.8070707071506563e+17	-0.15939393977811658	-12526.878831697797

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	16
1	42	16
2	42	16
done	42	16

end0.0ms

sample573.0ms

Algorithm

intervals

Results

190.0ms	1769×	body	1280	valid
112.0ms	1250×	body	640	valid
96.0ms	4076×	body	80	valid
38.0ms	615×	body	320	valid
12.0ms	290×	body	160	valid