Details

sample20.0ms

Algorithm

intervals

Results

6.0ms	67×	body	1280	valid
3.0ms	130×	body	80	valid
2.0ms	32×	body	640	valid
1.0ms	20×	body	320	valid
0.0ms	7×	body	160	valid

simplify21.0ms

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)))

rewrite207.0ms

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))
25.0ms	(/ (+ x 1.0) (- x 1.0))
115.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series202.0ms

Counts

3 → 9

Calls

3 calls:

33.0ms	(/ x (+ x 1.0))
42.0ms	(/ (+ x 1.0) (- x 1.0))
128.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify187.0ms

Counts

605 → 605

Iterations

Useful iterations: 2 (75.0ms)

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

prune717.0ms

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))))

rewrite41.0ms

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:

14.0ms	(/ 1 (+ x 1.0))
23.0ms	(/ (+ x 1.0) (- x 1.0))
0.0ms	(fma x (/ 1 (+ x 1.0)) (- (/ (+ x 1.0) (- x 1.0))))

series198.0ms

Counts

3 → 9

Calls

3 calls:

22.0ms	(/ 1 (+ x 1.0))
43.0ms	(/ (+ x 1.0) (- x 1.0))
132.0ms	(fma x (/ 1 (+ x 1.0)) (- (/ (+ x 1.0) (- x 1.0))))

simplify41.0ms

Counts

105 → 105

Iterations

Useful iterations: 2 (33.0ms)

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

prune179.0ms

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)))))

rewrite154.0ms

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))))
10.0ms	(/ (- 1.0) (pow x 2))
99.0ms	(- (/ (- 1.0) (pow x 2)) (fma 3.0 (/ 1 x) (* 3.0 (/ 1 (pow x 3)))))

series393.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(/ 1 (pow x 3))
292.0ms	(fma 3.0 (/ 1 x) (* 3.0 (/ 1 (pow x 3))))
33.0ms	(/ (- 1.0) (pow x 2))
36.0ms	(- (/ (- 1.0) (pow x 2)) (fma 3.0 (/ 1 x) (* 3.0 (/ 1 (pow x 3)))))

simplify174.0ms

Counts

571 → 571

Iterations

Useful iterations: 2 (80.0ms)

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

prune774.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(* 3.0 (/ 1 (pow x 3)))
0.2b	(/ 1 (pow x 3))
0.5b	(/ (- 1.0) (pow x 2))
8.4b	(- (/ (- 1.0) (pow x 2)) (+ (/ 3.0 x) (* 3.0 (/ 1 (pow x 3)))))

rewrite230.0ms

Algorithm

rewrite-expression-head

Rules

564×	`times-frac`
442×	`add-sqr-sqrt`
416×	`*-un-lft-identity`
410×	`add-cube-cbrt`
336×	`prod-diff`
207×	`unpow-prod-down`
147×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
92×	`div-inv`
84×	`fma-neg` `distribute-lft-out`
71×	`sqr-pow`
62×	`unpow2`
49×	`neg-mul-1`
40×	`associate-r`
38×	`add-exp-log`
23×	`cube-prod`
20×	`associate-/r*`
15×	`div-exp`
13×	`add-cbrt-cube` `associate-/l*`
10×	`prod-exp`
9×	`add-log-exp` `unswap-sqr`
7×	`cube-mult` `pow-to-exp` `unpow3` `pow-exp`
6×	`pow1` `rec-exp` `1-exp`
5×	`difference-of-squares`
4×	`expm1-log1p-u` `frac-sub` `log1p-expm1-u`
3×	`cbrt-undiv` `associate-l`
2×	`neg-sub0` `frac-2neg` `diff-log` `div-sub` `associate-*r/` `frac-add` `clear-num` `un-div-inv` `cbrt-unprod`
1×	`associate--l-` `sub-neg` `flip3--` `pow-flip` `flip3-+` `distribute-frac-neg` `pow-prod-down` `sum-log` `*-commutative` `flip--` `flip-+` `associate--r+` `distribute-lft-out--` `inv-pow`

Counts

4 → 715

Calls

4 calls:

26.0ms	(* 3.0 (/ 1 (pow x 3)))
9.0ms	(/ 1 (pow x 3))
11.0ms	(/ (- 1.0) (pow x 2))
138.0ms	(- (/ (- 1.0) (pow x 2)) (+ (/ 3.0 x) (* 3.0 (/ 1 (pow x 3)))))

series140.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(* 3.0 (/ 1 (pow x 3)))
32.0ms	(/ 1 (pow x 3))
26.0ms	(/ (- 1.0) (pow x 2))
40.0ms	(- (/ (- 1.0) (pow x 2)) (+ (/ 3.0 x) (* 3.0 (/ 1 (pow x 3)))))

simplify142.0ms

Counts

727 → 727

Iterations

Useful iterations: 1 (33.0ms)

Iter	Nodes	Cost
0	1651	14818
1	5001	9063
done	5001	9063

prune867.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

regimes32.0ms

Accuracy

100% (0.0b remaining)

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

bsearch83.0ms

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	39	16
1	42	16
2	42	16
done	42	16

end0.0ms

sample555.0ms

Algorithm

intervals

Results

178.0ms	1769×	body	1280	valid
101.0ms	1250×	body	640	valid
92.0ms	4076×	body	80	valid
45.0ms	615×	body	320	valid
12.0ms	290×	body	160	valid