Details

sample40.0ms

Algorithm

intervals

Results

13.0ms	46×	body	1280	valid
9.0ms	46×	body	640	valid
8.0ms	138×	body	80	valid
2.0ms	16×	body	320	valid
1.0ms	10×	body	160	valid

simplify23.0ms

Algorithm

egg-herbie

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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.4b

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ x (+ x 1.0))
0.0b	(/ (+ x 1.0) (- x 1.0))
2.3b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite146.0ms

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))
75.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series205.0ms

Counts

3 → 9

Calls

3 calls:

35.0ms	(/ x (+ x 1.0))
37.0ms	(/ (+ x 1.0) (- x 1.0))
133.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify225.0ms

Algorithm

egg-herbie

Counts

605 → 605

Iterations

Useful iterations: 2 (102.0ms)

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

prune736.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.2b

localize15.0ms

Local error

Found 4 expressions with local error:

12.9b	(/ x (- (* x x) (* 1.0 1.0)))
12.9b	(/ (+ x 1.0) (- (* x x) (* 1.0 1.0)))
12.9b	(/ (+ x 1.0) (- (* x x) (* 1.0 1.0)))
28.0b	(fma (/ x (- (* x x) (* 1.0 1.0))) (- x 1.0) (- (* (+ x 1.0) (/ (+ x 1.0) (- (* x x) (* 1.0 1.0))))))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

53×	`*-un-lft-identity`
44×	`times-frac`
33×	`add-sqr-sqrt` `add-cube-cbrt`
14×	`difference-of-squares`
12×	`associate-/r*`
11×	`associate-/l*`
10×	`add-exp-log` `add-cbrt-cube` `distribute-lft-out`
6×	`associate-/r/`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `associate-/l/` `add-log-exp`
3×	`cbrt-undiv` `flip3--` `frac-2neg` `div-exp` `clear-num` `flip--` `div-inv`
2×	`flip3-+` `flip-+`
1×	`fma-udef`

Counts

4 → 129

Calls

4 calls:

5.0ms	(/ x (- (* x x) (* 1.0 1.0)))
11.0ms	(/ (+ x 1.0) (- (* x x) (* 1.0 1.0)))
14.0ms	(/ (+ x 1.0) (- (* x x) (* 1.0 1.0)))
0.0ms	(fma (/ x (- (* x x) (* 1.0 1.0))) (- x 1.0) (- (* (+ x 1.0) (/ (+ x 1.0) (- (* x x) (* 1.0 1.0))))))

series325.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(/ x (- (* x x) (* 1.0 1.0)))
41.0ms	(/ (+ x 1.0) (- (* x x) (* 1.0 1.0)))
36.0ms	(/ (+ x 1.0) (- (* x x) (* 1.0 1.0)))
177.0ms	(fma (/ x (- (* x x) (* 1.0 1.0))) (- x 1.0) (- (* (+ x 1.0) (/ (+ x 1.0) (- (* x x) (* 1.0 1.0))))))

simplify54.0ms

Algorithm

egg-herbie

Counts

141 → 141

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	393	1262
1	1600	1156
2	5001	1097

prune408.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.2b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)))) (+ (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))))
0.0b	(* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)))
0.0b	(* (/ x (+ x 1.0)) (/ x (+ x 1.0)))
2.2b	(- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0))))

rewrite225.0ms

Algorithm

rewrite-expression-head

Rules

544×	`*-un-lft-identity`
320×	`times-frac`
170×	`add-sqr-sqrt`
141×	`distribute-lft-out`
106×	`add-cube-cbrt`
72×	`swap-sqr`
52×	`distribute-lft-out--`
44×	`associate-r` `associate-l`
34×	`difference-of-squares`
30×	`add-exp-log` `add-cbrt-cube`
19×	`associate-/r/`
18×	`pow1` `frac-sub`
14×	`frac-times` `associate-r/` `associate-l/`
12×	`associate-/r*`
11×	`associate-/l/`
9×	`cbrt-undiv` `div-exp` `div-inv`
8×	`prod-exp` `cbrt-unprod` `unswap-sqr`
6×	`flip3--` `flip--` `add-log-exp`
5×	`flip3-+` `flip-+`
4×	`expm1-log1p-u` `log1p-expm1-u` `associate-/l*`
2×	`pow2` `pow-plus` `pow-prod-down` `pow-sqr` `*-commutative` `pow-prod-up`
1×	`sub-neg` `frac-2neg` `fma-neg` `diff-log` `div-sub` `prod-diff` `frac-add` `clear-num`

Counts

4 → 339

Calls

4 calls:

109.0ms	(/ (- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)))) (+ (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))))
50.0ms	(* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)))
33.0ms	(* (/ x (+ x 1.0)) (/ x (+ x 1.0)))
11.0ms	(- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0))))

series862.0ms

Counts

4 → 12

Calls

4 calls:

549.0ms	(/ (- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)))) (+ (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))))
58.0ms	(* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)))
47.0ms	(* (/ x (+ x 1.0)) (/ x (+ x 1.0)))
207.0ms	(- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0))))

simplify77.0ms

Algorithm

egg-herbie

Counts

351 → 351

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1339	5093
1	5001	4844

prune518.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.1b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (+ x 1.0) (- x 1.0))
0.0b	(* (+ (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))) (/ (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))) (+ (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))))
0.0b	(/ (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))) (+ (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))))
2.3b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite1.1s

Algorithm

rewrite-expression-head

Rules

3739×	`*-un-lft-identity`
2153×	`times-frac`
963×	`distribute-lft-out`
942×	`add-sqr-sqrt`
551×	`distribute-lft-out--`
471×	`add-cube-cbrt`
468×	`prod-diff`
199×	`associate-r`
181×	`difference-of-squares`
98×	`associate-/r/`
48×	`div-inv`
32×	`flip3-+` `flip-+`
21×	`flip3--` `flip--`
20×	`associate-/l*`
18×	`fma-neg`
17×	`associate-/r*`
13×	`add-exp-log` `add-cbrt-cube`
12×	`associate-l`
6×	`pow1` `add-log-exp`
5×	`associate-/l/`
4×	`expm1-log1p-u` `frac-add` `log1p-expm1-u`
3×	`cbrt-undiv` `frac-times` `div-exp` `associate-*l/`
2×	`frac-2neg` `prod-exp` `clear-num` `frac-sub` `cbrt-unprod` `unswap-sqr`
1×	`sub-neg` `diff-log` `div-sub` `associate-r/` `pow-prod-down` `-commutative`

Counts

4 → 1037

Calls

4 calls:

11.0ms	(/ (+ x 1.0) (- x 1.0))
563.0ms	(* (+ (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))) (/ (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))) (+ (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))))
271.0ms	(/ (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))) (+ (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))))
75.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series582.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(/ (+ x 1.0) (- x 1.0))
135.0ms	(* (+ (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))) (/ (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))) (+ (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))))
272.0ms	(/ (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))) (+ (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))))
137.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify247.0ms

Algorithm

egg-herbie

Counts

1049 → 1049

Iterations

Useful iterations: 1 (34.0ms)

Iter	Nodes	Cost
0	1634	26096
1	5001	21903

prune1.1s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.1b

regimes53.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.2b against oracle of 0.2b and baseline of 28.7b

bsearch108.0ms

Steps

Iters	Range		Point
9	1654.2658435481542	671819857.7007226	11170.255305991283
9	-27324391.726681516	-29.541817090935037	-10556.320992542807

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	49	45
1	49	45

end0.0ms

sample1.1s

Algorithm

intervals

Results

388.0ms	1670×	body	1280	valid
261.0ms	4159×	body	80	valid
239.0ms	1261×	body	640	valid
89.0ms	603×	body	320	valid
37.0ms	307×	body	160	valid

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

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

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