Details

sample22.0ms

Algorithm

intervals

Results

6.0ms	51×	body	1280	valid
4.0ms	44×	body	640	valid
4.0ms	145×	body	80	valid
1.0ms	11×	body	320	valid
0.0ms	5×	body	160	valid

simplify21.0ms

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

prune1.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 26.5b

Counts

2 → 1

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ x (+ x 1.0))
0.0b	(/ (+ x 1.0) (- x 1.0))
1.5b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite110.0ms

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))
7.0ms	(/ (+ x 1.0) (- x 1.0))
42.0ms	(- (/ 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)))

simplify210.0ms

Algorithm

egg-herbie

Counts

605 → 605

Iterations

Useful iterations: 2 (80.0ms)

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

prune869.0ms

Filtered

605 candidates to 217 candidates (35.9%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	601	4	605
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	602	4	606

Merged error: 0.2b

Counts

606 → 4

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (+ x 1.0) (- 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)
1.5b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite181.0ms

Algorithm

rewrite-expression-head

Rules

1155×	`*-un-lft-identity`
804×	`times-frac`
631×	`add-sqr-sqrt`
468×	`prod-diff`
417×	`add-cube-cbrt`
217×	`distribute-lft-out`
142×	`distribute-lft-out--`
97×	`difference-of-squares`
92×	`associate-/r/`
46×	`div-inv`
38×	`cbrt-prod`
32×	`unpow-prod-down` `cube-prod`
28×	`flip3-+` `flip-+`
22×	`flip3--` `flip--`
18×	`fma-neg`
7×	`add-exp-log` `add-cbrt-cube`
6×	`cube-div` `add-log-exp`
5×	`pow1` `associate-/r*`
4×	`expm1-log1p-u` `log1p-expm1-u` `associate-/l*`
3×	`pow-unpow` `cbrt-div` `frac-sub`
2×	`cube-mult` `unpow3` `associate-/l/` `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 → 667

Calls

4 calls:

8.0ms	(/ (+ x 1.0) (- x 1.0))
34.0ms	(cbrt (pow (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))) 3))
30.0ms	(pow (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))) 3)
44.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series480.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(/ (+ x 1.0) (- x 1.0))
126.0ms	(cbrt (pow (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))) 3))
177.0ms	(pow (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))) 3)
135.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify254.0ms

Algorithm

egg-herbie

Counts

679 → 679

Iterations

Useful iterations: 2 (103.0ms)

Iter	Nodes	Cost
0	1399	19382
1	4621	14418
2	5001	14397

prune816.0ms

Filtered

679 candidates to 244 candidates (35.9%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	678	1	679
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	678	5	683

Merged error: 0.2b

Counts

683 → 5

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 1 (+ x 1.0))
0.0b	(/ (+ x 1.0) (- x 1.0))
27.0b	(fma x (/ 1 (+ x 1.0)) (- (/ (+ x 1.0) (- x 1.0))))

rewrite20.0ms

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:

9.0ms	(/ 1 (+ x 1.0))
7.0ms	(/ (+ x 1.0) (- x 1.0))
1.0ms	(fma x (/ 1 (+ x 1.0)) (- (/ (+ x 1.0) (- x 1.0))))

series199.0ms

Counts

3 → 9

Calls

3 calls:

23.0ms	(/ 1 (+ x 1.0))
41.0ms	(/ (+ x 1.0) (- x 1.0))
135.0ms	(fma x (/ 1 (+ x 1.0)) (- (/ (+ x 1.0) (- x 1.0))))

simplify42.0ms

Algorithm

egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 2 (32.0ms)

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

prune147.0ms

Filtered

105 candidates to 66 candidates (62.9%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	105	0	105
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	105	5	110

Merged error: 0.2b

Counts

110 → 5

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (+ x 1.0) (- x 1.0))
0.0b	(* (sqrt (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))) (sqrt (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))))
1.5b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))
1.5b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite303.0ms

Algorithm

rewrite-expression-head

Rules

2707×	`*-un-lft-identity`
1732×	`times-frac`
1197×	`add-sqr-sqrt`
936×	`prod-diff`
815×	`add-cube-cbrt`
508×	`distribute-lft-out`
397×	`distribute-lft-out--`
186×	`sqrt-prod`
182×	`associate-/r/`
173×	`difference-of-squares`
91×	`div-inv`
79×	`swap-sqr`
55×	`flip3-+` `flip-+`
47×	`flip3--` `flip--`
36×	`fma-neg`
24×	`sqrt-div`
19×	`pow1` `associate-r` `associate-l`
10×	`frac-sub`
9×	`frac-times`
8×	`add-exp-log` `sqrt-pow1` `pow1/2` `add-cbrt-cube` `add-log-exp`
5×	`associate-/r*` `pow-prod-up`
4×	`expm1-log1p-u` `log1p-expm1-u` `associate-/l*` `unswap-sqr`
3×	`associate-r/` `pow-prod-down` `associate-l/` `pow-sqr`
2×	`sub-neg` `diff-log` `associate-/l/`
1×	`cbrt-undiv` `pow2` `frac-2neg` `pow-plus` `sqrt-unprod` `div-exp` `prod-exp` `clear-num` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 1238

Calls

4 calls:

8.0ms	(/ (+ x 1.0) (- x 1.0))
70.0ms	(* (sqrt (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))) (sqrt (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))))
44.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))
44.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series437.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(/ (+ x 1.0) (- x 1.0))
133.0ms	(* (sqrt (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))) (sqrt (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))))
127.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))
135.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify404.0ms

Algorithm

egg-herbie

Counts

1250 → 1250

Iterations

Useful iterations: 2 (118.0ms)

Iter	Nodes	Cost
0	1303	37798
1	4509	27854
2	5001	27798

prune1.6s

Filtered

1250 candidates to 409 candidates (32.7%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	1250	0	1250
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	1250	5	1255

Merged error: 0.2b

Counts

1255 → 5

regimes62.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.2b against oracle of 0.2b and baseline of 29.7b

bsearch78.0ms

Steps

Iters	Range		Point
8	1.3894494120209264	29774.780359327975	12691.331728809522
9	-3141188.981794727	-6.238959787773506	-12810.725084609585

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	16
1	41	16
2	41	16

end0.0ms

sample628.0ms

Algorithm

intervals

Results

222.0ms	1739×	body	1280	valid
131.0ms	1289×	body	640	valid
115.0ms	4045×	body	80	valid
51.0ms	600×	body	320	valid
17.0ms	327×	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

Details

sample22.0ms

simplify21.0ms

prune1.0ms

localize6.0ms

rewrite110.0ms

series207.0ms

simplify210.0ms

prune869.0ms

localize9.0ms

rewrite181.0ms

series480.0ms

simplify254.0ms

prune816.0ms

localize8.0ms

rewrite20.0ms

series199.0ms

simplify42.0ms

prune147.0ms

localize9.0ms

rewrite303.0ms

series437.0ms

simplify404.0ms

prune1.6s

regimes62.0ms

bsearch78.0ms

simplify2.0ms

end0.0ms

sample628.0ms

Profiling

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