Details

sample24.0ms

Algorithm

intervals

Results

8.0ms	56×	body	1280	valid
4.0ms	144×	body	80	valid
4.0ms	37×	body	640	valid
1.0ms	12×	body	320	valid
0.0ms	7×	body	160	valid

simplify18.0ms

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

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

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

99×	`*-un-lft-identity`
52×	`times-frac`
45×	`add-sqr-sqrt`
23×	`add-cube-cbrt`
18×	`distribute-lft-out` `distribute-lft-out--`
9×	`associate-/r*` `difference-of-squares`
7×	`add-exp-log` `add-cbrt-cube` `associate-/l*`
5×	`add-log-exp`
4×	`associate-/r/`
3×	`pow1`
2×	`cbrt-undiv` `flip3--` `frac-2neg` `flip3-+` `div-exp` `clear-num` `flip--` `flip-+` `div-inv` `associate-/l/`
1×	`sub-neg` `diff-log` `frac-sub`

Counts

3 → 104

Calls

3 calls:

5.0ms	(/ x (+ x 1.0))
9.0ms	(/ (+ x 1.0) (- x 1.0))
28.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series13.0ms

Counts

3 → 9

Calls

3 calls:

3.0ms	(/ x (+ x 1.0))
3.0ms	(/ (+ x 1.0) (- x 1.0))
7.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify41.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	392	760
1	1379	726
2	5001	716

prune171.0ms

Filtered

76 candidates to 113 candidates (-48.7%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	108	5	113
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	109	5	114

Merged error: 0.1b

Counts

114 → 5

localize9.0ms

Local error

Found 4 expressions with local error:

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

rewrite100.0ms

Algorithm

rewrite-expression-head

Rules

178×	`*-un-lft-identity`
80×	`times-frac`
64×	`add-sqr-sqrt`
44×	`distribute-lft-out--`
32×	`exp-prod`
30×	`distribute-lft-out`
18×	`add-cube-cbrt`
17×	`log-pow` `difference-of-squares`
9×	`add-log-exp`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `log-prod` `associate-/r*`
4×	`exp-sum` `associate-/l*`
3×	`sub-neg`
2×	`flip3--` `exp-diff` `diff-log` `associate-/r/` `flip--` `rem-exp-log` `associate-/l/`
1×	`cbrt-undiv` `log-div` `frac-2neg` `flip3-+` `div-exp` `rem-log-exp` `clear-num` `frac-sub` `flip-+` `div-inv`

Counts

4 → 130

Calls

4 calls:

28.0ms	(exp (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))))
7.0ms	(/ (+ x 1.0) (- x 1.0))
31.0ms	(log (exp (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))))
27.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series28.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(exp (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))))
3.0ms	(/ (+ x 1.0) (- x 1.0))
7.0ms	(log (exp (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))))
7.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify51.0ms

Algorithm

egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	404	1009
1	1249	941
2	5001	931

prune192.0ms

Filtered

87 candidates to 142 candidates (-63.2%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	140	2	142
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	140	7	147

Merged error: 0.1b

Counts

147 → 7

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ x 1.0) (- x 1.0)) 3)) (+ (* (/ (+ x 1.0) (- x 1.0)) (+ (/ (+ x 1.0) (- x 1.0)) (/ x (+ x 1.0)))) (* (/ x (+ x 1.0)) (/ x (+ x 1.0)))))
0.0b	(pow (/ x (+ x 1.0)) 3)
0.0b	(pow (/ (+ x 1.0) (- x 1.0)) 3)
1.6b	(- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ x 1.0) (- x 1.0)) 3))

rewrite306.0ms

Algorithm

rewrite-expression-head

Rules

1102×	`*-un-lft-identity`
735×	`times-frac`
560×	`add-sqr-sqrt`
344×	`unpow-prod-down` `cube-prod`
273×	`distribute-lft-out--`
188×	`difference-of-squares`
176×	`distribute-lft-out`
124×	`add-cube-cbrt`
77×	`associate-/l*`
62×	`sqr-pow`
31×	`associate-/r/`
27×	`frac-add`
16×	`frac-times` `associate-*r/`
12×	`add-exp-log` `add-cbrt-cube`
10×	`associate-*l/`
9×	`flip3-+` `flip-+`
6×	`pow1` `cube-div` `pow-unpow` `add-log-exp`
5×	`difference-cubes` `div-inv`
4×	`flip3--` `pow-exp` `flip--` `rem-cube-cbrt`
3×	`cbrt-undiv` `div-exp` `associate-/r*` `associate-/l/`
2×	`cube-mult` `pow-to-exp` `pow-pow` `unpow3` `frac-sub`
1×	`sub-neg` `frac-2neg` `diff-log` `div-sub` `clear-num`

Counts

4 → 565

Calls

4 calls:

142.0ms	(/ (- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ x 1.0) (- x 1.0)) 3)) (+ (* (/ (+ x 1.0) (- x 1.0)) (+ (/ (+ x 1.0) (- x 1.0)) (/ x (+ x 1.0)))) (* (/ x (+ x 1.0)) (/ x (+ x 1.0)))))
6.0ms	(pow (/ x (+ x 1.0)) 3)
11.0ms	(pow (/ (+ x 1.0) (- x 1.0)) 3)
93.0ms	(- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ x 1.0) (- x 1.0)) 3))

series58.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(/ (- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ x 1.0) (- x 1.0)) 3)) (+ (* (/ (+ x 1.0) (- x 1.0)) (+ (/ (+ x 1.0) (- x 1.0)) (/ x (+ x 1.0)))) (* (/ x (+ x 1.0)) (/ x (+ x 1.0)))))
3.0ms	(pow (/ x (+ x 1.0)) 3)
3.0ms	(pow (/ (+ x 1.0) (- x 1.0)) 3)
15.0ms	(- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ x 1.0) (- x 1.0)) 3))

simplify190.0ms

Algorithm

egg-herbie

Counts

577 → 577

Iterations

Useful iterations: 1 (37.0ms)

Iter	Nodes	Cost
0	1677	17362
1	5001	17123

prune1.4s

Filtered

203 candidates to 577 candidates (-184.2%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	576	1	577
Fresh	0	5	5
Picked	1	0	1
Done	0	1	1
Total	577	7	584

Merged error: 0.1b

Counts

584 → 7

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (/ (+ x 1.0) (- x 1.0)) 3)
0.1b	(cbrt (pow (- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ x 1.0) (- x 1.0)) 3)) 3))
0.1b	(pow (- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ x 1.0) (- x 1.0)) 3)) 3)
1.6b	(- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ x 1.0) (- x 1.0)) 3))

rewrite360.0ms

Algorithm

rewrite-expression-head

Rules

997×	`*-un-lft-identity`
480×	`unpow-prod-down` `times-frac` `cube-prod`
467×	`add-sqr-sqrt`
273×	`distribute-lft-out--`
188×	`difference-of-squares`
170×	`distribute-lft-out`
160×	`cbrt-prod`
63×	`sqr-pow`
31×	`add-cube-cbrt`
13×	`cube-div`
8×	`add-exp-log` `add-cbrt-cube`
6×	`pow1` `pow-unpow` `add-log-exp`
5×	`difference-cubes` `flip3--` `flip--`
4×	`associate-/r/`
3×	`cube-mult` `cbrt-div` `unpow3` `pow-exp` `frac-sub` `rem-cube-cbrt`
2×	`pow-to-exp` `pow-pow` `div-inv`
1×	`cbrt-undiv` `sub-neg` `pow1/3` `diff-log` `div-exp` `rem-cbrt-cube`

Counts

4 → 505

Calls

4 calls:

10.0ms	(pow (/ (+ x 1.0) (- x 1.0)) 3)
105.0ms	(cbrt (pow (- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ x 1.0) (- x 1.0)) 3)) 3))
100.0ms	(pow (- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ x 1.0) (- x 1.0)) 3)) 3)
94.0ms	(- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ x 1.0) (- x 1.0)) 3))

series53.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(pow (/ (+ x 1.0) (- x 1.0)) 3)
14.0ms	(cbrt (pow (- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ x 1.0) (- x 1.0)) 3)) 3))
16.0ms	(pow (- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ x 1.0) (- x 1.0)) 3)) 3)
14.0ms	(- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ x 1.0) (- x 1.0)) 3))

simplify177.0ms

Algorithm

egg-herbie

Counts

517 → 517

Iterations

Useful iterations: 2 (96.0ms)

Iter	Nodes	Cost
0	1007	7140
1	4428	6978
2	5001	6848

prune554.0ms

Filtered

116 candidates to 517 candidates (-345.7%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	517	0	517
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	517	7	524

Merged error: 0.1b

Counts

524 → 7

regimes121.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 29.1b

bsearch24.0ms

Steps

Iters	Range		Point
7	306.28763118649994	38212.35684414374	11886.148758601244
7	-34031.803709614505	-497.50744917941546	-9873.42801087238

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	27
1	34	27

end0.0ms

sample709.0ms

Algorithm

intervals

Results

237.0ms	1654×	body	1280	valid
140.0ms	1239×	body	640	valid
128.0ms	4124×	body	80	valid
55.0ms	654×	body	320	valid
21.0ms	329×	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

sample24.0ms

simplify18.0ms

prune2.0ms

localize6.0ms

rewrite46.0ms

series13.0ms

simplify41.0ms

prune171.0ms

localize9.0ms

rewrite100.0ms

series28.0ms

simplify51.0ms

prune192.0ms

localize17.0ms

rewrite306.0ms

series58.0ms

simplify190.0ms

prune1.4s

localize17.0ms

rewrite360.0ms

series53.0ms

simplify177.0ms

prune554.0ms

regimes121.0ms

bsearch24.0ms

simplify1.0ms

end0.0ms

sample709.0ms

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