Details

sample22.0ms

Algorithm

intervals

Results

6.0ms	47×	body	1280	valid
4.0ms	139×	body	80	valid
3.0ms	35×	body	640	valid
2.0ms	22×	body	320	valid
1.0ms	13×	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

prune2.0ms

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: 27.6b

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))
3.4b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite121.0ms

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))
8.0ms	(/ (+ x 1.0) (- x 1.0))
46.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series200.0ms

Counts

3 → 9

Calls

3 calls:

33.0ms	(/ x (+ x 1.0))
39.0ms	(/ (+ x 1.0) (- x 1.0))
127.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify215.0ms

Algorithm

egg-herbie

Counts

605 → 605

Iterations

Useful iterations: 2 (82.0ms)

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

prune682.0ms

Filtered

605 candidates to 217 candidates (35.9%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	599	6	605
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	600	6	606

Merged error: 0.2b

Counts

606 → 6

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (/ (+ x 1.0) (- x 1.0)) 3)
0.1b	(pow (/ x (+ x 1.0)) 3)
0.1b	(/ (- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ x 1.0) (- x 1.0)) 3)) (fma (/ (+ x 1.0) (- x 1.0)) (+ (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))) (* (/ x (+ x 1.0)) (/ x (+ x 1.0)))))
3.4b	(- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ x 1.0) (- x 1.0)) 3))

rewrite894.0ms

Algorithm

rewrite-expression-head

Rules

5207×	`*-un-lft-identity`
3831×	`times-frac`
3117×	`add-sqr-sqrt`
2498×	`unpow-prod-down` `cube-prod`
2436×	`prod-diff`
2009×	`add-cube-cbrt`
950×	`distribute-lft-out`
609×	`distribute-lft-out--`
524×	`difference-of-squares`
412×	`associate-/r/`
207×	`div-inv`
163×	`sqr-pow`
120×	`flip3-+` `flip-+`
103×	`cube-mult` `unpow3`
88×	`flip3--` `flip--`
77×	`associate-/l*`
42×	`fma-neg`
12×	`add-exp-log` `add-cbrt-cube`
6×	`pow1` `cube-div` `pow-unpow` `add-log-exp`
5×	`difference-cubes`
4×	`expm1-log1p-u` `pow-exp` `log1p-expm1-u` `rem-cube-cbrt`
3×	`cbrt-undiv` `div-exp` `associate-/r*` `associate-/l/`
2×	`pow-to-exp` `pow-pow` `frac-sub`
1×	`sub-neg` `frac-2neg` `diff-log` `div-sub` `clear-num`

Counts

4 → 3028

Calls

4 calls:

10.0ms	(pow (/ (+ x 1.0) (- x 1.0)) 3)
7.0ms	(pow (/ x (+ x 1.0)) 3)
271.0ms	(/ (- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ x 1.0) (- x 1.0)) 3)) (fma (/ (+ x 1.0) (- x 1.0)) (+ (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))) (* (/ x (+ x 1.0)) (/ x (+ x 1.0)))))
169.0ms	(- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ x 1.0) (- x 1.0)) 3))

series948.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(pow (/ (+ x 1.0) (- x 1.0)) 3)
58.0ms	(pow (/ x (+ x 1.0)) 3)
536.0ms	(/ (- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ x 1.0) (- x 1.0)) 3)) (fma (/ (+ x 1.0) (- x 1.0)) (+ (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))) (* (/ x (+ x 1.0)) (/ x (+ x 1.0)))))
295.0ms	(- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ x 1.0) (- x 1.0)) 3))

simplify1.3s

Algorithm

egg-herbie

Counts

3040 → 3040

Iterations

Useful iterations: 1 (67.0ms)

Iter	Nodes	Cost
0	2484	116830
1	5001	106567

prune1.7s

Filtered

3040 candidates to 370 candidates (12.2%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	3036	4	3040
Fresh	1	4	5
Picked	0	1	1
Done	0	0	0
Total	3037	9	3046

Merged error: 0.1b

Counts

3046 → 9

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ x 1.0) (- x 1.0)) 3)) (fma (/ (+ x 1.0) (- x 1.0)) (+ (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))) (* (/ x (+ x 1.0)) (/ x (+ x 1.0)))))
0.1b	(cbrt (pow (/ (- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ x 1.0) (- x 1.0)) 3)) (fma (/ (+ x 1.0) (- x 1.0)) (+ (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))) (* (/ x (+ x 1.0)) (/ x (+ x 1.0))))) 3))
0.1b	(pow (/ (- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ x 1.0) (- x 1.0)) 3)) (fma (/ (+ x 1.0) (- x 1.0)) (+ (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))) (* (/ x (+ x 1.0)) (/ x (+ x 1.0))))) 3)
3.4b	(- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ x 1.0) (- x 1.0)) 3))

rewrite1.3s

Algorithm

rewrite-expression-head

Rules

7679×	`*-un-lft-identity`
5747×	`times-frac`
4397×	`add-sqr-sqrt`
3644×	`unpow-prod-down` `cube-prod`
2436×	`prod-diff`
2297×	`add-cube-cbrt`
1318×	`distribute-lft-out`
1237×	`distribute-lft-out--`
948×	`difference-of-squares`
476×	`cbrt-prod`
404×	`associate-/r/`
307×	`sqr-pow`
207×	`div-inv`
118×	`flip3-+` `flip-+`
103×	`cube-mult` `unpow3`
86×	`flip3--` `flip--`
77×	`associate-/l*`
42×	`fma-neg`
17×	`difference-cubes`
9×	`add-exp-log` `add-cbrt-cube`
6×	`cube-div` `add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`pow-unpow` `associate-/r*` `associate-/l/`
2×	`cbrt-undiv` `div-exp` `pow-exp` `frac-sub` `rem-cube-cbrt`
1×	`pow-to-exp` `sub-neg` `cbrt-div` `pow-pow` `frac-2neg` `pow1/3` `diff-log` `div-sub` `clear-num` `rem-cbrt-cube`

Counts

4 → 3876

Calls

4 calls:

274.0ms	(/ (- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ x 1.0) (- x 1.0)) 3)) (fma (/ (+ x 1.0) (- x 1.0)) (+ (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))) (* (/ x (+ x 1.0)) (/ x (+ x 1.0)))))
162.0ms	(cbrt (pow (/ (- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ x 1.0) (- x 1.0)) 3)) (fma (/ (+ x 1.0) (- x 1.0)) (+ (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))) (* (/ x (+ x 1.0)) (/ x (+ x 1.0))))) 3))
141.0ms	(pow (/ (- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ x 1.0) (- x 1.0)) 3)) (fma (/ (+ x 1.0) (- x 1.0)) (+ (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))) (* (/ x (+ x 1.0)) (/ x (+ x 1.0))))) 3)
170.0ms	(- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ x 1.0) (- x 1.0)) 3))

series1.9s

Counts

4 → 12

Calls

4 calls:

533.0ms	(/ (- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ x 1.0) (- x 1.0)) 3)) (fma (/ (+ x 1.0) (- x 1.0)) (+ (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))) (* (/ x (+ x 1.0)) (/ x (+ x 1.0)))))
537.0ms	(cbrt (pow (/ (- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ x 1.0) (- x 1.0)) 3)) (fma (/ (+ x 1.0) (- x 1.0)) (+ (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))) (* (/ x (+ x 1.0)) (/ x (+ x 1.0))))) 3))
559.0ms	(pow (/ (- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ x 1.0) (- x 1.0)) 3)) (fma (/ (+ x 1.0) (- x 1.0)) (+ (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))) (* (/ x (+ x 1.0)) (/ x (+ x 1.0))))) 3)
301.0ms	(- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ x 1.0) (- x 1.0)) 3))

simplify1.6s

Algorithm

egg-herbie

Counts

3888 → 3888

Iterations

Useful iterations: 1 (85.0ms)

Iter	Nodes	Cost
0	3545	163047
1	5003	154800

prune2.7s

Filtered

3888 candidates to 500 candidates (12.9%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	3887	1	3888
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	3887	10	3897

Merged error: 0.1b

Counts

3897 → 10

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- x 1.0) (+ x 1.0))
0.0b	(/ x (+ x 1.0))
0.0b	(/ 1 (/ (- x 1.0) (+ x 1.0)))
3.4b	(- (/ x (+ x 1.0)) (/ 1 (/ (- x 1.0) (+ x 1.0))))

rewrite365.0ms

Algorithm

rewrite-expression-head

Rules

3703×	`times-frac`
3383×	`*-un-lft-identity`
2296×	`add-sqr-sqrt`
1789×	`add-cube-cbrt`
1494×	`prod-diff`
553×	`distribute-lft-out`
307×	`associate-/r/`
247×	`difference-of-squares`
241×	`distribute-lft-out--`
164×	`div-inv`
144×	`flip3-+` `flip-+`
34×	`associate-/r*`
19×	`add-exp-log`
18×	`fma-neg`
13×	`add-cbrt-cube`
11×	`associate-/l*`
9×	`div-exp`
6×	`add-log-exp`
5×	`pow1` `cbrt-undiv`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`frac-2neg` `clear-num`
2×	`rec-exp` `flip3--` `1-exp` `flip--` `associate-/l/`
1×	`sub-neg` `pow-flip` `diff-log` `div-sub` `frac-sub` `inv-pow`

Counts

4 → 1754

Calls

4 calls:

8.0ms	(/ (- x 1.0) (+ x 1.0))
5.0ms	(/ x (+ x 1.0))
13.0ms	(/ 1 (/ (- x 1.0) (+ x 1.0)))
107.0ms	(- (/ x (+ x 1.0)) (/ 1 (/ (- x 1.0) (+ x 1.0))))

series237.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(/ (- x 1.0) (+ x 1.0))
36.0ms	(/ x (+ x 1.0))
36.0ms	(/ 1 (/ (- x 1.0) (+ x 1.0)))
131.0ms	(- (/ x (+ x 1.0)) (/ 1 (/ (- x 1.0) (+ x 1.0))))

simplify768.0ms

Algorithm

egg-herbie

Counts

1766 → 1766

Iterations

Useful iterations: 1 (71.0ms)

Iter	Nodes	Cost
0	3287	74392
1	5001	61456

prune1.0s

Filtered

1766 candidates to 357 candidates (20.2%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	1764	2	1766
Fresh	2	5	7
Picked	0	1	1
Done	0	2	2
Total	1766	10	1776

Merged error: 0.1b

Counts

1776 → 10

regimes56.0ms

Accuracy

99.7% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 29.3b

bsearch78.0ms

Steps

Iters	Range		Point
6	14028.172733867412	57946.35045805707	14949.242297652785
10	-7888799.454350161	-0.0014566459989916651	-15417.922011129276

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	33
1	42	33

end0.0ms

sample611.0ms

Algorithm

intervals

Results

211.0ms	1668×	body	1280	valid
125.0ms	1266×	body	640	valid
117.0ms	4110×	body	80	valid
49.0ms	638×	body	320	valid
16.0ms	318×	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