Details

sample19.0ms

Algorithm

intervals

Results

5.0ms	47×	body	1280	valid
3.0ms	139×	body	80	valid
3.0ms	35×	body	640	valid
1.0ms	22×	body	320	valid
1.0ms	13×	body	160	valid

simplify22.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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

localize9.0ms

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)))

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

series212.0ms

Counts

3 → 9

Calls

3 calls:

38.0ms	(/ x (+ x 1.0))
37.0ms	(/ (+ x 1.0) (- x 1.0))
137.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify214.0ms

Algorithm

egg-herbie

Counts

605 → 605

Iterations

Useful iterations: 2 (83.0ms)

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

prune690.0ms

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))

rewrite824.0ms

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:

9.0ms	(pow (/ (+ x 1.0) (- x 1.0)) 3)
7.0ms	(pow (/ x (+ x 1.0)) 3)
250.0ms	(/ (- (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)))))
152.0ms	(- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ x 1.0) (- x 1.0)) 3))

series1.2s

Counts

4 → 12

Calls

4 calls:

62.0ms	(pow (/ (+ x 1.0) (- x 1.0)) 3)
57.0ms	(pow (/ x (+ x 1.0)) 3)
768.0ms	(/ (- (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)))))
310.0ms	(- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ x 1.0) (- x 1.0)) 3))

simplify1.1s

Algorithm

egg-herbie

Counts

3040 → 3040

Iterations

Useful iterations: 1 (70.0ms)

Iter	Nodes	Cost
0	2484	116827
1	5002	94047

prune1.7s

Filtered

3040 candidates to 370 candidates (12.2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	3036	4	3040
Fresh	1	4	5
Picked	1	0	1
Done	0	0	0
Total	3038	8	3046

Merged error: 0.1b

Counts

3046 → 8

localize16.0ms

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))

rewrite1.2s

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:

250.0ms	(/ (- (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)))))
141.0ms	(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))
124.0ms	(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)
149.0ms	(- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ x 1.0) (- x 1.0)) 3))

series1.9s

Counts

4 → 12

Calls

4 calls:

541.0ms	(/ (- (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)))))
539.0ms	(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))
565.0ms	(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)
302.0ms	(- (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 501 candidates (12.9%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	3886	2	3888
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	3886	10	3896

Merged error: 0.1b

Counts

3896 → 10

localize7.0ms

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))))

rewrite357.0ms

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))
11.0ms	(/ 1 (/ (- x 1.0) (+ x 1.0)))
100.0ms	(- (/ x (+ x 1.0)) (/ 1 (/ (- x 1.0) (+ x 1.0))))

series238.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(/ (- x 1.0) (+ x 1.0))
33.0ms	(/ x (+ x 1.0))
37.0ms	(/ 1 (/ (- x 1.0) (+ x 1.0)))
130.0ms	(- (/ x (+ x 1.0)) (/ 1 (/ (- x 1.0) (+ x 1.0))))

simplify627.0ms

Algorithm

egg-herbie

Counts

1766 → 1766

Iterations

Useful iterations: 1 (67.0ms)

Iter	Nodes	Cost
0	3287	74392
1	5001	61456

prune1.1s

Filtered

1766 candidates to 357 candidates (20.2%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	1764	2	1766
Fresh	2	6	8
Picked	0	1	1
Done	0	1	1
Total	1766	10	1776

Merged error: 0.1b

Counts

1776 → 10

regimes75.0ms

Accuracy

99.7% (0.1b remaining)

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

bsearch81.0ms

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	44	35
1	44	35

end0.0ms

sample512.0ms

Algorithm

intervals

Results

179.0ms	1668×	body	1280	valid
100.0ms	1266×	body	640	valid
93.0ms	4110×	body	80	valid
39.0ms	638×	body	320	valid
13.0ms	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

Details

sample19.0ms

simplify22.0ms

prune2.0ms

localize9.0ms

rewrite110.0ms

series212.0ms

simplify214.0ms

prune690.0ms

localize14.0ms

rewrite824.0ms

series1.2s

simplify1.1s

prune1.7s

localize16.0ms

rewrite1.2s

series1.9s

simplify1.6s

prune2.7s

localize7.0ms

rewrite357.0ms

series238.0ms

simplify627.0ms

prune1.1s

regimes75.0ms

bsearch81.0ms

simplify2.0ms

end0.0ms

sample512.0ms

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