Details

sample20.0ms

Algorithm

intervals

Results

5.0ms	47×	body	1280	valid
4.0ms	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

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)))

rewrite51.0ms

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))
8.0ms	(/ (+ x 1.0) (- x 1.0))
34.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series215.0ms

Counts

3 → 9

Calls

3 calls:

34.0ms	(/ x (+ x 1.0))
44.0ms	(/ (+ x 1.0) (- x 1.0))
136.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify44.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (34.0ms)

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

prune217.0ms

Filtered

113 candidates to 76 candidates (67.3%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	107	6	113
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	108	6	114

Merged error: 0.0b

Counts

114 → 6

localize16.0ms

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

rewrite343.0ms

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:

14.0ms	(pow (/ (+ x 1.0) (- x 1.0)) 3)
7.0ms	(pow (/ x (+ x 1.0)) 3)
155.0ms	(/ (- (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)))))
105.0ms	(- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ x 1.0) (- x 1.0)) 3))

series1.1s

Counts

4 → 12

Calls

4 calls:

68.0ms	(pow (/ (+ x 1.0) (- x 1.0)) 3)
64.0ms	(pow (/ x (+ x 1.0)) 3)
612.0ms	(/ (- (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)))))
313.0ms	(- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ x 1.0) (- x 1.0)) 3))

simplify201.0ms

Algorithm

egg-herbie

Counts

577 → 577

Iterations

Useful iterations: 1 (40.0ms)

Iter	Nodes	Cost
0	1677	17362
1	5001	17123

prune760.0ms

Filtered

577 candidates to 203 candidates (35.2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	574	3	577
Fresh	0	5	5
Picked	1	0	1
Done	0	0	0
Total	575	8	583

Merged error: 0.0b

Counts

583 → 8

localize19.0ms

Local error

Found 4 expressions with local error:

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

rewrite862.0ms

Algorithm

rewrite-expression-head

Rules

3574×	`*-un-lft-identity`
2651×	`times-frac`
1840×	`add-sqr-sqrt`
1536×	`unpow-prod-down` `cube-prod`
901×	`distribute-lft-out--`
612×	`difference-of-squares`
544×	`distribute-lft-out`
522×	`cbrt-prod`
412×	`add-cube-cbrt`
206×	`sqr-pow`
135×	`frac-add`
115×	`associate-/r/`
80×	`frac-times` `associate-*r/`
77×	`associate-/l*`
50×	`associate-*l/`
35×	`flip3-+` `flip-+`
17×	`difference-cubes`
9×	`add-exp-log` `add-cbrt-cube`
6×	`cube-div` `add-log-exp`
5×	`pow1` `div-inv`
3×	`pow-unpow` `associate-/r*` `associate-/l/`
2×	`cbrt-undiv` `cube-mult` `flip3--` `unpow3` `div-exp` `pow-exp` `frac-sub` `flip--` `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 → 1505

Calls

4 calls:

159.0ms	(/ (- (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)))))
197.0ms	(cbrt (pow (/ (- (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))
179.0ms	(pow (/ (- (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)
103.0ms	(- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ x 1.0) (- x 1.0)) 3))

series2.4s

Counts

4 → 12

Calls

4 calls:

605.0ms	(/ (- (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)))))
826.0ms	(cbrt (pow (/ (- (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))
637.0ms	(pow (/ (- (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)
321.0ms	(- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ x 1.0) (- x 1.0)) 3))

simplify688.0ms

Algorithm

egg-herbie

Counts

1517 → 1517

Iterations

Useful iterations: 1 (60.0ms)

Iter	Nodes	Cost
0	2720	70091
1	5001	69548

prune1.4s

Filtered

1517 candidates to 325 candidates (21.4%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	1517	0	1517
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	1517	8	1525

Merged error: 0.0b

Counts

1525 → 8

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (+ x 1.0))
0.0b	(/ (+ x 1.0) (- x 1.0))
0.1b	(* x (/ 1 (+ x 1.0)))
8.5b	(- (* x (/ 1 (+ x 1.0))) (/ (+ x 1.0) (- x 1.0)))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

70×	`*-un-lft-identity`
50×	`add-sqr-sqrt`
46×	`times-frac`
33×	`add-cube-cbrt`
19×	`add-exp-log`
18×	`associate-r`
13×	`add-cbrt-cube` `distribute-lft-out`
9×	`associate-/r*`
7×	`pow1` `associate-/l*`
6×	`associate-/r/` `add-log-exp`
5×	`div-exp` `distribute-lft-out--` `difference-of-squares`
4×	`prod-exp`
3×	`cbrt-undiv` `flip3-+` `associate-l` `flip-+` `div-inv` `unswap-sqr`
2×	`rec-exp` `flip3--` `frac-2neg` `1-exp` `associate-*r/` `clear-num` `un-div-inv` `frac-sub` `flip--` `cbrt-unprod` `associate-/l/`
1×	`sub-neg` `pow-flip` `diff-log` `pow-prod-down` `*-commutative` `inv-pow`

Counts

4 → 137

Calls

4 calls:

6.0ms	(/ 1 (+ x 1.0))
7.0ms	(/ (+ x 1.0) (- x 1.0))
14.0ms	(* x (/ 1 (+ x 1.0)))
15.0ms	(- (* x (/ 1 (+ x 1.0))) (/ (+ x 1.0) (- x 1.0)))

series245.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(/ 1 (+ x 1.0))
39.0ms	(/ (+ x 1.0) (- x 1.0))
40.0ms	(* x (/ 1 (+ x 1.0)))
137.0ms	(- (* x (/ 1 (+ x 1.0))) (/ (+ x 1.0) (- x 1.0)))

simplify63.0ms

Algorithm

egg-herbie

Counts

149 → 149

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	507	875
1	2099	793
2	5001	754

prune178.0ms

Filtered

149 candidates to 92 candidates (61.7%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	149	0	149
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	149	8	157

Merged error: 0.0b

Counts

157 → 8

regimes46.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.1b against oracle of 0.0b 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	42	35
1	42	35

end0.0ms

sample548.0ms

Algorithm

intervals

Results

185.0ms	1668×	body	1280	valid
108.0ms	1266×	body	640	valid
96.0ms	4110×	body	80	valid
49.0ms	638×	body	320	valid
14.0ms	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

sample20.0ms

simplify22.0ms

prune2.0ms

localize6.0ms

rewrite51.0ms

series215.0ms

simplify44.0ms

prune217.0ms

localize16.0ms

rewrite343.0ms

series1.1s

simplify201.0ms

prune760.0ms

localize19.0ms

rewrite862.0ms

series2.4s

simplify688.0ms

prune1.4s

localize8.0ms

rewrite47.0ms

series245.0ms

simplify63.0ms

prune178.0ms

regimes46.0ms

bsearch81.0ms

simplify2.0ms

end0.0ms

sample548.0ms

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