Details

sample24.0ms

Algorithm

intervals

Results

7.0ms	53×	body	1280	valid
4.0ms	38×	body	640	valid
4.0ms	136×	body	80	valid
1.0ms	20×	body	320	valid
0.0ms	9×	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

prune3.0ms

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: 28.3b

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))
2.7b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite47.0ms

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:

7.0ms	(/ x (+ x 1.0))
7.0ms	(/ (+ x 1.0) (- x 1.0))
28.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series411.0ms

Counts

3 → 9

Calls

3 calls:

36.0ms	(/ x (+ x 1.0))
247.0ms	(/ (+ x 1.0) (- x 1.0))
129.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify41.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	390	760
1	1367	728
2	5001	716

prune268.0ms

Filtered

113 candidates to 76 candidates (67.3%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	109	4	113
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	110	4	114

Merged error: 0.0b

Counts

114 → 4

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (/ (+ x 1.0) (- x 1.0)) 3)
0.0b	(* (/ x (+ x 1.0)) (/ x (+ x 1.0)))
0.0b	(pow (/ x (+ x 1.0)) 3)
2.7b	(- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ x 1.0) (- x 1.0)) 3))

rewrite150.0ms

Algorithm

rewrite-expression-head

Rules

354×	`*-un-lft-identity`
216×	`times-frac`
190×	`add-sqr-sqrt`
104×	`unpow-prod-down` `cube-prod`
78×	`add-cube-cbrt`
66×	`distribute-lft-out`
61×	`distribute-lft-out--`
44×	`difference-of-squares`
24×	`swap-sqr`
22×	`add-exp-log` `add-cbrt-cube`
18×	`associate-r` `associate-l`
16×	`associate-/r/`
14×	`sqr-pow`
13×	`pow1`
8×	`div-inv`
6×	`cbrt-undiv` `pow-unpow` `flip3-+` `div-exp` `flip-+` `add-log-exp`
4×	`cube-div` `pow-exp` `prod-exp` `cbrt-unprod` `rem-cube-cbrt` `unswap-sqr`
3×	`flip3--` `flip--`
2×	`cube-mult` `pow-to-exp` `pow-pow` `unpow3`
1×	`difference-cubes` `pow2` `frac-times` `sub-neg` `pow-plus` `diff-log` `associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `*-commutative` `pow-prod-up` `frac-sub`

Counts

4 → 303

Calls

4 calls:

9.0ms	(pow (/ (+ x 1.0) (- x 1.0)) 3)
18.0ms	(* (/ x (+ x 1.0)) (/ x (+ x 1.0)))
7.0ms	(pow (/ x (+ x 1.0)) 3)
98.0ms	(- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ x 1.0) (- x 1.0)) 3))

series495.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(pow (/ (+ x 1.0) (- x 1.0)) 3)
50.0ms	(* (/ x (+ x 1.0)) (/ x (+ x 1.0)))
61.0ms	(pow (/ x (+ x 1.0)) 3)
317.0ms	(- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ x 1.0) (- x 1.0)) 3))

simplify61.0ms

Algorithm

egg-herbie

Counts

315 → 315

Iterations

Useful iterations: 1 (30.0ms)

Iter	Nodes	Cost
0	1164	2932
1	5002	2690

prune634.0ms

Filtered

315 candidates to 141 candidates (44.8%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	313	2	315
Fresh	0	3	3
Picked	1	0	1
Done	0	0	0
Total	314	5	319

Merged error: 0.0b

Counts

319 → 5

localize25.0ms

Local error

Found 4 expressions with local error:

0.4b	(cbrt (/ x (+ x 1.0)))
0.4b	(pow (cbrt (/ x (+ x 1.0))) 4)
2.7b	(- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ x 1.0) (- x 1.0)) 3))
15.4b	(cbrt (* (/ x (+ x 1.0)) (/ x (+ x 1.0))))

rewrite131.0ms

Algorithm

rewrite-expression-head

Rules

220×	`*-un-lft-identity`
112×	`times-frac`
106×	`add-sqr-sqrt`
81×	`unpow-prod-down`
60×	`cube-prod`
53×	`distribute-lft-out--`
38×	`distribute-lft-out`
37×	`cbrt-prod`
36×	`difference-of-squares`
22×	`add-cube-cbrt`
13×	`sqr-pow`
6×	`add-log-exp`
5×	`pow1` `add-exp-log`
4×	`cbrt-div` `associate-/r/` `add-cbrt-cube`
3×	`pow-unpow` `pow1/3`
2×	`cube-div` `pow-pow` `flip3-+` `flip-+` `div-inv`
1×	`difference-cubes` `frac-times` `pow-to-exp` `sub-neg` `flip3--` `diff-log` `associate-r/` `associate-l/` `pow-exp` `frac-sub` `flip--`

Counts

4 → 162

Calls

4 calls:

4.0ms	(cbrt (/ x (+ x 1.0)))
7.0ms	(pow (cbrt (/ x (+ x 1.0))) 4)
100.0ms	(- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ x 1.0) (- x 1.0)) 3))
9.0ms	(cbrt (* (/ x (+ x 1.0)) (/ x (+ x 1.0))))

series892.0ms

Counts

4 → 12

Calls

4 calls:

169.0ms	(cbrt (/ x (+ x 1.0)))
237.0ms	(pow (cbrt (/ x (+ x 1.0))) 4)
326.0ms	(- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ x 1.0) (- x 1.0)) 3))
159.0ms	(cbrt (* (/ x (+ x 1.0)) (/ x (+ x 1.0))))

simplify84.0ms

Algorithm

egg-herbie

Counts

174 → 174

Iterations

Useful iterations: 2 (63.0ms)

Iter	Nodes	Cost
0	751	2034
1	2520	1966
2	5002	1940

prune563.0ms

Filtered

174 candidates to 96 candidates (55.2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	174	0	174
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	174	5	179

Merged error: 0.0b

Counts

179 → 5

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (+ x 1.0) (- x 1.0))
0.1b	(pow (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))) 3)
0.1b	(cbrt (pow (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))) 3))
2.7b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite115.0ms

Algorithm

rewrite-expression-head

Rules

273×	`*-un-lft-identity`
120×	`times-frac`
91×	`add-sqr-sqrt`
70×	`distribute-lft-out--`
46×	`distribute-lft-out`
38×	`cbrt-prod`
32×	`unpow-prod-down` `cube-prod`
25×	`difference-of-squares`
21×	`add-cube-cbrt`
7×	`add-exp-log` `add-cbrt-cube`
6×	`cube-div` `add-log-exp`
5×	`pow1` `associate-/r*`
4×	`flip3--` `flip--` `associate-/l*`
3×	`pow-unpow` `cbrt-div` `frac-sub`
2×	`cube-mult` `unpow3` `associate-/r/` `associate-/l/` `sqr-pow`
1×	`cbrt-undiv` `pow-to-exp` `sub-neg` `pow-pow` `frac-2neg` `flip3-+` `pow1/3` `diff-log` `div-exp` `pow-exp` `clear-num` `rem-cbrt-cube` `flip-+` `div-inv` `rem-cube-cbrt`

Counts

4 → 173

Calls

4 calls:

8.0ms	(/ (+ x 1.0) (- x 1.0))
34.0ms	(pow (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))) 3)
31.0ms	(cbrt (pow (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))) 3))
33.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series488.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(/ (+ x 1.0) (- x 1.0))
182.0ms	(pow (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))) 3)
134.0ms	(cbrt (pow (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))) 3))
131.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify71.0ms

Algorithm

egg-herbie

Counts

185 → 185

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	545	1756
1	2145	1700
2	5001	1689

prune305.0ms

Filtered

185 candidates to 91 candidates (49.2%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	185	0	185
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	185	5	190

Merged error: 0.0b

Counts

190 → 5

regimes93.0ms

Accuracy

99.9% (0.0b remaining)

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

bsearch112.0ms

Steps

Iters	Range		Point
9	41.84587058567329	170944420.23003155	280783.13854657294
8	-103568517.90772113	-41296.44367278978	-485575.57811715995

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	39
1	46	39

end0.0ms

sample651.0ms

Algorithm

intervals

Results

222.0ms	1720×	body	1280	valid
128.0ms	1266×	body	640	valid
109.0ms	4117×	body	80	valid
46.0ms	579×	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

Details

sample24.0ms

simplify18.0ms

prune3.0ms

localize6.0ms

rewrite47.0ms

series411.0ms

simplify41.0ms

prune268.0ms

localize15.0ms

rewrite150.0ms

series495.0ms

simplify61.0ms

prune634.0ms

localize25.0ms

rewrite131.0ms

series892.0ms

simplify84.0ms

prune563.0ms

localize9.0ms

rewrite115.0ms

series488.0ms

simplify71.0ms

prune305.0ms

regimes93.0ms

bsearch112.0ms

simplify2.0ms

end0.0ms

sample651.0ms

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