Details

analyze3.0ms

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	50%	0%	2
50%	25%	25%	3
62.5%	12.5%	25%	4
68.7%	6.2%	25%	5
71.8%	3.1%	25%	6
73.4%	1.6%	25%	7
74.2%	0.8%	25%	8
74.6%	0.4%	25%	9
74.8%	0.2%	25%	10
74.9%	0.1%	25%	11
74.9%	0%	25%	12
74.9%	0%	25%	13
74.9%	0%	25%	14

sample13.0ms

Algorithm

intervals

Results

7.0ms	255×	body	80	valid
0.0ms	1×	body	1280	valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	93	8
1	93	8

prune3.0ms

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: 0.2b

Counts

2 → 1

localize5.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (+ x 1.0))
0.0b	(+ 1.0 (sqrt (+ x 1.0)))
0.2b	(/ x (+ 1.0 (sqrt (+ x 1.0))))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

25×	`*-un-lft-identity`
14×	`add-sqr-sqrt`
13×	`add-cube-cbrt`
12×	`times-frac`
6×	`distribute-lft-out`
5×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
4×	`pow1` `associate-/r*` `sqrt-prod`
3×	`flip3-+` `flip-+` `associate-/l*`
2×	`sqrt-div` `associate-/r/`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

3 → 61

Calls

3 calls:

3.0ms	(sqrt (+ x 1.0))
5.0ms	(+ 1.0 (sqrt (+ x 1.0)))
7.0ms	(/ x (+ 1.0 (sqrt (+ x 1.0))))

series28.0ms

Counts

3 → 9

Calls

3 calls:

3.0ms	(sqrt (+ x 1.0))
5.0ms	(+ 1.0 (sqrt (+ x 1.0)))
19.0ms	(/ x (+ 1.0 (sqrt (+ x 1.0))))

simplify46.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	4965	1017
1	4965	1017

prune135.0ms

Filtered

52 candidates to 70 candidates (-34.6%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	66	4	70
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	67	4	71

Merged error: 0b

Counts

71 → 4

localize7.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ x 1.0))
0.0b	(+ 1.0 (sqrt (+ x 1.0)))
0.1b	(/ (+ 1.0 (sqrt (+ x 1.0))) x)
0.2b	(/ 1 (/ (+ 1.0 (sqrt (+ x 1.0))) x))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

108×	`times-frac`
99×	`*-un-lft-identity`
64×	`add-sqr-sqrt`
63×	`add-cube-cbrt`
19×	`associate-/r*`
18×	`distribute-lft-out`
17×	`add-exp-log`
11×	`add-cbrt-cube`
8×	`div-exp`
7×	`associate-/l*`
6×	`pow1` `div-inv` `add-log-exp`
4×	`cbrt-undiv` `sqrt-prod`
3×	`flip3-+` `flip-+`
2×	`rec-exp` `frac-2neg` `sqrt-div` `1-exp` `clear-num` `associate-/l/`
1×	`+-commutative` `rem-sqrt-square` `pow-flip` `sqrt-pow1` `pow1/2` `sum-log` `associate-/r/` `inv-pow`

Counts

4 → 149

Calls

4 calls:

3.0ms	(sqrt (+ x 1.0))
5.0ms	(+ 1.0 (sqrt (+ x 1.0)))
9.0ms	(/ (+ 1.0 (sqrt (+ x 1.0))) x)
10.0ms	(/ 1 (/ (+ 1.0 (sqrt (+ x 1.0))) x))

series32.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(sqrt (+ x 1.0))
4.0ms	(+ 1.0 (sqrt (+ x 1.0)))
9.0ms	(/ (+ 1.0 (sqrt (+ x 1.0))) x)
15.0ms	(/ 1 (/ (+ 1.0 (sqrt (+ x 1.0))) x))

simplify45.0ms

Algorithm

egg-herbie

Counts

161 → 161

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	5170	2489

prune259.0ms

Filtered

107 candidates to 161 candidates (-50.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	161	0	161
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	161	4	165

Merged error: 0b

Counts

165 → 4

localize8.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (+ 1.0 (sqrt (+ x 1.0))))
0.1b	(sqrt (+ 1.0 (sqrt (+ x 1.0))))
0.4b	(/ x (sqrt (+ 1.0 (sqrt (+ x 1.0)))))
0.4b	(/ (/ x (sqrt (+ 1.0 (sqrt (+ x 1.0))))) (sqrt (+ 1.0 (sqrt (+ x 1.0)))))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

378×	`times-frac`
306×	`*-un-lft-identity`
232×	`sqrt-prod`
192×	`add-sqr-sqrt`
190×	`add-cube-cbrt`
58×	`distribute-lft-out`
30×	`associate-/l*`
24×	`sqrt-div`
20×	`associate-/r/`
14×	`associate-/r*`
12×	`flip3-+` `flip-+`
11×	`add-exp-log` `add-cbrt-cube`
10×	`div-inv`
6×	`pow1`
4×	`cbrt-undiv` `div-exp` `add-log-exp`
2×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num`
1×	`associate-/l/`

Counts

4 → 317

Calls

4 calls:

5.0ms	(sqrt (+ 1.0 (sqrt (+ x 1.0))))
5.0ms	(sqrt (+ 1.0 (sqrt (+ x 1.0))))
8.0ms	(/ x (sqrt (+ 1.0 (sqrt (+ x 1.0)))))
20.0ms	(/ (/ x (sqrt (+ 1.0 (sqrt (+ x 1.0))))) (sqrt (+ 1.0 (sqrt (+ x 1.0)))))

series68.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(sqrt (+ 1.0 (sqrt (+ x 1.0))))
14.0ms	(sqrt (+ 1.0 (sqrt (+ x 1.0))))
28.0ms	(/ x (sqrt (+ 1.0 (sqrt (+ x 1.0)))))
15.0ms	(/ (/ x (sqrt (+ 1.0 (sqrt (+ x 1.0))))) (sqrt (+ 1.0 (sqrt (+ x 1.0)))))

simplify93.0ms

Algorithm

egg-herbie

Counts

329 → 329

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4958	8606
1	4958	8606

prune604.0ms

Filtered

147 candidates to 329 candidates (-123.8%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	329	0	329
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	329	4	333

Merged error: 0b

Counts

333 → 4

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 1.0 (sqrt (+ x 1.0)))
0.2b	(/ x (cbrt (pow (+ 1.0 (sqrt (+ x 1.0))) 3)))
0.2b	(pow (+ 1.0 (sqrt (+ x 1.0))) 3)
6.4b	(cbrt (pow (+ 1.0 (sqrt (+ x 1.0))) 3))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

70×	`cbrt-prod` `*-un-lft-identity`
51×	`times-frac`
44×	`add-sqr-sqrt` `add-cube-cbrt`
24×	`unpow-prod-down` `cube-prod`
17×	`associate-/r*`
13×	`distribute-lft-out`
7×	`add-exp-log`
6×	`cube-div` `cube-mult` `unpow3` `add-cbrt-cube` `add-log-exp` `sqr-pow`
5×	`pow1`
4×	`cbrt-div` `flip3-+` `flip-+`
3×	`pow-unpow` `associate-/l*`
2×	`associate-/r/`
1×	`cbrt-undiv` `+-commutative` `pow-to-exp` `pow-pow` `frac-2neg` `pow1/3` `div-exp` `pow-exp` `clear-num` `sum-log` `rem-cbrt-cube` `div-inv` `rem-cube-cbrt`

Counts

4 → 149

Calls

4 calls:

5.0ms	(+ 1.0 (sqrt (+ x 1.0)))
10.0ms	(/ x (cbrt (pow (+ 1.0 (sqrt (+ x 1.0))) 3)))
7.0ms	(pow (+ 1.0 (sqrt (+ x 1.0))) 3)
7.0ms	(cbrt (pow (+ 1.0 (sqrt (+ x 1.0))) 3))

series42.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(+ 1.0 (sqrt (+ x 1.0)))
18.0ms	(/ x (cbrt (pow (+ 1.0 (sqrt (+ x 1.0))) 3)))
14.0ms	(pow (+ 1.0 (sqrt (+ x 1.0))) 3)
5.0ms	(cbrt (pow (+ 1.0 (sqrt (+ x 1.0))) 3))

simplify62.0ms

Algorithm

egg-herbie

Counts

161 → 161

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5072	2603

prune235.0ms

Filtered

94 candidates to 161 candidates (-71.3%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	161	0	161
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	161	4	165

Merged error: 0b

Counts

165 → 4

regimes34.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	10
1	27	10

end0.0ms

sample324.0ms

Algorithm

intervals

Results

229.0ms	7996×	body	80	valid
1.0ms	4×	body	1280	valid

Details

analyze3.0ms

sample13.0ms

simplify5.0ms

prune3.0ms

localize5.0ms

rewrite17.0ms

series28.0ms

simplify46.0ms

prune135.0ms

localize7.0ms

rewrite33.0ms

series32.0ms

simplify45.0ms

prune259.0ms

localize8.0ms

rewrite60.0ms

series68.0ms

simplify93.0ms

prune604.0ms

localize8.0ms

rewrite34.0ms

series42.0ms

simplify62.0ms

prune235.0ms

regimes34.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample324.0ms

Profiling