Details

analyze2.0ms

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

sample12.0ms

Algorithm

intervals

Results

6.0ms

256×

body

valid

simplify3.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	8	8
1	8	8

prune2.0ms

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

rewrite18.0ms

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:

6.0ms	(+ 1.0 (sqrt (+ x 1.0)))
3.0ms	(sqrt (+ x 1.0))
7.0ms	(/ x (+ 1.0 (sqrt (+ x 1.0))))

series25.0ms

Counts

3 → 9

Calls

3 calls:

5.0ms	(+ 1.0 (sqrt (+ x 1.0)))
4.0ms	(sqrt (+ x 1.0))
16.0ms	(/ x (+ 1.0 (sqrt (+ x 1.0))))

simplify29.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 0 (18.0ms)

Iter	Nodes	Cost
0	4963	1021
1	4963	1021

prune121.0ms

Filtered

52 candidates to 70 candidates (-34.6%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	65	5	70
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	66	5	71

Merged error: 0b

Counts

71 → 5

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	(* x (/ 1 (+ 1.0 (sqrt (+ x 1.0)))))
0.1b	(/ 1 (+ 1.0 (sqrt (+ x 1.0))))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

42×	`*-un-lft-identity`
31×	`add-sqr-sqrt`
26×	`times-frac`
23×	`add-cube-cbrt`
18×	`associate-r`
17×	`add-exp-log`
11×	`add-cbrt-cube`
9×	`distribute-lft-out`
8×	`pow1`
6×	`add-log-exp`
4×	`flip3-+` `div-exp` `prod-exp` `associate-/r*` `sqrt-prod` `associate-/r/` `flip-+`
3×	`associate-l` `associate-/l*` `unswap-sqr`
2×	`cbrt-undiv` `rec-exp` `sqrt-div` `1-exp` `cbrt-unprod` `div-inv`
1×	`+-commutative` `rem-sqrt-square` `pow-flip` `frac-2neg` `sqrt-pow1` `pow1/2` `associate-r/` `pow-prod-down` `clear-num` `sum-log` `un-div-inv` `-commutative` `inv-pow`

Counts

4 → 106

Calls

4 calls:

3.0ms	(sqrt (+ x 1.0))
6.0ms	(+ 1.0 (sqrt (+ x 1.0)))
12.0ms	(* x (/ 1 (+ 1.0 (sqrt (+ x 1.0)))))
8.0ms	(/ 1 (+ 1.0 (sqrt (+ x 1.0))))

series40.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(sqrt (+ x 1.0))
5.0ms	(+ 1.0 (sqrt (+ x 1.0)))
17.0ms	(* x (/ 1 (+ 1.0 (sqrt (+ x 1.0)))))
14.0ms	(/ 1 (+ 1.0 (sqrt (+ x 1.0))))

simplify34.0ms

Algorithm

egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	5182	1663

prune176.0ms

Filtered

82 candidates to 118 candidates (-43.9%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	118	0	118
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	118	5	123

Merged error: 0b

Counts

123 → 5

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))))
0.3b	(/ x (sqrt (+ 1.0 (sqrt (+ x 1.0)))))
0.5b	(/ (/ x (sqrt (+ 1.0 (sqrt (+ x 1.0))))) (sqrt (+ 1.0 (sqrt (+ x 1.0)))))

rewrite64.0ms

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:

6.0ms	(sqrt (+ 1.0 (sqrt (+ x 1.0))))
6.0ms	(sqrt (+ 1.0 (sqrt (+ x 1.0))))
9.0ms	(/ x (sqrt (+ 1.0 (sqrt (+ x 1.0)))))
25.0ms	(/ (/ x (sqrt (+ 1.0 (sqrt (+ x 1.0))))) (sqrt (+ 1.0 (sqrt (+ x 1.0)))))

series74.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(sqrt (+ 1.0 (sqrt (+ x 1.0))))
11.0ms	(sqrt (+ 1.0 (sqrt (+ x 1.0))))
35.0ms	(/ x (sqrt (+ 1.0 (sqrt (+ x 1.0)))))
17.0ms	(/ (/ x (sqrt (+ 1.0 (sqrt (+ x 1.0))))) (sqrt (+ 1.0 (sqrt (+ x 1.0)))))

simplify83.0ms

Algorithm

egg-herbie

Counts

329 → 329

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5484	8179

prune537.0ms

Filtered

146 candidates to 329 candidates (-125.3%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	329	0	329
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	329	5	334

Merged error: 0b

Counts

334 → 5

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(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)
5.2b	(cbrt (pow (+ 1.0 (sqrt (+ x 1.0))) 3))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 153

Calls

4 calls:

3.0ms	(sqrt (+ x 1.0))
11.0ms	(/ 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))

series44.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(sqrt (+ x 1.0))
17.0ms	(/ x (cbrt (pow (+ 1.0 (sqrt (+ x 1.0))) 3)))
15.0ms	(pow (+ 1.0 (sqrt (+ x 1.0))) 3)
8.0ms	(cbrt (pow (+ 1.0 (sqrt (+ x 1.0))) 3))

simplify56.0ms

Algorithm

egg-herbie

Counts

165 → 165

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5113	2594

prune204.0ms

Filtered

96 candidates to 165 candidates (-71.9%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	165	0	165
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	165	5	170

Merged error: 0b

Counts

170 → 5

regimes72.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	10
1	12	10

end0.0ms

sample288.0ms

Algorithm

intervals

Results

204.0ms	7998×	body	80	valid
0.0ms	2×	body	1280	valid

Details

analyze2.0ms

sample12.0ms

simplify3.0ms

prune2.0ms

localize5.0ms

rewrite18.0ms

series25.0ms

simplify29.0ms

prune121.0ms

localize7.0ms

rewrite32.0ms

series40.0ms

simplify34.0ms

prune176.0ms

localize8.0ms

rewrite64.0ms

series74.0ms

simplify83.0ms

prune537.0ms

localize8.0ms

rewrite34.0ms

series44.0ms

simplify56.0ms

prune204.0ms

regimes72.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample288.0ms

Profiling