Details

analyze1.0ms

Algorithm: search

sample27.0ms

Algorithm

intervals

Results

8.0ms	55×	body	640	valid
6.0ms	33×	body	1280	valid
5.0ms	139×	body	80	valid
2.0ms	18×	body	320	valid
1.0ms	11×	body	160	valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	6
1	14	6
2	14	6

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: 19.3b

Counts

2 → 1

localize7.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ 1.0 (sqrt (+ x 1.0)))
0.2b	(/ 1.0 (sqrt x))
3.6b	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

71×	`*-un-lft-identity`
70×	`add-sqr-sqrt`
69×	`times-frac`
46×	`sqrt-prod`
40×	`add-cube-cbrt`
13×	`associate-/r*`
11×	`distribute-lft-out--`
9×	`difference-of-squares`
7×	`add-exp-log` `add-cbrt-cube` `distribute-lft-out`
6×	`associate-/l*`
5×	`add-log-exp`
4×	`div-inv`
3×	`pow1`
2×	`cbrt-undiv` `frac-2neg` `sqrt-div` `div-exp` `clear-num` `associate-/r/`
1×	`sub-neg` `flip3--` `flip3-+` `diff-log` `frac-sub` `flip--` `flip-+`

Counts

3 → 117

Calls

3 calls:

7.0ms	(/ 1.0 (sqrt (+ x 1.0)))
7.0ms	(/ 1.0 (sqrt x))
30.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

series25.0ms

Counts

3 → 9

Calls

3 calls:

6.0ms	(/ 1.0 (sqrt (+ x 1.0)))
7.0ms	(/ 1.0 (sqrt x))
12.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

simplify58.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	541	1048
1	2015	1014
2	5002	983

prune223.0ms

Filtered

85 candidates to 126 candidates (-48.2%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	115	11	126
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	116	11	127

Merged error: 18.7b

Counts

127 → 11

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- (* (/ 1.0 (sqrt x)) (/ 1.0 (sqrt x))) (* (/ 1.0 (sqrt (+ x 1.0))) (/ 1.0 (sqrt (+ x 1.0))))) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))))
0.3b	(* (/ 1.0 (sqrt (+ x 1.0))) (/ 1.0 (sqrt (+ x 1.0))))
0.5b	(* (/ 1.0 (sqrt x)) (/ 1.0 (sqrt x)))
3.5b	(- (* (/ 1.0 (sqrt x)) (/ 1.0 (sqrt x))) (* (/ 1.0 (sqrt (+ x 1.0))) (/ 1.0 (sqrt (+ x 1.0)))))

rewrite116.0ms

Algorithm

rewrite-expression-head

Rules

362×	`times-frac`
331×	`*-un-lft-identity`
258×	`add-sqr-sqrt`
180×	`sqrt-prod`
174×	`add-cube-cbrt`
88×	`distribute-lft-out`
67×	`swap-sqr`
49×	`associate-r` `associate-l`
30×	`add-exp-log` `add-cbrt-cube`
19×	`div-inv`
18×	`pow1` `frac-sub` `unswap-sqr`
16×	`difference-of-squares`
14×	`frac-times` `associate-r/` `associate-l/` `associate-/r*`
11×	`associate-/r/` `associate-/l/`
9×	`cbrt-undiv` `div-exp`
8×	`sqrt-div` `prod-exp` `cbrt-unprod`
6×	`add-log-exp`
5×	`flip3-+` `flip-+`
4×	`associate-/l*`
2×	`pow2` `flip3--` `pow-plus` `pow-prod-down` `pow-sqr` `*-commutative` `pow-prod-up` `flip--`
1×	`sub-neg` `frac-2neg` `diff-log` `div-sub` `frac-add` `clear-num`

Counts

4 → 354

Calls

4 calls:

44.0ms	(/ (- (* (/ 1.0 (sqrt x)) (/ 1.0 (sqrt x))) (* (/ 1.0 (sqrt (+ x 1.0))) (/ 1.0 (sqrt (+ x 1.0))))) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))))
25.0ms	(* (/ 1.0 (sqrt (+ x 1.0))) (/ 1.0 (sqrt (+ x 1.0))))
16.0ms	(* (/ 1.0 (sqrt x)) (/ 1.0 (sqrt x)))
9.0ms	(- (* (/ 1.0 (sqrt x)) (/ 1.0 (sqrt x))) (* (/ 1.0 (sqrt (+ x 1.0))) (/ 1.0 (sqrt (+ x 1.0)))))

series40.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(/ (- (* (/ 1.0 (sqrt x)) (/ 1.0 (sqrt x))) (* (/ 1.0 (sqrt (+ x 1.0))) (/ 1.0 (sqrt (+ x 1.0))))) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))))
2.0ms	(* (/ 1.0 (sqrt (+ x 1.0))) (/ 1.0 (sqrt (+ x 1.0))))
3.0ms	(* (/ 1.0 (sqrt x)) (/ 1.0 (sqrt x)))
6.0ms	(- (* (/ 1.0 (sqrt x)) (/ 1.0 (sqrt x))) (* (/ 1.0 (sqrt (+ x 1.0))) (/ 1.0 (sqrt (+ x 1.0)))))

simplify86.0ms

Algorithm

egg-herbie

Counts

366 → 366

Iterations

Useful iterations: 1 (35.0ms)

Iter	Nodes	Cost
0	1718	5942
1	5001	5479

prune928.0ms

Filtered

203 candidates to 366 candidates (-80.3%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	359	7	366
Fresh	9	1	10
Picked	1	0	1
Done	0	0	0
Total	369	8	377

Merged error: 4.0b

Counts

377 → 8

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1.0 (sqrt (+ x 1.0)))
0.2b	(/ 1.0 (sqrt x))
0.2b	(/ (/ (* (* 1.0 1.0) (- (+ x 1.0) x)) (* (+ x 1.0) x)) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))))
3.2b	(- (+ x 1.0) x)

rewrite77.0ms

Algorithm

rewrite-expression-head

Rules

303×	`*-un-lft-identity`
296×	`times-frac`
124×	`sqrt-prod`
117×	`distribute-lft-out`
108×	`add-sqr-sqrt`
106×	`add-cube-cbrt`
37×	`add-exp-log` `add-cbrt-cube`
35×	`associate-/r/`
34×	`div-inv`
30×	`associate-*l/`
27×	`associate-/r*`
17×	`flip3-+` `flip-+`
15×	`cbrt-undiv` `div-exp`
13×	`associate-/l*`
9×	`prod-exp` `cbrt-unprod` `add-log-exp`
4×	`pow1`
3×	`frac-2neg` `clear-num`
2×	`sqrt-div` `diff-log` `distribute-lft-out--`
1×	`sub-neg` `flip3--` `frac-add` `associate--l+` `sum-log` `flip--` `associate-/l/` `difference-of-squares`

Counts

4 → 248

Calls

4 calls:

5.0ms	(/ 1.0 (sqrt (+ x 1.0)))
4.0ms	(/ 1.0 (sqrt x))
46.0ms	(/ (/ (* (* 1.0 1.0) (- (+ x 1.0) x)) (* (+ x 1.0) x)) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))))
6.0ms	(- (+ x 1.0) x)

series47.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(/ 1.0 (sqrt (+ x 1.0)))
7.0ms	(/ 1.0 (sqrt x))
33.0ms	(/ (/ (* (* 1.0 1.0) (- (+ x 1.0) x)) (* (+ x 1.0) x)) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))))
1.0ms	(- (+ x 1.0) x)

simplify67.0ms

Algorithm

egg-herbie

Counts

260 → 260

Iterations

Useful iterations: 1 (30.0ms)

Iter	Nodes	Cost
0	1494	4115
1	5002	3785

prune440.0ms

Filtered

144 candidates to 260 candidates (-80.6%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	256	4	260
Fresh	4	3	7
Picked	1	0	1
Done	0	0	0
Total	261	7	268

Merged error: 4.0b

Counts

268 → 7

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (* (* 1.0 1.0) 1.0) (* (+ x 1.0) x))
0.1b	(/ 1.0 (sqrt (+ x 1.0)))
0.2b	(/ 1.0 (sqrt x))
4.2b	(/ (/ (* (* 1.0 1.0) 1.0) (* (+ x 1.0) x)) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))))

rewrite80.0ms

Algorithm

rewrite-expression-head

Rules

298×	`*-un-lft-identity`
297×	`times-frac`
124×	`sqrt-prod`
116×	`distribute-lft-out`
106×	`add-sqr-sqrt` `add-cube-cbrt`
58×	`add-exp-log` `add-cbrt-cube`
37×	`associate-/r/`
35×	`div-inv`
32×	`associate-*l/`
28×	`associate-/r*`
21×	`cbrt-undiv` `div-exp`
18×	`flip3-+` `prod-exp` `cbrt-unprod` `flip-+`
14×	`associate-/l*`
4×	`pow1` `frac-2neg` `clear-num` `add-log-exp`
2×	`sqrt-div`
1×	`frac-add` `associate-/l/`

Counts

4 → 258

Calls

4 calls:

10.0ms	(/ (* (* 1.0 1.0) 1.0) (* (+ x 1.0) x))
6.0ms	(/ 1.0 (sqrt (+ x 1.0)))
4.0ms	(/ 1.0 (sqrt x))
44.0ms	(/ (/ (* (* 1.0 1.0) 1.0) (* (+ x 1.0) x)) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))))

series50.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(/ (* (* 1.0 1.0) 1.0) (* (+ x 1.0) x))
6.0ms	(/ 1.0 (sqrt (+ x 1.0)))
7.0ms	(/ 1.0 (sqrt x))
34.0ms	(/ (/ (* (* 1.0 1.0) 1.0) (* (+ x 1.0) x)) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))))

simplify68.0ms

Algorithm

egg-herbie

Counts

270 → 270

Iterations

Useful iterations: 1 (32.0ms)

Iter	Nodes	Cost
0	1449	3810
1	5001	3418

prune412.0ms

Filtered

147 candidates to 270 candidates (-83.7%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	260	10	270
Fresh	5	1	6
Picked	1	0	1
Done	0	0	0
Total	266	11	277

Merged error: 0.0b

Counts

277 → 11

regimes64.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 0.5b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	12
1	16	12

end0.0ms

analyze1.0ms

Algorithm: search

sample789.0ms

Algorithm

intervals

Results

256.0ms	1833×	body	640	valid
201.0ms	1126×	body	1280	valid
153.0ms	4100×	body	80	valid
66.0ms	632×	body	320	valid
22.0ms	309×	body	160	valid

Details

analyze1.0ms

sample27.0ms

simplify5.0ms

prune3.0ms

localize7.0ms

rewrite48.0ms

series25.0ms

simplify58.0ms

prune223.0ms

localize13.0ms

rewrite116.0ms

series40.0ms

simplify86.0ms

prune928.0ms

localize12.0ms

rewrite77.0ms

series47.0ms

simplify67.0ms

prune440.0ms

localize12.0ms

rewrite80.0ms

series50.0ms

simplify68.0ms

prune412.0ms

regimes64.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

analyze1.0ms

sample789.0ms

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