Details

sample33.0ms

Algorithm

intervals

Results

7.0ms	139×	body	80	valid
5.0ms	43×	body	1280	valid
5.0ms	54×	body	640	valid
5.0ms	243×	body	80	nan
1.0ms	14×	body	320	valid
0.0ms	6×	body	160	valid

simplify6.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.0b

localize7.0ms

Local error

Found 3 expressions with local error:

0.2b	(/ 1.0 (sqrt (+ x 1.0)))
0.3b	(/ 1.0 (sqrt x))
1.7b	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

rewrite146.0ms

Algorithm

rewrite-expression-head

Rules

1035×	`times-frac`
875×	`*-un-lft-identity`
742×	`add-sqr-sqrt`
712×	`add-cube-cbrt`
594×	`prod-diff`
562×	`sqrt-prod`
73×	`distribute-lft-out`
54×	`div-inv`
46×	`sqrt-div` `associate-/r/`
23×	`flip3-+` `flip-+`
22×	`fma-neg`
13×	`associate-/r*`
11×	`distribute-lft-out--`
9×	`difference-of-squares`
7×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/l*`
5×	`add-log-exp`
3×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
2×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num`
1×	`sub-neg` `flip3--` `diff-log` `frac-sub` `flip--`

Counts

3 → 739

Calls

3 calls:

6.0ms	(/ 1.0 (sqrt (+ x 1.0)))
3.0ms	(/ 1.0 (sqrt x))
67.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

series263.0ms

Counts

3 → 9

Calls

3 calls:

79.0ms	(/ 1.0 (sqrt (+ x 1.0)))
39.0ms	(/ 1.0 (sqrt x))
144.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

simplify249.0ms

Algorithm

egg-herbie

Counts

748 → 748

Iterations

Useful iterations: 2 (84.0ms)

Iter	Nodes	Cost
0	1517	24924
1	4197	18301
2	5001	18266

prune1.3s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 16.4b

localize12.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 1.0 (sqrt x))
0.3b	(/ 1.0 (sqrt x))
0.5b	(* (/ 1.0 (sqrt x)) (/ 1.0 (sqrt x)))
1.7b	(- (* (/ 1.0 (sqrt x)) (/ 1.0 (sqrt x))) (* (/ 1.0 (sqrt (+ x 1.0))) (/ 1.0 (sqrt (+ x 1.0)))))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

132×	`add-sqr-sqrt` `times-frac`
90×	`add-cube-cbrt` `*-un-lft-identity`
72×	`sqrt-prod`
28×	`swap-sqr`
22×	`associate-r` `associate-l`
20×	`add-exp-log` `add-cbrt-cube`
12×	`associate-/r*`
11×	`pow1`
9×	`frac-sub` `unswap-sqr`
7×	`frac-times` `associate-r/` `associate-l/`
6×	`cbrt-undiv` `div-exp` `div-inv` `associate-/l*` `add-log-exp`
4×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `log1p-expm1-u`
2×	`frac-2neg` `clear-num`
1×	`pow2` `sub-neg` `flip3--` `pow-plus` `fma-neg` `diff-log` `prod-diff` `pow-prod-down` `pow-sqr` `*-commutative` `pow-prod-up` `flip--` `difference-of-squares`

Counts

4 → 215

Calls

4 calls:

6.0ms	(/ 1.0 (sqrt x))
3.0ms	(/ 1.0 (sqrt x))
24.0ms	(* (/ 1.0 (sqrt x)) (/ 1.0 (sqrt x)))
10.0ms	(- (* (/ 1.0 (sqrt x)) (/ 1.0 (sqrt x))) (* (/ 1.0 (sqrt (+ x 1.0))) (/ 1.0 (sqrt (+ x 1.0)))))

series176.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(/ 1.0 (sqrt x))
37.0ms	(/ 1.0 (sqrt x))
34.0ms	(* (/ 1.0 (sqrt x)) (/ 1.0 (sqrt x)))
60.0ms	(- (* (/ 1.0 (sqrt x)) (/ 1.0 (sqrt x))) (* (/ 1.0 (sqrt (+ x 1.0))) (/ 1.0 (sqrt (+ x 1.0)))))

simplify93.0ms

Algorithm

egg-herbie

Counts

227 → 227

Iterations

Useful iterations: 2 (75.0ms)

Iter	Nodes	Cost
0	759	2006
1	3539	1754
2	5001	1717

prune508.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 4.7b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1.0 (sqrt (+ x 1.0)))
0.3b	(/ (/ (* (* 1.0 1.0) (- (+ x 1.0) x)) (* (+ x 1.0) x)) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))))
0.3b	(/ 1.0 (sqrt x))
1.2b	(- (+ x 1.0) x)

rewrite157.0ms

Algorithm

rewrite-expression-head

Rules

319×	`*-un-lft-identity`
296×	`times-frac`
124×	`sqrt-prod`
121×	`distribute-lft-out`
116×	`add-sqr-sqrt`
114×	`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*`
12×	`prod-diff`
9×	`prod-exp` `cbrt-unprod` `add-log-exp`
4×	`pow1` `expm1-log1p-u` `fma-neg` `log1p-expm1-u`
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 → 272

Calls

4 calls:

6.0ms	(/ 1.0 (sqrt (+ x 1.0)))
109.0ms	(/ (/ (* (* 1.0 1.0) (- (+ x 1.0) x)) (* (+ x 1.0) x)) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))))
3.0ms	(/ 1.0 (sqrt x))
22.0ms	(- (+ x 1.0) x)

series615.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(/ 1.0 (sqrt (+ x 1.0)))
493.0ms	(/ (/ (* (* 1.0 1.0) (- (+ x 1.0) x)) (* (+ x 1.0) x)) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))))
43.0ms	(/ 1.0 (sqrt x))
1.0ms	(- (+ x 1.0) x)

simplify70.0ms

Algorithm

egg-herbie

Counts

284 → 284

Iterations

Useful iterations: 1 (32.0ms)

Iter	Nodes	Cost
0	1327	4194
1	5002	3759

prune551.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 4.7b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (* (* 1.0 1.0) 1.0) (* (+ x 1.0) x))
0.2b	(/ 1.0 (sqrt (+ x 1.0)))
0.3b	(/ 1.0 (sqrt x))
4.9b	(/ (/ (* (* 1.0 1.0) 1.0) (* (+ x 1.0) x)) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))))

rewrite133.0ms

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` `expm1-log1p-u` `frac-2neg` `clear-num` `log1p-expm1-u` `add-log-exp`
2×	`sqrt-div`
1×	`frac-add` `associate-/l/`

Counts

4 → 266

Calls

4 calls:

12.0ms	(/ (* (* 1.0 1.0) 1.0) (* (+ x 1.0) x))
7.0ms	(/ 1.0 (sqrt (+ x 1.0)))
3.0ms	(/ 1.0 (sqrt x))
92.0ms	(/ (/ (* (* 1.0 1.0) 1.0) (* (+ x 1.0) x)) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))))

series664.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(/ (* (* 1.0 1.0) 1.0) (* (+ x 1.0) x))
80.0ms	(/ 1.0 (sqrt (+ x 1.0)))
38.0ms	(/ 1.0 (sqrt x))
500.0ms	(/ (/ (* (* 1.0 1.0) 1.0) (* (+ x 1.0) x)) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))))

simplify65.0ms

Algorithm

egg-herbie

Counts

278 → 278

Iterations

Useful iterations: 1 (32.0ms)

Iter	Nodes	Cost
0	1238	3739
1	5001	3341

prune537.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

regimes37.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	13
1	20	13

end0.0ms

sample821.0ms

Algorithm

intervals

Results

167.0ms	8106×	body	80	nan
166.0ms	1781×	body	640	valid
145.0ms	1170×	body	1280	valid
110.0ms	4131×	body	80	valid
41.0ms	586×	body	320	valid
16.0ms	332×	body	160	valid