Details

sample33.0ms

Algorithm

intervals

Results

6.0ms	140×	body	80	valid
6.0ms	259×	body	80	nan
5.0ms	59×	body	640	valid
5.0ms	38×	body	1280	valid
1.0ms	13×	body	320	valid
0.0ms	6×	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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.4b

localize7.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ 1.0 (sqrt (+ x 1.0)))
0.3b	(/ 1.0 (sqrt x))
1.6b	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

rewrite133.0ms

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)))
4.0ms	(/ 1.0 (sqrt x))
51.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

series262.0ms

Counts

3 → 9

Calls

3 calls:

78.0ms	(/ 1.0 (sqrt (+ x 1.0)))
46.0ms	(/ 1.0 (sqrt x))
138.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

simplify248.0ms

Algorithm

egg-herbie

Counts

748 → 748

Iterations

Useful iterations: 2 (83.0ms)

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

prune1.2s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 18.0b

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)))
1.6b	(- (* (/ 1.0 (sqrt x)) (/ 1.0 (sqrt x))) (* (/ 1.0 (sqrt (+ x 1.0))) (/ 1.0 (sqrt (+ x 1.0)))))

rewrite47.0ms

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:

4.0ms	(/ 1.0 (sqrt x))
4.0ms	(/ 1.0 (sqrt x))
18.0ms	(* (/ 1.0 (sqrt x)) (/ 1.0 (sqrt x)))
11.0ms	(- (* (/ 1.0 (sqrt x)) (/ 1.0 (sqrt x))) (* (/ 1.0 (sqrt (+ x 1.0))) (/ 1.0 (sqrt (+ x 1.0)))))

series179.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(/ 1.0 (sqrt x))
39.0ms	(/ 1.0 (sqrt x))
33.0ms	(* (/ 1.0 (sqrt x)) (/ 1.0 (sqrt x)))
67.0ms	(- (* (/ 1.0 (sqrt x)) (/ 1.0 (sqrt x))) (* (/ 1.0 (sqrt (+ x 1.0))) (/ 1.0 (sqrt (+ x 1.0)))))

simplify100.0ms

Algorithm

egg-herbie

Counts

227 → 227

Iterations

Useful iterations: 2 (76.0ms)

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

prune533.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.8b

localize14.0ms

Local error

Found 4 expressions with local error:

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

rewrite90.0ms

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)))
55.0ms	(/ (/ (* (* 1.0 1.0) (- (+ x 1.0) x)) (* (+ x 1.0) x)) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))))
4.0ms	(/ 1.0 (sqrt x))
7.0ms	(- (+ x 1.0) x)

series621.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(/ 1.0 (sqrt (+ x 1.0)))
496.0ms	(/ (/ (* (* 1.0 1.0) (- (+ x 1.0) x)) (* (+ x 1.0) x)) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))))
47.0ms	(/ 1.0 (sqrt x))
1.0ms	(- (+ x 1.0) x)

simplify67.0ms

Algorithm

egg-herbie

Counts

284 → 284

Iterations

Useful iterations: 1 (31.0ms)

Iter	Nodes	Cost
0	1327	4194
1	5002	3759

prune577.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.8b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1.0 (sqrt (+ x 1.0)))
0.3b	(/ 1.0 (sqrt x))
0.7b	(/ (* (* 1.0 1.0) 1.0) (* (+ x 1.0) x))
6.0b	(/ (/ (* (* 1.0 1.0) 1.0) (* (+ x 1.0) x)) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))))

rewrite90.0ms

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:

6.0ms	(/ 1.0 (sqrt (+ x 1.0)))
4.0ms	(/ 1.0 (sqrt x))
12.0ms	(/ (* (* 1.0 1.0) 1.0) (* (+ x 1.0) x))
51.0ms	(/ (/ (* (* 1.0 1.0) 1.0) (* (+ x 1.0) x)) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))))

series667.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(/ 1.0 (sqrt (+ x 1.0)))
46.0ms	(/ 1.0 (sqrt x))
35.0ms	(/ (* (* 1.0 1.0) 1.0) (* (+ x 1.0) x))
513.0ms	(/ (/ (* (* 1.0 1.0) 1.0) (* (+ x 1.0) x)) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))))

simplify70.0ms

Algorithm

egg-herbie

Counts

278 → 278

Iterations

Useful iterations: 1 (29.0ms)

Iter	Nodes	Cost
0	1238	3739
1	5001	3341

prune554.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.0b

regimes54.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	13
1	20	13

end0.0ms

sample1.0s

Algorithm

intervals

Results

357.0ms	1846×	body	640	valid
180.0ms	8043×	body	80	nan
131.0ms	1116×	body	1280	valid
104.0ms	4060×	body	80	valid
43.0ms	635×	body	320	valid
20.0ms	343×	body	160	valid