Details

sample24.0ms

Algorithm

intervals

Results

4.0ms	237×	body	80	nan
4.0ms	51×	body	1280	valid
2.0ms	130×	body	80	valid
2.0ms	35×	body	640	valid
1.0ms	25×	body	320	valid
0.0ms	15×	body	160	valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	9	4
1	10	4
2	10	4

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.9b

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt (+ x 1.0))
3.8b	(- (sqrt (+ x 1.0)) (sqrt x))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `*-un-lft-identity` `sqrt-prod`
4×	`add-log-exp` `difference-of-squares`
3×	`pow1` `add-cube-cbrt` `distribute-lft-out--`
2×	`add-exp-log` `sqrt-div` `add-cbrt-cube` `distribute-lft-out`
1×	`sub-neg` `rem-sqrt-square` `flip3--` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `flip--` `flip-+`

Counts

2 → 35

Calls

2 calls:

7.0ms	(sqrt (+ x 1.0))
43.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

series89.0ms

Counts

2 → 6

Calls

2 calls:

26.0ms	(sqrt (+ x 1.0))
63.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

simplify56.0ms

Algorithm

egg-herbie

Counts

41 → 41

Iterations

Useful iterations: 3 (52.0ms)

Iter	Nodes	Cost
0	182	265
1	544	243
2	2020	233
3	5002	230

prune86.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize6.0ms

Local error

Found 2 expressions with local error:

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

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

44×	`*-un-lft-identity`
20×	`sqrt-prod`
18×	`times-frac`
17×	`distribute-lft-out`
15×	`add-sqr-sqrt`
14×	`add-cube-cbrt`
6×	`associate-/r*`
4×	`add-exp-log` `add-cbrt-cube`
3×	`pow1` `associate-/l*`
2×	`flip3-+` `sqrt-div` `associate-/r/` `flip-+` `add-log-exp`
1×	`cbrt-undiv` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `clear-num` `div-inv`

Counts

2 → 57

Calls

2 calls:

9.0ms	(sqrt (+ x 1.0))
42.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

series151.0ms

Counts

2 → 6

Calls

2 calls:

27.0ms	(sqrt (+ x 1.0))
124.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify38.0ms

Algorithm

egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	309	501
1	1128	459
2	5002	430

prune128.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize8.0ms

Local error

Found 4 expressions with local error:

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

rewrite118.0ms

Algorithm

rewrite-expression-head

Rules

106×	`sqrt-prod`
62×	`add-sqr-sqrt`
46×	`*-un-lft-identity`
40×	`sqrt-pow1`
32×	`sqrt-div`
31×	`pow1`
28×	`add-cube-cbrt`
20×	`pow1/2`
18×	`swap-sqr`
10×	`associate-r` `associate-l`
9×	`flip3-+` `times-frac` `pow-prod-up` `flip-+` `unswap-sqr`
8×	`add-exp-log` `add-cbrt-cube` `distribute-lft-out`
5×	`pow-prod-down` `pow-sqr`
4×	`frac-times` `rem-sqrt-square` `add-log-exp`
3×	`associate-/r` `associate-/l`
2×	`associate-r/` `associate-l/` `associate-/r/`
1×	`cbrt-undiv` `pow2` `frac-2neg` `pow-plus` `sqrt-unprod` `div-exp` `prod-exp` `clear-num` `rem-square-sqrt` `*-commutative` `cbrt-unprod` `div-inv`

Counts

4 → 161

Calls

4 calls:

8.0ms	(sqrt (sqrt (+ x 1.0)))
8.0ms	(sqrt (sqrt (+ x 1.0)))
46.0ms	(/ 1.0 (+ (* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0)))) (sqrt x)))
49.0ms	(* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0))))

series309.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(sqrt (sqrt (+ x 1.0)))
78.0ms	(sqrt (sqrt (+ x 1.0)))
126.0ms	(/ 1.0 (+ (* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0)))) (sqrt x)))
27.0ms	(* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0))))

simplify71.0ms

Algorithm

egg-herbie

Counts

173 → 173

Iterations

Useful iterations: 2 (56.0ms)

Iter	Nodes	Cost
0	525	1350
1	2329	1176
2	5001	1152

prune333.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.0b

localize8.0ms

Local error

Found 4 expressions with local error:

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

rewrite344.0ms

Algorithm

rewrite-expression-head

Rules

297×	`*-un-lft-identity`
274×	`sqrt-prod`
157×	`times-frac`
119×	`add-sqr-sqrt`
116×	`distribute-lft-out`
88×	`add-cube-cbrt`
41×	`swap-sqr`
27×	`associate-r` `associate-l`
20×	`pow1`
14×	`associate-/r/`
12×	`associate-/r*`
10×	`add-exp-log` `add-cbrt-cube`
9×	`sqrt-pow1` `pow1/2` `unswap-sqr`
7×	`flip3-+` `flip-+` `div-inv`
6×	`associate-/l*`
5×	`sqrt-div` `pow-prod-up`
4×	`add-log-exp`
3×	`pow-prod-down` `pow-sqr`
2×	`cbrt-undiv` `rem-sqrt-square` `frac-2neg` `div-exp` `clear-num`
1×	`pow2` `frac-times` `pow-plus` `sqrt-unprod` `associate-r/` `associate-l/` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 250

Calls

4 calls:

44.0ms	(sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))
43.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
42.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
200.0ms	(* (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))))

series708.0ms

Counts

4 → 12

Calls

4 calls:

312.0ms	(sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))
126.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
122.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
148.0ms	(* (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))))

simplify100.0ms

Algorithm

egg-herbie

Counts

262 → 262

Iterations

Useful iterations: 2 (75.0ms)

Iter	Nodes	Cost
0	647	2845
1	3152	2529
2	5002	2489

prune498.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0b

regimes36.0ms

Accuracy

0% (0.1b 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	9	5
1	9	5

end0.0ms

sample704.0ms

Algorithm

intervals

Results

135.0ms	8191×	body	80	nan
135.0ms	1727×	body	1280	valid
76.0ms	1282×	body	640	valid
74.0ms	4038×	body	80	valid
29.0ms	649×	body	320	valid
9.0ms	304×	body	160	valid