Details

sample26.0ms

Algorithm

intervals

Results

5.0ms	293×	body	80	nan
4.0ms	43×	body	1280	valid
3.0ms	141×	body	80	valid
2.0ms	37×	body	640	valid
1.0ms	19×	body	320	valid
1.0ms	16×	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: 27.3b

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt (+ x 1.0))
4.3b	(- (sqrt (+ x 1.0)) (sqrt x))

rewrite50.0ms

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))

series103.0ms

Counts

2 → 6

Calls

2 calls:

30.0ms	(sqrt (+ x 1.0))
73.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

simplify57.0ms

Algorithm

egg-herbie

Counts

41 → 41

Iterations

Useful iterations: 3 (53.0ms)

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

prune86.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize6.0ms

Local error

Found 3 expressions with local error:

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

rewrite81.0ms

Algorithm

rewrite-expression-head

Rules

52×	`*-un-lft-identity`
24×	`sqrt-prod`
21×	`distribute-lft-out`
18×	`times-frac`
16×	`add-sqr-sqrt`
15×	`add-cube-cbrt`
6×	`associate-/r*`
5×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
4×	`pow1`
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 → 71

Calls

3 calls:

7.0ms	(sqrt (+ x 1.0))
32.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
40.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

series240.0ms

Counts

3 → 9

Calls

3 calls:

37.0ms	(sqrt (+ x 1.0))
61.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
142.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify39.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	341	624
1	1239	566
2	5001	533

prune168.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize9.0ms

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)))))

rewrite335.0ms

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:

41.0ms	(sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))
41.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
41.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
194.0ms	(* (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))))

series806.0ms

Counts

4 → 12

Calls

4 calls:

345.0ms	(sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))
148.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
138.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
175.0ms	(* (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))))

simplify99.0ms

Algorithm

egg-herbie

Counts

262 → 262

Iterations

Useful iterations: 2 (75.0ms)

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

prune518.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

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

rewrite957.0ms

Algorithm

rewrite-expression-head

Rules

1687×	`sqrt-prod`
1429×	`*-un-lft-identity`
1208×	`times-frac`
570×	`add-sqr-sqrt`
540×	`distribute-lft-out`
484×	`add-cube-cbrt`
306×	`associate-l`
48×	`sqrt-div` `associate-/r/`
39×	`associate-/l*`
27×	`associate-r`
24×	`flip3-+` `associate-/r*` `flip-+` `div-inv` `unswap-sqr`
15×	`add-exp-log` `add-cbrt-cube`
8×	`pow1`
5×	`cbrt-undiv` `div-exp`
4×	`add-log-exp`
3×	`frac-2neg` `pow-prod-down` `clear-num`
2×	`sqrt-pow1` `pow1/2`
1×	`frac-times` `sqrt-unprod` `associate-r/` `associate-l/` `prod-exp` `*-commutative` `cbrt-unprod` `associate-/l/`

Counts

4 → 824

Calls

4 calls:

43.0ms	(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
40.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
665.0ms	(* (sqrt (/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))) (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))))
118.0ms	(/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

series755.0ms

Counts

4 → 12

Calls

4 calls:

322.0ms	(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
135.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
161.0ms	(* (sqrt (/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))) (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))))
136.0ms	(/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

simplify160.0ms

Algorithm

egg-herbie

Counts

836 → 836

Iterations

Useful iterations: 1 (31.0ms)

Iter	Nodes	Cost
0	1462	16754
1	5001	15131

prune1.5s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

regimes37.0ms

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

sample717.0ms

Algorithm

intervals

Results

146.0ms	1719×	body	1280	valid
135.0ms	7890×	body	80	nan
82.0ms	4122×	body	80	valid
77.0ms	1221×	body	640	valid
30.0ms	624×	body	320	valid
10.0ms	314×	body	160	valid