Details

sample27.0ms

Algorithm

intervals

Results

5.0ms	296×	body	80	nan
5.0ms	56×	body	1280	valid
3.0ms	44×	body	640	valid
2.0ms	126×	body	80	valid
1.0ms	16×	body	320	valid
1.0ms	14×	body	160	valid

simplify6.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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: 31.0b

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt (+ x 1.0))
3.7b	(- (sqrt (+ x 1.0)) (sqrt x))

rewrite17.0ms

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:

8.0ms	(sqrt (+ x 1.0))
8.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

series105.0ms

Counts

2 → 6

Calls

2 calls:

35.0ms	(sqrt (+ x 1.0))
70.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

simplify58.0ms

Algorithm

egg-herbie

Counts

41 → 41

Iterations

Useful iterations: 3 (54.0ms)

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

prune78.0ms

Pruning

3 alts after pruning (3 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)))

rewrite25.0ms

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:

3.0ms	(sqrt (+ x 1.0))
11.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
9.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

series237.0ms

Counts

3 → 9

Calls

3 calls:

34.0ms	(sqrt (+ x 1.0))
66.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
137.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify38.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 2 (31.0ms)

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

prune150.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 4 expressions with local error:

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

rewrite90.0ms

Algorithm

rewrite-expression-head

Rules

742×	`*-un-lft-identity`
700×	`sqrt-prod`
594×	`times-frac`
280×	`distribute-lft-out`
254×	`add-sqr-sqrt`
252×	`add-cube-cbrt`
36×	`associate-/l*`
28×	`sqrt-div`
24×	`associate-/r/`
18×	`associate-/r*`
14×	`flip3-+` `flip-+`
12×	`div-inv`
11×	`add-exp-log` `add-cbrt-cube`
6×	`pow1`
4×	`cbrt-undiv` `div-exp` `add-log-exp`
2×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num`
1×	`associate-/l/`

Counts

4 → 445

Calls

4 calls:

7.0ms	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
8.0ms	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
10.0ms	(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
27.0ms	(/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

series818.0ms

Counts

4 → 12

Calls

4 calls:

167.0ms	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
170.0ms	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
336.0ms	(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
144.0ms	(/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

simplify135.0ms

Algorithm

egg-herbie

Counts

457 → 457

Iterations

Useful iterations: 2 (64.0ms)

Iter	Nodes	Cost
0	1033	8862
1	4120	7704
2	5001	7681

prune529.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize12.0ms

Local error

Found 4 expressions with local error:

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

rewrite130.0ms

Algorithm

rewrite-expression-head

Rules

476×	`sqrt-prod`
326×	`*-un-lft-identity`
223×	`times-frac`
188×	`add-sqr-sqrt`
124×	`add-cube-cbrt`
112×	`distribute-lft-out`
56×	`swap-sqr`
36×	`associate-r` `associate-l`
27×	`associate-/r*`
22×	`sqrt-div`
19×	`pow1`
16×	`unswap-sqr`
15×	`add-exp-log` `add-cbrt-cube`
14×	`associate-/r/`
8×	`sqrt-pow1` `pow1/2`
7×	`flip3-+` `flip-+` `div-inv` `associate-/l*`
5×	`pow-prod-up`
4×	`cbrt-undiv` `div-exp` `add-log-exp`
3×	`frac-2neg` `pow-prod-down` `clear-num` `pow-sqr` `associate-/l/`
2×	`frac-times` `sqrt-unprod` `associate-r/` `associate-l/` `prod-exp` `cbrt-unprod`
1×	`pow2` `sqrt-undiv` `pow-plus` `rem-square-sqrt` `*-commutative`

Counts

4 → 317

Calls

4 calls:

11.0ms	(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
11.0ms	(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
36.0ms	(/ (* (sqrt (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))) (sqrt (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
48.0ms	(* (sqrt (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))) (sqrt (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))))

series1.2s

Counts

4 → 12

Calls

4 calls:

345.0ms	(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
349.0ms	(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
177.0ms	(/ (* (sqrt (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))) (sqrt (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
363.0ms	(* (sqrt (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))) (sqrt (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))))

simplify161.0ms

Algorithm

egg-herbie

Counts

329 → 329

Iterations

Useful iterations: 2 (112.0ms)

Iter	Nodes	Cost
0	799	4818
1	4184	4156
2	5001	4069

prune679.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

regimes32.0ms

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

sample710.0ms

Algorithm

intervals

Results

160.0ms	1740×	body	1280	valid
147.0ms	7974×	body	80	nan
87.0ms	1267×	body	640	valid
84.0ms	4077×	body	80	valid
31.0ms	600×	body	320	valid
11.0ms	316×	body	160	valid