Details

sample33.0ms

Algorithm

intervals

Results

6.0ms	241×	body	80	nan
5.0ms	41×	body	1280	valid
4.0ms	42×	body	640	valid
4.0ms	136×	body	80	valid
2.0ms	24×	body	320	valid
1.0ms	13×	body	160	valid

simplify4.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

prune3.0ms

Filtered

1 candidates to 0 candidates (100.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 28.6b

Counts

2 → 1

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt (+ x 1.0))
3.5b	(- (sqrt (+ x 1.0)) (sqrt x))

rewrite12.0ms

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:

3.0ms	(sqrt (+ x 1.0))
8.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

series14.0ms

Counts

2 → 6

Calls

2 calls:

4.0ms	(sqrt (+ x 1.0))
10.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

simplify35.0ms

Algorithm

egg-herbie

Counts

41 → 41

Iterations

Useful iterations: 2 (27.0ms)

Iter	Nodes	Cost
0	282	318
1	1037	308
2	5001	297

prune80.0ms

Filtered

41 candidates to 31 candidates (24.4%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	37	4	41
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	38	4	42

Merged error: 0.1b

Counts

42 → 4

localize7.0ms

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 0) (+ (sqrt (+ x 1.0)) (sqrt x)))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

74×	`*-un-lft-identity`
32×	`distribute-lft-out`
28×	`sqrt-prod`
24×	`times-frac`
17×	`add-sqr-sqrt`
16×	`add-cube-cbrt`
6×	`associate-/r*`
5×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
4×	`pow1` `flip3-+` `flip-+` `associate-/l*`
2×	`sqrt-div` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

3 → 80

Calls

3 calls:

3.0ms	(sqrt (+ x 1.0))
7.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
12.0ms	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))

series21.0ms

Counts

3 → 9

Calls

3 calls:

3.0ms	(sqrt (+ x 1.0))
8.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
10.0ms	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify69.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 2 (59.0ms)

Iter	Nodes	Cost
0	514	800
1	2206	753
2	5001	721

prune163.0ms

Filtered

89 candidates to 59 candidates (33.7%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	82	7	89
Fresh	2	1	3
Picked	0	1	1
Done	0	0	0
Total	84	9	93

Merged error: 0.0b

Counts

93 → 9

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x))))
0.1b	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
0.1b	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
0.2b	(* (sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))))

rewrite105.0ms

Algorithm

rewrite-expression-head

Rules

597×	`*-un-lft-identity`
420×	`sqrt-prod`
256×	`distribute-lft-out`
247×	`times-frac`
130×	`add-sqr-sqrt`
99×	`add-cube-cbrt`
71×	`swap-sqr`
33×	`associate-r` `associate-l`
20×	`pow1`
14×	`associate-/r/`
12×	`associate-/r*`
10×	`add-exp-log` `add-cbrt-cube`
9×	`sqrt-pow1` `flip3-+` `pow1/2` `flip-+` `unswap-sqr`
8×	`associate-/l*`
7×	`div-inv`
5×	`sqrt-div` `pow-prod-up`
4×	`associate-/l/` `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 → 316

Calls

4 calls:

12.0ms	(sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x))))
12.0ms	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
14.0ms	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
44.0ms	(* (sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))))

series56.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x))))
9.0ms	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
10.0ms	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
17.0ms	(* (sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))))

simplify168.0ms

Algorithm

egg-herbie

Counts

328 → 328

Iterations

Useful iterations: 2 (125.0ms)

Iter	Nodes	Cost
0	827	3981
1	4531	3471
2	5001	3422

prune576.0ms

Filtered

328 candidates to 151 candidates (54.0%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	324	4	328
Fresh	2	5	7
Picked	0	1	1
Done	0	1	1
Total	326	11	337

Merged error: 0.0b

Counts

337 → 11

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
0.0b	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
0.2b	(/ (/ (+ 1.0 0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
0.2b	(/ (+ 1.0 0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

rewrite112.0ms

Algorithm

rewrite-expression-head

Rules

1122×	`*-un-lft-identity`
900×	`sqrt-prod`
774×	`times-frac`
460×	`distribute-lft-out`
294×	`add-sqr-sqrt`
292×	`add-cube-cbrt`
46×	`associate-/l*`
28×	`sqrt-div`
24×	`associate-/r/`
18×	`associate-/r*`
15×	`flip3-+` `flip-+`
12×	`div-inv`
11×	`add-exp-log` `add-cbrt-cube`
6×	`pow1`
4×	`cbrt-undiv` `div-exp` `add-log-exp`
3×	`associate-/l/`
2×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num`

Counts

4 → 547

Calls

4 calls:

8.0ms	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
8.0ms	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
32.0ms	(/ (/ (+ 1.0 0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
14.0ms	(/ (+ 1.0 0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

series57.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
11.0ms	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
9.0ms	(/ (/ (+ 1.0 0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
26.0ms	(/ (+ 1.0 0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

simplify120.0ms

Algorithm

egg-herbie

Counts

559 → 559

Iterations

Useful iterations: 1 (31.0ms)

Iter	Nodes	Cost
0	1304	11535
1	5001	9909

prune665.0ms

Filtered

559 candidates to 153 candidates (72.6%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	555	4	559
Fresh	4	4	8
Picked	1	0	1
Done	1	1	2
Total	561	9	570

Merged error: 0b

Counts

570 → 9

regimes82.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	15
1	18	15
2	18	15

end0.0ms

sample985.0ms

Algorithm

intervals

Results

231.0ms	1730×	body	1280	valid
204.0ms	7825×	body	80	nan
130.0ms	1265×	body	640	valid
115.0ms	4110×	body	80	valid
45.0ms	595×	body	320	valid
17.0ms	300×	body	160	valid

Details

sample33.0ms

simplify4.0ms

prune3.0ms

localize5.0ms

rewrite12.0ms

series14.0ms

simplify35.0ms

prune80.0ms

localize7.0ms

rewrite26.0ms

series21.0ms

simplify69.0ms

prune163.0ms

localize10.0ms

rewrite105.0ms

series56.0ms

simplify168.0ms

prune576.0ms

localize12.0ms

rewrite112.0ms

series57.0ms

simplify120.0ms

prune665.0ms

regimes82.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample985.0ms

Profiling