Details

sample34.0ms

Algorithm

intervals

Results

6.0ms	250×	body	80	nan
6.0ms	48×	body	1280	valid
4.0ms	39×	body	640	valid
4.0ms	134×	body	80	valid
2.0ms	24×	body	320	valid
1.0ms	11×	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

prune7.0ms

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: 28.9b

Counts

2 → 1

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt (+ x 1.0))
2.6b	(- (sqrt (+ x 1.0)) (sqrt x))

rewrite11.0ms

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))

series13.0ms

Counts

2 → 6

Calls

2 calls:

3.0ms	(sqrt (+ x 1.0))
10.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

simplify32.0ms

Algorithm

egg-herbie

Counts

41 → 41

Iterations

Useful iterations: 2 (27.0ms)

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

prune136.0ms

Filtered

41 candidates to 31 candidates (24.4%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	38	3	41
Fresh	0	0	0
Picked	0	1	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))
0.2b	(/ (+ 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))
11.0ms	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))

series18.0ms

Counts

3 → 9

Calls

3 calls:

3.0ms	(sqrt (+ x 1.0))
5.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
9.0ms	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify65.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 2 (56.0ms)

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

prune349.0ms

Filtered

89 candidates to 59 candidates (33.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	83	6	89
Fresh	2	0	2
Picked	0	1	1
Done	1	0	1
Total	86	7	93

Merged error: 0.0b

Counts

93 → 7

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x))))
0.2b	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
0.2b	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
0.3b	(* (sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))))

rewrite100.0ms

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)))
12.0ms	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
43.0ms	(* (sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))))

series54.0ms

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)))
9.0ms	(/ (+ 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)))))

simplify159.0ms

Algorithm

egg-herbie

Counts

328 → 328

Iterations

Useful iterations: 2 (118.0ms)

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

prune1.3s

Filtered

328 candidates to 152 candidates (53.7%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	321	7	328
Fresh	3	2	5
Picked	1	0	1
Done	0	1	1
Total	325	10	335

Merged error: 0b

Counts

335 → 10

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (pow (sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))) 4))
0.1b	(sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x))))
0.2b	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
0.5b	(pow (sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))) 4)

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

222×	`*-un-lft-identity`
197×	`sqrt-prod`
98×	`times-frac`
93×	`distribute-lft-out`
69×	`unpow-prod-down`
61×	`add-sqr-sqrt`
53×	`add-cube-cbrt`
8×	`associate-/r/`
7×	`pow1` `add-exp-log` `rem-sqrt-square`
6×	`associate-/r*` `add-cbrt-cube`
5×	`flip3-+` `flip-+`
4×	`div-inv` `associate-/l*` `add-log-exp`
3×	`pow-unpow` `pow-pow` `sqrt-pow1` `pow1/2` `sqr-pow`
2×	`associate-/l/`
1×	`cbrt-undiv` `pow-to-exp` `frac-2neg` `sqrt-div` `div-exp` `pow-exp` `clear-num` `sqrt-pow2`

Counts

4 → 193

Calls

4 calls:

20.0ms	(sqrt (pow (sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))) 4))
11.0ms	(sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x))))
12.0ms	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
14.0ms	(pow (sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))) 4)

series79.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(sqrt (pow (sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))) 4))
19.0ms	(sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x))))
13.0ms	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
34.0ms	(pow (sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))) 4)

simplify132.0ms

Algorithm

egg-herbie

Counts

205 → 205

Iterations

Useful iterations: 2 (106.0ms)

Iter	Nodes	Cost
0	1021	2939
1	4574	2581
2	5001	2479

prune1.6s

Filtered

205 candidates to 116 candidates (43.4%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	205	0	205
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	205	10	215

Merged error: 0b

Counts

215 → 10

regimes67.0ms

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	12	6
1	16	6
2	16	6

end0.0ms

sample962.0ms

Algorithm

intervals

Results

228.0ms	1727×	body	1280	valid
205.0ms	7856×	body	80	nan
131.0ms	1251×	body	640	valid
116.0ms	4130×	body	80	valid
45.0ms	591×	body	320	valid
15.0ms	301×	body	160	valid

Details

sample34.0ms

simplify4.0ms

prune7.0ms

localize5.0ms

rewrite11.0ms

series13.0ms

simplify32.0ms

prune136.0ms

localize7.0ms

rewrite26.0ms

series18.0ms

simplify65.0ms

prune349.0ms

localize10.0ms

rewrite100.0ms

series54.0ms

simplify159.0ms

prune1.3s

localize11.0ms

rewrite69.0ms

series79.0ms

simplify132.0ms

prune1.6s

regimes67.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample962.0ms

Profiling