Details

sample31.0ms

Algorithm

intervals

Results

6.0ms	258×	body	80	nan
6.0ms	50×	body	1280	valid
4.0ms	45×	body	640	valid
3.0ms	123×	body	80	valid
2.0ms	28×	body	320	valid
0.0ms	10×	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

Filtered

1 candidates to 0 candidates (0.0%)

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: 31.6b

Counts

2 → 1

localize5.0ms

Local error

Found 1 expressions with local error:

2.9b	(- (sqrt (+ x 1.0)) (sqrt x))

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-sqr-sqrt`
8×	`*-un-lft-identity` `sqrt-prod`
4×	`difference-of-squares`
3×	`distribute-lft-out--` `add-log-exp`
1×	`pow1` `add-exp-log` `add-cube-cbrt` `sub-neg` `flip3--` `diff-log` `add-cbrt-cube` `flip--` `distribute-lft-out`

Counts

1 → 19

Calls

1 calls:

8.0ms

(- (sqrt (+ x 1.0)) (sqrt x))

series72.0ms

Counts

1 → 3

Calls

1 calls:

72.0ms

(- (sqrt (+ x 1.0)) (sqrt x))

simplify46.0ms

Algorithm

egg-herbie

Counts

22 → 22

Iterations

Useful iterations: 3 (42.0ms)

Iter	Nodes	Cost
0	132	175
1	400	159
2	1559	153
3	5001	149

prune44.0ms

Filtered

22 candidates to 14 candidates (63.6%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	19	3	22
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	20	3	23

Merged error: 0.2b

Counts

23 → 3

localize6.0ms

Local error

Found 2 expressions with local error:

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

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 55

Calls

2 calls:

7.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
9.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

series209.0ms

Counts

2 → 6

Calls

2 calls:

67.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
141.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify35.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 2 (28.0ms)

Iter	Nodes	Cost
0	295	535
1	1077	482
2	5002	453

prune111.0ms

Filtered

61 candidates to 39 candidates (63.9%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	55	6	61
Fresh	1	1	2
Picked	0	1	1
Done	0	0	0
Total	56	8	64

Merged error: 0.0b

Counts

64 → 8

localize8.0ms

Local error

Found 4 expressions with local error:

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

rewrite91.0ms

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:

18.0ms	(sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))
16.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
9.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
32.0ms	(* (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))))

series797.0ms

Counts

4 → 12

Calls

4 calls:

343.0ms	(sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))
140.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
145.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
169.0ms	(* (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))))

simplify112.0ms

Algorithm

egg-herbie

Counts

262 → 262

Iterations

Useful iterations: 2 (78.0ms)

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

prune432.0ms

Filtered

262 candidates to 137 candidates (52.3%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	258	4	262
Fresh	3	3	6
Picked	0	1	1
Done	0	1	1
Total	261	9	270

Merged error: 0.0b

Counts

270 → 9

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
0.3b	(* (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (cbrt (pow (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) 3)))
0.3b	(cbrt (pow (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) 3))
0.4b	(pow (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) 3)

rewrite115.0ms

Algorithm

rewrite-expression-head

Rules

298×	`sqrt-prod`
271×	`*-un-lft-identity`
162×	`add-sqr-sqrt`
159×	`times-frac`
144×	`cbrt-prod`
100×	`distribute-lft-out`
96×	`add-cube-cbrt`
90×	`unpow-prod-down` `cube-prod`
63×	`associate-r`
27×	`associate-l` `unswap-sqr`
16×	`associate-/r/`
9×	`add-exp-log`
8×	`pow1` `flip3-+` `add-cbrt-cube` `flip-+` `div-inv`
6×	`sqrt-div` `associate-/r*` `sqr-pow`
4×	`cube-div` `add-log-exp`
3×	`cube-mult` `pow-unpow` `cbrt-div` `pow-pow` `unpow3` `associate-/l*`
1×	`cbrt-undiv` `frac-times` `pow-to-exp` `frac-2neg` `sqrt-pow1` `pow1/2` `pow1/3` `associate-r/` `div-exp` `pow-prod-down` `associate-l/` `pow-exp` `prod-exp` `clear-num` `*-commutative` `sqrt-pow2` `rem-cbrt-cube` `cbrt-unprod` `rem-cube-cbrt`

Counts

4 → 317

Calls

4 calls:

9.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
54.0ms	(* (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (cbrt (pow (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) 3)))
14.0ms	(cbrt (pow (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) 3))
13.0ms	(pow (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) 3)

series1.5s

Counts

4 → 12

Calls

4 calls:

143.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
376.0ms	(* (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (cbrt (pow (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) 3)))
343.0ms	(cbrt (pow (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) 3))
664.0ms	(pow (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) 3)

simplify142.0ms

Algorithm

egg-herbie

Counts

329 → 329

Iterations

Useful iterations: 2 (102.0ms)

Iter	Nodes	Cost
0	1017	4585
1	4410	3911
2	5001	3807

prune466.0ms

Filtered

329 candidates to 133 candidates (40.4%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	328	1	329
Fresh	1	5	6
Picked	0	1	1
Done	0	2	2
Total	329	9	338

Merged error: 0.0b

Counts

338 → 9

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

sample912.0ms

Algorithm

intervals

Results

218.0ms	1768×	body	1280	valid
207.0ms	7956×	body	80	nan
118.0ms	1249×	body	640	valid
111.0ms	4035×	body	80	valid
48.0ms	644×	body	320	valid
15.0ms	304×	body	160	valid

Details

sample31.0ms

simplify5.0ms

prune2.0ms

localize5.0ms

rewrite8.0ms

series72.0ms

simplify46.0ms

prune44.0ms

localize6.0ms

rewrite18.0ms

series209.0ms

simplify35.0ms

prune111.0ms

localize8.0ms

rewrite91.0ms

series797.0ms

simplify112.0ms

prune432.0ms

localize12.0ms

rewrite115.0ms

series1.5s

simplify142.0ms

prune466.0ms

regimes36.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample912.0ms

Profiling