Details

sample32.0ms

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 49.996948%

Guaranteed chance to sample good point: 99.993897%

Results

8.0ms	62×	body	1280	valid
4.0ms	46×	body	640	valid
3.0ms	125×	body	80	valid
1.0ms	20×	body	320	valid
0.0ms	3×	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

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: 31.2b

Counts

2 → 1

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt (+ x 1.0))
1.3b	(- (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))

simplify34.0ms

Algorithm

egg-herbie

Counts

41 → 41

Iterations

Useful iterations: 2 (28.0ms)

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

prune81.0ms

Filtered

31 candidates to 41 candidates (-32.3%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	39	2	41
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	40	2	42

Merged error: 0.1b

Counts

42 → 2

localize8.0ms

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

series19.0ms

Counts

3 → 9

Calls

3 calls:

4.0ms	(sqrt (+ x 1.0))
6.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
10.0ms	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify70.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 2 (61.0ms)

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

prune170.0ms

Filtered

59 candidates to 89 candidates (-50.8%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	82	7	89
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	82	9	91

Merged error: 0.0b

Counts

91 → 9

localize10.0ms

Local error

Found 4 expressions with local error:

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

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

106×	`sqrt-prod`
63×	`add-sqr-sqrt`
55×	`*-un-lft-identity`
40×	`sqrt-pow1`
32×	`sqrt-div`
31×	`pow1`
29×	`add-cube-cbrt`
20×	`pow1/2`
18×	`swap-sqr`
12×	`times-frac` `distribute-lft-out`
10×	`flip3-+` `associate-r` `associate-l` `flip-+`
9×	`pow-prod-up` `unswap-sqr`
8×	`add-exp-log` `add-cbrt-cube`
5×	`pow-prod-down` `pow-sqr`
4×	`frac-times` `rem-sqrt-square` `associate-/l*` `add-log-exp`
3×	`associate-/r*`
2×	`associate-r/` `associate-l/` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `pow2` `frac-2neg` `pow-plus` `sqrt-unprod` `div-exp` `prod-exp` `clear-num` `rem-square-sqrt` `*-commutative` `cbrt-unprod` `div-inv`

Counts

4 → 167

Calls

4 calls:

4.0ms	(sqrt (sqrt (+ x 1.0)))
4.0ms	(sqrt (sqrt (+ x 1.0)))
18.0ms	(/ (+ 1.0 0) (+ (* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0)))) (sqrt x)))
18.0ms	(* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0))))

series26.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(sqrt (sqrt (+ x 1.0)))
6.0ms	(sqrt (sqrt (+ x 1.0)))
9.0ms	(/ (+ 1.0 0) (+ (* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0)))) (sqrt x)))
4.0ms	(* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0))))

simplify111.0ms

Algorithm

egg-herbie

Counts

179 → 179

Iterations

Useful iterations: 2 (90.0ms)

Iter	Nodes	Cost
0	679	1539
1	3301	1371
2	5002	1347

prune341.0ms

Filtered

97 candidates to 179 candidates (-84.5%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	178	1	179
Fresh	1	6	7
Picked	0	1	1
Done	0	1	1
Total	179	9	188

Merged error: 0.0b

Counts

188 → 9

localize12.0ms

Local error

Found 4 expressions with local error:

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

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

33×	`*-un-lft-identity`
25×	`add-sqr-sqrt`
19×	`add-cube-cbrt`
13×	`cbrt-prod`
12×	`times-frac`
10×	`associate-r`
9×	`sqrt-prod`
8×	`add-exp-log` `add-cbrt-cube`
7×	`distribute-lft-out`
6×	`pow1` `cbrt-div`
5×	`flip3-+` `flip-+`
4×	`associate-/l*` `add-log-exp`
3×	`associate-l` `associate-/r*` `unswap-sqr`
2×	`pow1/3` `sqrt-div` `associate-*r/` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `pow-prod-down` `prod-exp` `clear-num` `*-commutative` `cbrt-unprod` `div-inv`

Counts

4 → 92

Calls

4 calls:

12.0ms	(/ (+ 1.0 0) (+ (* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0)))) (sqrt x)))
8.0ms	(* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0))))
3.0ms	(cbrt (+ x 1.0))
3.0ms	(cbrt (+ x 1.0))

series69.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(/ (+ 1.0 0) (+ (* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0)))) (sqrt x)))
11.0ms	(* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0))))
6.0ms	(cbrt (+ x 1.0))
6.0ms	(cbrt (+ x 1.0))

simplify133.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 1 (23.0ms)

Iter	Nodes	Cost
0	931	1718
1	4945	1624
2	5001	1624

prune400.0ms

Filtered

86 candidates to 104 candidates (-20.9%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	103	1	104
Fresh	1	5	6
Picked	1	0	1
Done	0	2	2
Total	105	8	113

Merged error: 0.0b

Counts

113 → 8

regimes54.0ms

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

sample632.0ms

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 49.996948%

Guaranteed chance to sample good point: 99.993897%

Results

219.0ms	1755×	body	1280	valid
117.0ms	1235×	body	640	valid
110.0ms	4143×	body	80	valid
40.0ms	574×	body	320	valid
17.0ms	293×	body	160	valid

Details

sample32.0ms

simplify4.0ms

prune3.0ms

localize5.0ms

rewrite12.0ms

series14.0ms

simplify34.0ms

prune81.0ms

localize8.0ms

rewrite26.0ms

series19.0ms

simplify70.0ms

prune170.0ms

localize10.0ms

rewrite52.0ms

series26.0ms

simplify111.0ms

prune341.0ms

localize12.0ms

rewrite29.0ms

series69.0ms

simplify133.0ms

prune400.0ms

regimes54.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample632.0ms

Profiling