Details

sample874.0ms

Algorithm

intervals

sampling

Space saved by range analysis: 88.898053%

Space saved by search: 0.195169%

Guaranteed chance to sample good point: 0%

Results

69.0ms	179×	body	640	valid
18.0ms	191×	body	80	nan
12.0ms	43×	body	320	valid
3.0ms	17×	body	160	valid
2.0ms	4×	body	1280	valid
1.0ms	13×	body	80	valid

simplify27.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	51	19
1	156	19
2	907	19
3	5001	19

prune5.0ms

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: 5.5b

Counts

2 → 1

localize26.0ms

Local error

Found 4 expressions with local error:

3.0b	(- (sqrt (+ t 1.0)) (sqrt t))
3.2b	(- (sqrt (+ z 1.0)) (sqrt z))
3.3b	(- (sqrt (+ y 1.0)) (sqrt y))
3.5b	(- (sqrt (+ x 1.0)) (sqrt x))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

36×	`add-sqr-sqrt`
32×	`*-un-lft-identity` `sqrt-prod`
16×	`difference-of-squares`
12×	`distribute-lft-out--` `add-log-exp`
4×	`pow1` `add-exp-log` `add-cube-cbrt` `sub-neg` `flip3--` `diff-log` `add-cbrt-cube` `flip--` `distribute-lft-out`

Counts

4 → 76

Calls

4 calls:

7.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
7.0ms	(- (sqrt (+ z 1.0)) (sqrt z))
7.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
8.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

series42.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
9.0ms	(- (sqrt (+ z 1.0)) (sqrt z))
9.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
10.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

simplify69.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 1 (17.0ms)

Iter	Nodes	Cost
0	692	864
1	2941	824
2	5003	824

prune261.0ms

Filtered

60 candidates to 88 candidates (-46.7%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	81	7	88
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	82	7	89

Merged error: 4.2b

Counts

89 → 7

localize26.0ms

Local error

Found 4 expressions with local error:

2.2b	(+ y (- 1.0 y))
3.0b	(- (sqrt (+ t 1.0)) (sqrt t))
3.2b	(- (sqrt (+ z 1.0)) (sqrt z))
3.5b	(- (sqrt (+ x 1.0)) (sqrt x))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

30×	`*-un-lft-identity`
28×	`add-sqr-sqrt`
24×	`sqrt-prod`
15×	`add-log-exp`
12×	`difference-of-squares`
10×	`distribute-lft-out--`
5×	`distribute-lft-out`
4×	`pow1` `add-exp-log` `add-cube-cbrt` `sub-neg` `diff-log` `add-cbrt-cube`
3×	`flip3--` `flip--`
2×	`associate-+r+` `sum-log`
1×	`+-commutative` `associate-+r-` `flip3-+` `flip-+`

Counts

4 → 74

Calls

4 calls:

7.0ms	(+ y (- 1.0 y))
7.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
7.0ms	(- (sqrt (+ z 1.0)) (sqrt z))
8.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

series28.0ms

Counts

4 → 12

Calls

4 calls:

1.0ms	(+ y (- 1.0 y))
9.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
9.0ms	(- (sqrt (+ z 1.0)) (sqrt z))
9.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

simplify56.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 1 (13.0ms)

Iter	Nodes	Cost
0	604	708
1	2432	673
2	5001	673

prune244.0ms

Filtered

59 candidates to 86 candidates (-45.8%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	83	3	86
Fresh	0	6	6
Picked	1	0	1
Done	0	0	0
Total	84	9	93

Merged error: 2.8b

Counts

93 → 9

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1.0 (+ (sqrt (+ y 1.0)) (sqrt y)))
3.0b	(- (sqrt (+ t 1.0)) (sqrt t))
3.2b	(- (sqrt (+ z 1.0)) (sqrt z))
3.5b	(- (sqrt (+ x 1.0)) (sqrt x))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

64×	`*-un-lft-identity`
40×	`sqrt-prod`
39×	`add-sqr-sqrt`
19×	`distribute-lft-out`
18×	`times-frac`
15×	`add-cube-cbrt`
12×	`difference-of-squares`
10×	`add-log-exp`
9×	`distribute-lft-out--`
6×	`add-exp-log` `associate-/r*` `add-cbrt-cube`
4×	`pow1`
3×	`sub-neg` `flip3--` `diff-log` `flip--` `associate-/l*`
2×	`associate-/r/`
1×	`cbrt-undiv` `frac-2neg` `flip3-+` `div-exp` `clear-num` `flip-+` `div-inv`

Counts

4 → 98

Calls

4 calls:

9.0ms	(/ 1.0 (+ (sqrt (+ y 1.0)) (sqrt y)))
7.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
7.0ms	(- (sqrt (+ z 1.0)) (sqrt z))
8.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

series39.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(/ 1.0 (+ (sqrt (+ y 1.0)) (sqrt y)))
9.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
9.0ms	(- (sqrt (+ z 1.0)) (sqrt z))
12.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

simplify85.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 2 (72.0ms)

Iter	Nodes	Cost
0	813	1083
1	3571	1022
2	5003	1005

prune338.0ms

Filtered

72 candidates to 110 candidates (-52.8%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	104	6	110
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	104	15	119

Merged error: 2.8b

Counts

119 → 15

localize31.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (/ 1.0 (sqrt (+ (sqrt (+ y 1.0)) (sqrt y)))) (sqrt (+ (sqrt (+ y 1.0)) (sqrt y))))
3.0b	(- (sqrt (+ t 1.0)) (sqrt t))
3.2b	(- (sqrt (+ z 1.0)) (sqrt z))
3.5b	(- (sqrt (+ x 1.0)) (sqrt x))

rewrite85.0ms

Algorithm

rewrite-expression-head

Rules

701×	`*-un-lft-identity`
664×	`sqrt-prod`
567×	`times-frac`
259×	`distribute-lft-out`
256×	`add-sqr-sqrt`
232×	`add-cube-cbrt`
33×	`associate-/l*`
22×	`sqrt-div` `associate-/r/`
12×	`difference-of-squares`
11×	`flip3-+` `flip-+` `div-inv`
10×	`add-log-exp`
9×	`add-exp-log` `associate-/r*` `add-cbrt-cube` `distribute-lft-out--`
4×	`pow1`
3×	`cbrt-undiv` `sub-neg` `flip3--` `diff-log` `div-exp` `flip--`
1×	`frac-2neg` `clear-num` `associate-/l/`

Counts

4 → 413

Calls

4 calls:

26.0ms	(/ (/ 1.0 (sqrt (+ (sqrt (+ y 1.0)) (sqrt y)))) (sqrt (+ (sqrt (+ y 1.0)) (sqrt y))))
7.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
7.0ms	(- (sqrt (+ z 1.0)) (sqrt z))
7.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

series38.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(/ (/ 1.0 (sqrt (+ (sqrt (+ y 1.0)) (sqrt y)))) (sqrt (+ (sqrt (+ y 1.0)) (sqrt y))))
9.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
9.0ms	(- (sqrt (+ z 1.0)) (sqrt z))
10.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

simplify105.0ms

Algorithm

egg-herbie

Counts

425 → 425

Iterations

Useful iterations: 1 (31.0ms)

Iter	Nodes	Cost
0	1404	8413
1	5002	7359

prune710.0ms

Filtered

133 candidates to 425 candidates (-219.5%)

Pruning

17 alts after pruning (16 fresh and 1 done)

	Pruned	Kept	Total
New	420	5	425
Fresh	2	11	13
Picked	1	0	1
Done	0	1	1
Total	423	17	440

Merged error: 2.8b

Counts

440 → 17

regimes1.8s

Accuracy

0% (1.2b remaining)

Error of 4.1b against oracle of 2.9b and baseline of 4.1b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	20
1	33	20

end0.0ms

sample4.1s

Algorithm

intervals

sampling

Space saved by range analysis: 88.898053%

Space saved by search: 0.195169%

Guaranteed chance to sample good point: 0%

Results

2.0s	5180×	body	640	valid
604.0ms	6284×	body	80	nan
452.0ms	1579×	body	320	valid
90.0ms	465×	body	160	valid
70.0ms	148×	body	1280	valid
59.0ms	628×	body	80	valid

Details

sample874.0ms

simplify27.0ms

prune5.0ms

localize26.0ms

rewrite32.0ms

series42.0ms

simplify69.0ms

prune261.0ms

localize26.0ms

rewrite32.0ms

series28.0ms

simplify56.0ms

prune244.0ms

localize24.0ms

rewrite34.0ms

series39.0ms

simplify85.0ms

prune338.0ms

localize31.0ms

rewrite85.0ms

series38.0ms

simplify105.0ms

prune710.0ms

regimes1.8s

bsearch0.0ms

simplify1.0ms

end0.0ms

sample4.1s

Profiling