Details

analyze664.0ms

Algorithm

sampling

Space saved by range analysis: 0.195169%

Space saved by search: 88.898053%

Guaranteed chance to sample good point: 56.186557%

sample125.0ms

Algorithm

intervals

Results

68.0ms	170×	body	640	valid
19.0ms	198×	body	80	nan
14.0ms	49×	body	320	valid
3.0ms	6×	body	1280	valid
2.0ms	23×	body	80	valid
1.0ms	8×	body	160	valid

simplify26.0ms

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

prune6.0ms

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: 6.2b

Counts

2 → 1

localize25.0ms

Local error

Found 4 expressions with local error:

1.9b	(- (sqrt (+ y 1.0)) (sqrt y))
2.4b	(- (sqrt (+ x 1.0)) (sqrt x))
3.1b	(- (sqrt (+ z 1.0)) (sqrt z))
4.4b	(- (sqrt (+ t 1.0)) (sqrt t))

rewrite36.0ms

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:

8.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
10.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
8.0ms	(- (sqrt (+ z 1.0)) (sqrt z))
8.0ms	(- (sqrt (+ t 1.0)) (sqrt t))

series38.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify62.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 1 (14.0ms)

Iter	Nodes	Cost
0	692	864
1	2941	824
2	5001	824

prune268.0ms

Filtered

60 candidates to 88 candidates (-46.7%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	79	9	88
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	80	9	89

Merged error: 4.3b

Counts

89 → 9

localize30.0ms

Local error

Found 4 expressions with local error:

1.9b	(- (sqrt (+ y 1.0)) (sqrt y))
2.4b	(- (sqrt (+ x 1.0)) (sqrt x))
2.7b	(+ t (- 1.0 t))
3.1b	(- (sqrt (+ z 1.0)) (sqrt z))

rewrite34.0ms

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:

8.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
9.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
6.0ms	(+ t (- 1.0 t))
9.0ms	(- (sqrt (+ z 1.0)) (sqrt z))

series37.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
10.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
1.0ms	(+ t (- 1.0 t))
10.0ms	(- (sqrt (+ z 1.0)) (sqrt z))

simplify61.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 1 (15.0ms)

Iter	Nodes	Cost
0	601	708
1	2432	673
2	5001	673

prune286.0ms

Filtered

59 candidates to 86 candidates (-45.8%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	84	2	86
Fresh	0	8	8
Picked	1	0	1
Done	0	0	0
Total	85	10	95

Merged error: 3.2b

Counts

95 → 10

localize28.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1.0 (+ (sqrt (+ t 1.0)) (sqrt t)))
1.9b	(- (sqrt (+ y 1.0)) (sqrt y))
2.4b	(- (sqrt (+ x 1.0)) (sqrt x))
3.1b	(- (sqrt (+ z 1.0)) (sqrt z))

rewrite38.0ms

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:

10.0ms	(/ 1.0 (+ (sqrt (+ t 1.0)) (sqrt t)))
8.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
8.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
8.0ms	(- (sqrt (+ z 1.0)) (sqrt z))

series41.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(/ 1.0 (+ (sqrt (+ t 1.0)) (sqrt t)))
10.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
10.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
10.0ms	(- (sqrt (+ z 1.0)) (sqrt z))

simplify76.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 2 (65.0ms)

Iter	Nodes	Cost
0	814	1082
1	3594	1022
2	5002	1005

prune376.0ms

Filtered

72 candidates to 110 candidates (-52.8%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	101	9	110
Fresh	2	7	9
Picked	1	0	1
Done	0	0	0
Total	104	16	120

Merged error: 3.2b

Counts

120 → 16

localize31.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1.0 (+ (sqrt (+ t 1.0)) (sqrt t)))
1.7b	(+ x (- 1.0 x))
1.9b	(- (sqrt (+ y 1.0)) (sqrt y))
3.1b	(- (sqrt (+ z 1.0)) (sqrt z))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

62×	`*-un-lft-identity`
32×	`sqrt-prod`
31×	`add-sqr-sqrt`
20×	`distribute-lft-out`
18×	`times-frac`
15×	`add-cube-cbrt`
13×	`add-log-exp`
8×	`difference-of-squares`
7×	`distribute-lft-out--`
6×	`add-exp-log` `associate-/r*` `add-cbrt-cube`
4×	`pow1`
3×	`sub-neg` `diff-log` `associate-/l*`
2×	`associate-+r+` `flip3--` `flip3-+` `sum-log` `associate-/r/` `flip--` `flip-+`
1×	`cbrt-undiv` `+-commutative` `associate-+r-` `frac-2neg` `div-exp` `clear-num` `div-inv`

Counts

4 → 96

Calls

4 calls:

9.0ms	(/ 1.0 (+ (sqrt (+ t 1.0)) (sqrt t)))
6.0ms	(+ x (- 1.0 x))
8.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
8.0ms	(- (sqrt (+ z 1.0)) (sqrt z))

series33.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify67.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 2 (56.0ms)

Iter	Nodes	Cost
0	724	926
1	3074	871
2	5002	854

prune238.0ms

Filtered

70 candidates to 108 candidates (-54.3%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	107	1	108
Fresh	4	11	15
Picked	1	0	1
Done	0	0	0
Total	112	12	124

Merged error: 1.8b

Counts

124 → 12

regimes1.6s

Accuracy

0% (0.7b remaining)

Error of 2.9b against oracle of 2.3b and baseline of 2.9b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	21
1	35	21

end0.0ms

analyze574.0ms

Algorithm

sampling

Space saved by range analysis: 0.195169%

Space saved by search: 88.898053%

Guaranteed chance to sample good point: 56.186557%

sample3.7s

Algorithm

intervals

Results

2.1s	5219×	body	640	valid
614.0ms	6166×	body	80	nan
462.0ms	1596×	body	320	valid
81.0ms	414×	body	160	valid
70.0ms	134×	body	1280	valid
63.0ms	637×	body	80	valid

Details

analyze664.0ms

sample125.0ms

simplify26.0ms

prune6.0ms

localize25.0ms

rewrite36.0ms

series38.0ms

simplify62.0ms

prune268.0ms

localize30.0ms

rewrite34.0ms

series37.0ms

simplify61.0ms

prune286.0ms

localize28.0ms

rewrite38.0ms

series41.0ms

simplify76.0ms

prune376.0ms

localize31.0ms

rewrite34.0ms

series33.0ms

simplify67.0ms

prune238.0ms

regimes1.6s

bsearch0.0ms

simplify2.0ms

end0.0ms

analyze574.0ms

sample3.7s

Profiling