Details

sample728.0ms

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 88.876343%

Guaranteed chance to sample good point: 56.186557%

Results

73.0ms	172×	body	640	valid
19.0ms	184×	body	80	nan
16.0ms	53×	body	320	valid
2.0ms	4×	body	1280	valid
2.0ms	18×	body	80	valid
2.0ms	9×	body	160	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

localize22.0ms

Local error

Found 4 expressions with local error:

2.2b	(- (sqrt (+ t 1.0)) (sqrt t))
2.6b	(- (sqrt (+ x 1.0)) (sqrt x))
4.2b	(- (sqrt (+ y 1.0)) (sqrt y))
4.2b	(- (sqrt (+ z 1.0)) (sqrt z))

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:

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

series38.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify63.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 1 (15.0ms)

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

prune229.0ms

Filtered

60 candidates to 88 candidates (-46.7%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	82	6	88
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	83	6	89

Merged error: 4.8b

Counts

89 → 6

localize26.0ms

Local error

Found 4 expressions with local error:

2.2b	(- (sqrt (+ t 1.0)) (sqrt t))
2.6b	(- (sqrt (+ x 1.0)) (sqrt x))
3.6b	(+ z (- 1.0 z))
4.2b	(- (sqrt (+ y 1.0)) (sqrt y))

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:

8.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
9.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
5.0ms	(+ z (- 1.0 z))
8.0ms	(- (sqrt (+ y 1.0)) (sqrt y))

series29.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify54.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 1 (12.0ms)

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

prune233.0ms

Filtered

59 candidates to 86 candidates (-45.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	83	3	86
Fresh	0	5	5
Picked	1	0	1
Done	0	0	0
Total	84	8	92

Merged error: 3.5b

Counts

92 → 8

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1.0 (+ (sqrt (+ z 1.0)) (sqrt z)))
2.2b	(- (sqrt (+ t 1.0)) (sqrt t))
2.6b	(- (sqrt (+ x 1.0)) (sqrt x))
4.2b	(- (sqrt (+ y 1.0)) (sqrt y))

rewrite37.0ms

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

series40.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(/ 1.0 (+ (sqrt (+ z 1.0)) (sqrt z)))
9.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
12.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
10.0ms	(- (sqrt (+ y 1.0)) (sqrt y))

simplify78.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 2 (66.0ms)

Iter	Nodes	Cost
0	813	1082
1	3573	1020
2	5002	1003

prune280.0ms

Filtered

72 candidates to 110 candidates (-52.8%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	107	3	110
Fresh	1	6	7
Picked	1	0	1
Done	0	0	0
Total	109	9	118

Merged error: 3.5b

Counts

118 → 9

localize29.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sqrt (/ 1.0 (+ (sqrt (+ z 1.0)) (sqrt z)))) (sqrt (/ 1.0 (+ (sqrt (+ z 1.0)) (sqrt z)))))
2.2b	(- (sqrt (+ t 1.0)) (sqrt t))
2.6b	(- (sqrt (+ x 1.0)) (sqrt x))
4.2b	(- (sqrt (+ y 1.0)) (sqrt y))

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

230×	`sqrt-prod`
209×	`*-un-lft-identity`
108×	`add-sqr-sqrt`
102×	`times-frac`
75×	`distribute-lft-out`
56×	`add-cube-cbrt`
41×	`swap-sqr`
27×	`associate-r` `associate-l`
19×	`pow1`
12×	`difference-of-squares`
10×	`add-log-exp`
9×	`distribute-lft-out--` `unswap-sqr`
8×	`sqrt-pow1` `pow1/2` `associate-/r/`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow-prod-up`
4×	`flip3-+` `sqrt-div` `flip-+` `div-inv`
3×	`sub-neg` `flip3--` `diff-log` `pow-prod-down` `pow-sqr` `flip--`
1×	`pow2` `frac-times` `pow-plus` `sqrt-unprod` `associate-r/` `associate-l/` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 189

Calls

4 calls:

38.0ms	(* (sqrt (/ 1.0 (+ (sqrt (+ z 1.0)) (sqrt z)))) (sqrt (/ 1.0 (+ (sqrt (+ z 1.0)) (sqrt z)))))
7.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
8.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
8.0ms	(- (sqrt (+ y 1.0)) (sqrt y))

series40.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(* (sqrt (/ 1.0 (+ (sqrt (+ z 1.0)) (sqrt z)))) (sqrt (/ 1.0 (+ (sqrt (+ z 1.0)) (sqrt z)))))
9.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
9.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
9.0ms	(- (sqrt (+ y 1.0)) (sqrt y))

simplify115.0ms

Algorithm

egg-herbie

Counts

201 → 201

Iterations

Useful iterations: 2 (89.0ms)

Iter	Nodes	Cost
0	918	2240
1	4365	2043
2	5002	2010

prune468.0ms

Filtered

107 candidates to 201 candidates (-87.9%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	198	3	201
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	198	12	210

Merged error: 3.5b

Counts

210 → 12

regimes1.2s

Accuracy

0% (1.1b remaining)

Error of 4.2b against oracle of 3.1b and baseline of 4.2b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	28
1	35	28

end0.0ms

sample4.6s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 88.876343%

Guaranteed chance to sample good point: 56.186557%

Results

2.1s	5284×	body	640	valid
630.0ms	6083×	body	80	nan
448.0ms	1492×	body	320	valid
90.0ms	446×	body	160	valid
73.0ms	140×	body	1280	valid
65.0ms	638×	body	80	valid

Details

sample728.0ms

simplify27.0ms

prune5.0ms

localize22.0ms

rewrite36.0ms

series38.0ms

simplify63.0ms

prune229.0ms

localize26.0ms

rewrite32.0ms

series29.0ms

simplify54.0ms

prune233.0ms

localize25.0ms

rewrite37.0ms

series40.0ms

simplify78.0ms

prune280.0ms

localize29.0ms

rewrite73.0ms

series40.0ms

simplify115.0ms

prune468.0ms

regimes1.2s

bsearch0.0ms

simplify1.0ms

end0.0ms

sample4.6s

Profiling