Details

sample1.1s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 88.876343%

Guaranteed chance to sample good point: 28.230453%

Results

66.0ms	162×	body	640	valid
21.0ms	59×	body	320	valid
19.0ms	190×	body	80	nan
3.0ms	15×	body	160	valid
3.0ms	5×	body	1280	valid
1.0ms	15×	body	80	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: 4.6b

Counts

2 → 1

localize25.0ms

Local error

Found 4 expressions with local error:

2.1b	(- (sqrt (+ y 1.0)) (sqrt y))
2.8b	(- (sqrt (+ x 1.0)) (sqrt x))
3.5b	(- (sqrt (+ t 1.0)) (sqrt t))
3.9b	(- (sqrt (+ z 1.0)) (sqrt z))

rewrite34.0ms

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

series41.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify67.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 1 (15.0ms)

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

prune275.0ms

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: 3.6b

Counts

89 → 9

localize25.0ms

Local error

Found 4 expressions with local error:

2.1b	(- (sqrt (+ y 1.0)) (sqrt y))
2.8b	(- (sqrt (+ x 1.0)) (sqrt x))
2.9b	(+ z (- 1.0 z))
3.5b	(- (sqrt (+ t 1.0)) (sqrt t))

rewrite33.0ms

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

series29.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify55.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 1 (13.0ms)

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

prune266.0ms

Filtered

59 candidates to 86 candidates (-45.8%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	83	3	86
Fresh	0	8	8
Picked	1	0	1
Done	0	0	0
Total	84	11	95

Merged error: 2.6b

Counts

95 → 11

localize23.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1.0 (+ (sqrt (+ z 1.0)) (sqrt z)))
2.1b	(- (sqrt (+ y 1.0)) (sqrt y))
2.8b	(- (sqrt (+ x 1.0)) (sqrt x))
3.5b	(- (sqrt (+ t 1.0)) (sqrt t))

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:

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

series38.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify77.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 2 (65.0ms)

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

prune331.0ms

Filtered

72 candidates to 110 candidates (-52.8%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	108	2	110
Fresh	0	10	10
Picked	1	0	1
Done	0	0	0
Total	109	12	121

Merged error: 2.6b

Counts

121 → 12

localize28.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (cbrt (+ (sqrt (+ z 1.0)) (sqrt z))) (cbrt (+ (sqrt (+ z 1.0)) (sqrt z))))
2.1b	(- (sqrt (+ y 1.0)) (sqrt y))
2.8b	(- (sqrt (+ x 1.0)) (sqrt x))
3.5b	(- (sqrt (+ t 1.0)) (sqrt t))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

77×	`*-un-lft-identity`
48×	`sqrt-prod`
44×	`add-sqr-sqrt`
36×	`cbrt-prod`
27×	`distribute-lft-out`
13×	`swap-sqr`
12×	`add-cube-cbrt` `cbrt-div` `difference-of-squares`
11×	`pow1`
10×	`add-log-exp`
9×	`associate-r` `associate-l` `distribute-lft-out--`
6×	`add-exp-log` `flip3-+` `pow1/3` `flip-+`
4×	`frac-times` `add-cbrt-cube` `unswap-sqr`
3×	`sub-neg` `flip3--` `diff-log` `flip--`
2×	`associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 118

Calls

4 calls:

20.0ms	(* (cbrt (+ (sqrt (+ z 1.0)) (sqrt z))) (cbrt (+ (sqrt (+ z 1.0)) (sqrt z))))
8.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
9.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
8.0ms	(- (sqrt (+ t 1.0)) (sqrt t))

series49.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(* (cbrt (+ (sqrt (+ z 1.0)) (sqrt z))) (cbrt (+ (sqrt (+ z 1.0)) (sqrt z))))
9.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
9.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
10.0ms	(- (sqrt (+ t 1.0)) (sqrt t))

simplify90.0ms

Algorithm

egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 2 (75.0ms)

Iter	Nodes	Cost
0	881	1651
1	3762	1552
2	5001	1434

prune451.0ms

Filtered

79 candidates to 130 candidates (-64.6%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	127	3	130
Fresh	0	11	11
Picked	0	1	1
Done	0	0	0
Total	127	15	142

Merged error: 2.6b

Counts

142 → 15

regimes1.6s

Accuracy

0% (1.1b remaining)

Error of 4.1b against oracle of 3.0b and baseline of 4.1b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	34
1	41	34

end0.0ms

sample5.1s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 88.876343%

Guaranteed chance to sample good point: 28.230453%

Results

2.1s	5192×	body	640	valid
641.0ms	6248×	body	80	nan
483.0ms	1593×	body	320	valid
86.0ms	433×	body	160	valid
71.0ms	141×	body	1280	valid
70.0ms	641×	body	80	valid

Details

sample1.1s

simplify26.0ms

prune6.0ms

localize25.0ms

rewrite34.0ms

series41.0ms

simplify67.0ms

prune275.0ms

localize25.0ms

rewrite33.0ms

series29.0ms

simplify55.0ms

prune266.0ms

localize23.0ms

rewrite38.0ms

series38.0ms

simplify77.0ms

prune331.0ms

localize28.0ms

rewrite50.0ms

series49.0ms

simplify90.0ms

prune451.0ms

regimes1.6s

bsearch0.0ms

simplify2.0ms

end0.0ms

sample5.1s

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