Details

analyze3.0ms

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	50%	0%	2
50%	25%	25%	3
62.5%	12.5%	25%	4
68.7%	6.2%	25%	5
71.8%	3.1%	25%	6
73.4%	1.6%	25%	7
74.2%	0.8%	25%	8
74.6%	0.4%	25%	9
74.8%	0.2%	25%	10
74.9%	0.1%	25%	11
74.9%	0%	25%	12
74.9%	0%	25%	13
74.9%	0%	25%	14

sample17.0ms

Algorithm

intervals

Results

12.0ms

256×

body

valid

simplify3.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	8	8
1	8	8

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: 0.2b

Counts

2 → 1

localize5.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (+ x 1.0))
0.0b	(+ 1.0 (sqrt (+ x 1.0)))
0.2b	(/ x (+ 1.0 (sqrt (+ x 1.0))))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

25×	`*-un-lft-identity`
14×	`add-sqr-sqrt`
13×	`add-cube-cbrt`
12×	`times-frac`
6×	`distribute-lft-out`
5×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
4×	`pow1` `associate-/r*` `sqrt-prod`
3×	`flip3-+` `flip-+` `associate-/l*`
2×	`sqrt-div` `associate-/r/`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

3 → 61

Calls

3 calls:

3.0ms	(sqrt (+ x 1.0))
5.0ms	(+ 1.0 (sqrt (+ x 1.0)))
7.0ms	(/ x (+ 1.0 (sqrt (+ x 1.0))))

series24.0ms

Counts

3 → 9

Calls

3 calls:

3.0ms	(sqrt (+ x 1.0))
4.0ms	(+ 1.0 (sqrt (+ x 1.0)))
16.0ms	(/ x (+ 1.0 (sqrt (+ x 1.0))))

simplify26.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 0 (17.0ms)

Iter	Nodes	Cost
0	4963	1021
1	4963	1021

prune123.0ms

Filtered

52 candidates to 70 candidates (-34.6%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	64	6	70
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	65	6	71

Merged error: 0b

Counts

71 → 6

localize6.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ x 1.0))
0.0b	(+ 1.0 (sqrt (+ x 1.0)))
0.1b	(* x (/ 1 (+ 1.0 (sqrt (+ x 1.0)))))
0.1b	(/ 1 (+ 1.0 (sqrt (+ x 1.0))))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

42×	`*-un-lft-identity`
31×	`add-sqr-sqrt`
26×	`times-frac`
23×	`add-cube-cbrt`
18×	`associate-r`
17×	`add-exp-log`
11×	`add-cbrt-cube`
9×	`distribute-lft-out`
8×	`pow1`
6×	`add-log-exp`
4×	`flip3-+` `div-exp` `prod-exp` `associate-/r*` `sqrt-prod` `associate-/r/` `flip-+`
3×	`associate-l` `associate-/l*` `unswap-sqr`
2×	`cbrt-undiv` `rec-exp` `sqrt-div` `1-exp` `cbrt-unprod` `div-inv`
1×	`+-commutative` `rem-sqrt-square` `pow-flip` `frac-2neg` `sqrt-pow1` `pow1/2` `associate-r/` `pow-prod-down` `clear-num` `sum-log` `un-div-inv` `-commutative` `inv-pow`

Counts

4 → 106

Calls

4 calls:

3.0ms	(sqrt (+ x 1.0))
5.0ms	(+ 1.0 (sqrt (+ x 1.0)))
11.0ms	(* x (/ 1 (+ 1.0 (sqrt (+ x 1.0)))))
7.0ms	(/ 1 (+ 1.0 (sqrt (+ x 1.0))))

series38.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(sqrt (+ x 1.0))
7.0ms	(+ 1.0 (sqrt (+ x 1.0)))
16.0ms	(* x (/ 1 (+ 1.0 (sqrt (+ x 1.0)))))
12.0ms	(/ 1 (+ 1.0 (sqrt (+ x 1.0))))

simplify33.0ms

Algorithm

egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 0 (22.0ms)

Iter	Nodes	Cost
0	5182	1663

prune177.0ms

Filtered

82 candidates to 118 candidates (-43.9%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	118	0	118
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	118	6	124

Merged error: 0b

Counts

124 → 6

localize7.0ms

Local error

Found 4 expressions with local error:

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

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

106×	`sqrt-prod`
62×	`add-sqr-sqrt`
46×	`*-un-lft-identity`
40×	`sqrt-pow1`
32×	`sqrt-div`
31×	`pow1`
28×	`add-cube-cbrt`
20×	`pow1/2`
18×	`swap-sqr`
10×	`associate-r` `associate-l`
9×	`flip3-+` `times-frac` `pow-prod-up` `flip-+` `unswap-sqr`
8×	`add-exp-log` `add-cbrt-cube` `distribute-lft-out`
5×	`pow-prod-down` `pow-sqr`
4×	`frac-times` `rem-sqrt-square` `add-log-exp`
3×	`associate-/r` `associate-/l`
2×	`associate-r/` `associate-l/` `associate-/r/`
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 → 161

Calls

4 calls:

4.0ms	(sqrt (sqrt (+ x 1.0)))
4.0ms	(sqrt (sqrt (+ x 1.0)))
14.0ms	(* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0))))
4.0ms	(/ x (+ 1.0 (* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0))))))

series34.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(sqrt (sqrt (+ x 1.0)))
6.0ms	(sqrt (sqrt (+ x 1.0)))
4.0ms	(* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0))))
19.0ms	(/ x (+ 1.0 (* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0))))))

simplify47.0ms

Algorithm

egg-herbie

Counts

173 → 173

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	4935	1773
1	4935	1773

prune216.0ms

Filtered

90 candidates to 173 candidates (-92.2%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	173	0	173
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	173	6	179

Merged error: 0b

Counts

179 → 6

localize10.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ (cbrt x) (sqrt (+ 1.0 (sqrt (+ x 1.0)))))
0.6b	(cbrt x)
0.6b	(cbrt x)
0.6b	(cbrt x)

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

51×	`*-un-lft-identity`
42×	`times-frac`
37×	`add-sqr-sqrt` `add-cube-cbrt`
33×	`cbrt-prod`
28×	`sqrt-prod`
7×	`associate-/r*` `distribute-lft-out`
6×	`add-exp-log` `associate-/l*`
5×	`add-cbrt-cube`
4×	`pow1` `add-log-exp`
3×	`pow1/3`
2×	`sqrt-div` `associate-/r/`
1×	`cbrt-undiv` `frac-2neg` `flip3-+` `div-exp` `clear-num` `flip-+` `div-inv`

Counts

4 → 102

Calls

4 calls:

9.0ms	(/ (cbrt x) (sqrt (+ 1.0 (sqrt (+ x 1.0)))))
1.0ms	(cbrt x)
1.0ms	(cbrt x)
1.0ms	(cbrt x)

series109.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(/ (cbrt x) (sqrt (+ 1.0 (sqrt (+ x 1.0)))))
22.0ms	(cbrt x)
21.0ms	(cbrt x)
25.0ms	(cbrt x)

simplify31.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 0 (19.0ms)

Iter	Nodes	Cost
0	5235	1796

prune412.0ms

Filtered

79 candidates to 114 candidates (-44.3%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	114	0	114
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	114	6	120

Merged error: 0b

Counts

120 → 6

regimes39.0ms

Accuracy

0% (0.2b 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	10
1	12	10

end0.0ms

sample298.0ms

Algorithm

intervals

Results

211.0ms	7999×	body	80	valid
0.0ms	1×	body	1280	valid

Details

analyze3.0ms

sample17.0ms

simplify3.0ms

prune3.0ms

localize5.0ms

rewrite17.0ms

series24.0ms

simplify26.0ms

prune123.0ms

localize6.0ms

rewrite31.0ms

series38.0ms

simplify33.0ms

prune177.0ms

localize7.0ms

rewrite33.0ms

series34.0ms

simplify47.0ms

prune216.0ms

localize10.0ms

rewrite16.0ms

series109.0ms

simplify31.0ms

prune412.0ms

regimes39.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample298.0ms

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