Details

analyze233.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
25%	74.9%	0.1%	6
25%	74.9%	0.1%	7
43.7%	56.2%	0.1%	8
62.4%	37.4%	0.1%	9
65.5%	34.3%	0.1%	10
71.8%	27.7%	0.5%	11
79.2%	19.7%	1.1%	12
80.2%	18.7%	1.1%	13
82.8%	15%	2.2%	14

sample19.0ms

Algorithm

intervals

Results

9.0ms	256×	body	80	valid
1.0ms	19×	body	80	invalid

simplify3.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	82	11
1	82	11

prune9.0ms

Filtered

1 candidates to 1 candidates (0.0%)

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: 5.2b

Counts

2 → 2

localize7.0ms

Local error

Found 2 expressions with local error:

2.9b	(/ (/ 1.0 x) (* y (+ 1.0 (* z z))))
4.2b	(* y (+ 1.0 (* z z)))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

31×	`times-frac`
20×	`add-sqr-sqrt`
18×	`add-cube-cbrt` `*-un-lft-identity`
16×	`add-exp-log` `add-cbrt-cube`
13×	`associate-/l*`
6×	`cbrt-undiv` `div-exp`
4×	`pow1` `associate-*r/`
3×	`associate-r` `associate-l` `prod-exp` `cbrt-unprod` `div-inv`
2×	`flip3-+` `associate-/r/` `flip-+` `add-log-exp`
1×	`distribute-rgt-in` `frac-2neg` `distribute-lft-in` `pow-prod-down` `clear-num` `associate-/r` `-commutative` `associate-/l/` `unswap-sqr`

Counts

2 → 70

Calls

2 calls:

8.0ms	(/ (/ 1.0 x) (* y (+ 1.0 (* z z))))
7.0ms	(* y (+ 1.0 (* z z)))

series26.0ms

Counts

2 → 6

Calls

2 calls:

17.0ms	(/ (/ 1.0 x) (* y (+ 1.0 (* z z))))
10.0ms	(* y (+ 1.0 (* z z)))

simplify43.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	4985	885
1	4985	885

prune118.0ms

Filtered

56 candidates to 76 candidates (-35.7%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	69	7	76
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	70	8	78

Merged error: 4.4b

Counts

78 → 8

localize10.0ms

Local error

Found 3 expressions with local error:

0.5b	(/ 1 (* y (+ 1.0 (* z z))))
2.7b	(* (/ 1.0 x) (/ 1 (* y (+ 1.0 (* z z)))))
4.2b	(* y (+ 1.0 (* z z)))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

61×	`add-exp-log`
31×	`add-cbrt-cube`
24×	`prod-exp`
23×	`add-sqr-sqrt`
19×	`div-exp`
16×	`add-cube-cbrt` `-un-lft-identity` `times-frac` `associate-l*`
12×	`associate-r`
10×	`pow1` `cbrt-unprod`
9×	`cbrt-undiv`
7×	`associate-*r/`
6×	`rec-exp` `1-exp`
4×	`associate-/r/`
3×	`flip3-+` `pow-prod-down` `flip-+` `div-inv` `associate-/l*` `add-log-exp` `unswap-sqr`
2×	`pow-flip` `*-commutative`
1×	`distribute-rgt-in` `frac-times` `frac-2neg` `distribute-lft-in` `associate-l/` `clear-num` `associate-/r` `un-div-inv` `inv-pow`

Counts

3 → 109

Calls

3 calls:

6.0ms	(/ 1 (* y (+ 1.0 (* z z))))
12.0ms	(* (/ 1.0 x) (/ 1 (* y (+ 1.0 (* z z)))))
5.0ms	(* y (+ 1.0 (* z z)))

series39.0ms

Counts

3 → 9

Calls

3 calls:

12.0ms	(/ 1 (* y (+ 1.0 (* z z))))
17.0ms	(* (/ 1.0 x) (/ 1 (* y (+ 1.0 (* z z)))))
10.0ms	(* y (+ 1.0 (* z z)))

simplify71.0ms

Algorithm

egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	5263	1232

prune114.0ms

Filtered

68 candidates to 118 candidates (-73.5%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	116	2	118
Fresh	3	3	6
Picked	1	0	1
Done	0	1	1
Total	120	6	126

Merged error: 1.8b

Counts

126 → 6

localize7.0ms

Local error

Found 3 expressions with local error:

0.5b	(/ 1.0 (* y (+ 1.0 (* z z))))
2.6b	(/ (/ 1.0 (* y (+ 1.0 (* z z)))) x)
4.2b	(* y (+ 1.0 (* z z)))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

42×	`times-frac`
27×	`add-sqr-sqrt`
25×	`add-cube-cbrt` `*-un-lft-identity`
19×	`add-exp-log` `add-cbrt-cube`
12×	`associate-r/` `associate-/l`
10×	`associate-/r/`
7×	`cbrt-undiv` `div-exp`
6×	`flip3-+` `flip-+` `div-inv`
5×	`pow1`
4×	`associate-/r*`
3×	`associate-r` `associate-l` `prod-exp` `cbrt-unprod` `add-log-exp`
2×	`frac-2neg` `clear-num`
1×	`distribute-rgt-in` `distribute-lft-in` `pow-prod-down` `*-commutative` `associate-/l/` `unswap-sqr`

Counts

3 → 101

Calls

3 calls:

5.0ms	(/ 1.0 (* y (+ 1.0 (* z z))))
7.0ms	(/ (/ 1.0 (* y (+ 1.0 (* z z)))) x)
5.0ms	(* y (+ 1.0 (* z z)))

series38.0ms

Counts

3 → 9

Calls

3 calls:

13.0ms	(/ 1.0 (* y (+ 1.0 (* z z))))
16.0ms	(/ (/ 1.0 (* y (+ 1.0 (* z z)))) x)
10.0ms	(* y (+ 1.0 (* z z)))

simplify51.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	4949	1467
1	4949	1467

prune127.0ms

Filtered

85 candidates to 110 candidates (-29.4%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	110	0	110
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	110	6	116

Merged error: 1.8b

Counts

116 → 6

localize12.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt x)
1.3b	(* (cbrt x) (* (/ y 1.0) (+ 1.0 (* z z))))
1.9b	(/ (/ 1 (* (cbrt x) (cbrt x))) (* (cbrt x) (* (/ y 1.0) (+ 1.0 (* z z)))))
4.2b	(* (/ y 1.0) (+ 1.0 (* z z)))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

136×	`add-exp-log`
54×	`prod-exp`
53×	`div-exp`
52×	`add-cbrt-cube`
26×	`cbrt-unprod`
25×	`cbrt-undiv`
24×	`add-sqr-sqrt`
23×	`times-frac`
19×	`add-cube-cbrt` `-un-lft-identity` `associate-l*`
16×	`associate-*r/`
11×	`pow1`
8×	`rec-exp` `1-exp`
7×	`associate-/l*`
6×	`cbrt-prod` `frac-times` `flip3-+` `flip-+`
5×	`distribute-rgt-in` `distribute-lft-in` `associate-/r/`
4×	`associate-r` `pow-prod-down` `div-inv` `add-log-exp`
3×	`associate-*l/`
2×	`*-commutative` `unswap-sqr`
1×	`frac-2neg` `pow1/3` `clear-num` `associate-/r*` `associate-/l/`

Counts

4 → 152

Calls

4 calls:

1.0ms	(cbrt x)
9.0ms	(* (cbrt x) (* (/ y 1.0) (+ 1.0 (* z z))))
15.0ms	(/ (/ 1 (* (cbrt x) (cbrt x))) (* (cbrt x) (* (/ y 1.0) (+ 1.0 (* z z)))))
7.0ms	(* (/ y 1.0) (+ 1.0 (* z z)))

series115.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(cbrt x)
56.0ms	(* (cbrt x) (* (/ y 1.0) (+ 1.0 (* z z))))
21.0ms	(/ (/ 1 (* (cbrt x) (cbrt x))) (* (cbrt x) (* (/ y 1.0) (+ 1.0 (* z z)))))
14.0ms	(* (/ y 1.0) (+ 1.0 (* z z)))

simplify54.0ms

Algorithm

egg-herbie

Counts

164 → 164

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	4969	2057
1	4969	2057

prune143.0ms

Filtered

97 candidates to 164 candidates (-69.1%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	164	0	164
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	164	6	170

Merged error: 1.8b

Counts

170 → 6

regimes562.0ms

Accuracy

91.5% (0.4b remaining)

Error of 2.4b against oracle of 2.0b and baseline of 6.4b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	41
1	27	41

end0.0ms

sample560.0ms

Algorithm

intervals

Results

340.0ms	8000×	body	80	valid
20.0ms	428×	body	80	invalid

Details

analyze233.0ms

sample19.0ms

simplify3.0ms

prune9.0ms

localize7.0ms

rewrite17.0ms

series26.0ms

simplify43.0ms

prune118.0ms

localize10.0ms

rewrite26.0ms

series39.0ms

simplify71.0ms

prune114.0ms

localize7.0ms

rewrite21.0ms

series38.0ms

simplify51.0ms

prune127.0ms

localize12.0ms

rewrite39.0ms

series115.0ms

simplify54.0ms

prune143.0ms

regimes562.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample560.0ms

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