Details

sample51.0ms

Algorithm

intervals

Results

23.0ms

496×

body

valid

simplify120.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 2 (10.0ms)

Iter	Nodes	Cost
0	33	9
1	87	9
2	260	8
3	872	8
4	2436	8
5	4957	8
6	5001	8

prune16.0ms

Filtered

1 candidates to 1 candidates (100.0%)

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: 1.1b

Counts

2 → 2

localize18.0ms

Local error

Found 3 expressions with local error:

0.0b	(* 2.0 (* (- (fma c b a)) (* c i)))
0.0b	(fma 2.0 (fma x y (* z t)) (* 2.0 (* (- (fma c b a)) (* c i))))
6.0b	(* (- (fma c b a)) (* c i))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

17×	`pow1` `add-exp-log` `add-cbrt-cube`
13×	`associate-l`
9×	`pow-prod-down` `prod-exp` `cbrt-unprod`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
3×	`distribute-lft-neg-in` `expm1-log1p-u` `distribute-rgt-neg-in` `log1p-expm1-u` `add-log-exp`
2×	`distribute-lft-neg-out` `associate-r` `*-commutative`
1×	`neg-mul-1` `distribute-rgt-neg-out` `fma-udef`

Counts

3 → 62

Calls

3 calls:

8.0ms	(* 2.0 (* (- (fma c b a)) (* c i)))
1.0ms	(fma 2.0 (fma x y (* z t)) (* 2.0 (* (- (fma c b a)) (* c i))))
7.0ms	(* (- (fma c b a)) (* c i))

series895.0ms

Counts

3 → 9

Calls

3 calls:

75.0ms	(* 2.0 (* (- (fma c b a)) (* c i)))
751.0ms	(fma 2.0 (fma x y (* z t)) (* 2.0 (* (- (fma c b a)) (* c i))))
68.0ms	(* (- (fma c b a)) (* c i))

simplify51.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	270	485
1	1123	401
2	5001	391

prune253.0ms

Filtered

71 candidates to 48 candidates (67.6%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	64	7	71
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	64	9	73

Merged error: 0.7b

Counts

73 → 9

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma 2.0 (fma x y (* z t)) (* (sqrt 2.0) (* (sqrt 2.0) (* (- (fma c b a)) (* c i)))))
0.4b	(* (sqrt 2.0) (* (sqrt 2.0) (* (- (fma c b a)) (* c i))))
0.4b	(* (sqrt 2.0) (* (- (fma c b a)) (* c i)))
6.0b	(* (- (fma c b a)) (* c i))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

32×	`pow1` `add-exp-log` `add-cbrt-cube`
22×	`associate-l`
19×	`pow-prod-down` `prod-exp` `cbrt-unprod`
11×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`sqrt-prod`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`distribute-lft-neg-out` `distribute-lft-neg-in` `distribute-rgt-neg-in` `associate-r` `*-commutative` `distribute-rgt-neg-out`
1×	`neg-mul-1` `fma-udef`

Counts

4 → 95

Calls

4 calls:

1.0ms	(fma 2.0 (fma x y (* z t)) (* (sqrt 2.0) (* (sqrt 2.0) (* (- (fma c b a)) (* c i)))))
13.0ms	(* (sqrt 2.0) (* (sqrt 2.0) (* (- (fma c b a)) (* c i))))
10.0ms	(* (sqrt 2.0) (* (- (fma c b a)) (* c i)))
7.0ms	(* (- (fma c b a)) (* c i))

series1.6s

Counts

4 → 12

Calls

4 calls:

1.1s	(fma 2.0 (fma x y (* z t)) (* (sqrt 2.0) (* (sqrt 2.0) (* (- (fma c b a)) (* c i)))))
282.0ms	(* (sqrt 2.0) (* (sqrt 2.0) (* (- (fma c b a)) (* c i))))
175.0ms	(* (sqrt 2.0) (* (- (fma c b a)) (* c i)))
67.0ms	(* (- (fma c b a)) (* c i))

simplify68.0ms

Algorithm

egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	390	870
1	1708	708
2	5001	674

prune323.0ms

Filtered

107 candidates to 66 candidates (61.7%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	106	1	107
Fresh	1	6	7
Picked	0	1	1
Done	0	1	1
Total	107	9	116

Merged error: 0.7b

Counts

116 → 9

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sqrt (sqrt 2.0)) (* (sqrt (sqrt 2.0)) (* (- (fma c b a)) (* c i))))
0.3b	(* (sqrt (sqrt 2.0)) (* (- (fma c b a)) (* c i)))
0.4b	(* (sqrt 2.0) (* (sqrt (sqrt 2.0)) (* (sqrt (sqrt 2.0)) (* (- (fma c b a)) (* c i)))))
6.0b	(* (- (fma c b a)) (* c i))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

52×	`pow1` `add-exp-log` `add-cbrt-cube`
34×	`associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod`
21×	`sqrt-prod`
15×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`distribute-rgt-neg-out`
4×	`distribute-lft-neg-out` `expm1-log1p-u` `associate-r` `*-commutative` `log1p-expm1-u` `add-log-exp`
3×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
1×	`neg-mul-1`

Counts

4 → 124

Calls

4 calls:

15.0ms	(* (sqrt (sqrt 2.0)) (* (sqrt (sqrt 2.0)) (* (- (fma c b a)) (* c i))))
11.0ms	(* (sqrt (sqrt 2.0)) (* (- (fma c b a)) (* c i)))
18.0ms	(* (sqrt 2.0) (* (sqrt (sqrt 2.0)) (* (sqrt (sqrt 2.0)) (* (- (fma c b a)) (* c i)))))
6.0ms	(* (- (fma c b a)) (* c i))

series786.0ms

Counts

4 → 12

Calls

4 calls:

180.0ms	(* (sqrt (sqrt 2.0)) (* (sqrt (sqrt 2.0)) (* (- (fma c b a)) (* c i))))
262.0ms	(* (sqrt (sqrt 2.0)) (* (- (fma c b a)) (* c i)))
285.0ms	(* (sqrt 2.0) (* (sqrt (sqrt 2.0)) (* (sqrt (sqrt 2.0)) (* (- (fma c b a)) (* c i)))))
59.0ms	(* (- (fma c b a)) (* c i))

simplify74.0ms

Algorithm

egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 2 (60.0ms)

Iter	Nodes	Cost
0	450	1294
1	2139	1008
2	5003	961

prune426.0ms

Filtered

136 candidates to 82 candidates (60.3%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	135	1	136
Fresh	1	5	6
Picked	1	0	1
Done	0	2	2
Total	137	8	145

Merged error: 0.7b

Counts

145 → 8

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma 2.0 (fma x y (* z t)) (* (pow (sqrt (sqrt 2.0)) 3) (* (sqrt (sqrt 2.0)) (* (- (fma c b a)) (* c i)))))
0.3b	(* (sqrt (sqrt 2.0)) (* (- (fma c b a)) (* c i)))
0.3b	(* (pow (sqrt (sqrt 2.0)) 3) (* (sqrt (sqrt 2.0)) (* (- (fma c b a)) (* c i))))
6.0b	(* (- (fma c b a)) (* c i))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

56×	`add-exp-log`
43×	`associate-l`
39×	`prod-exp`
32×	`add-cbrt-cube`
27×	`sqrt-prod`
19×	`cbrt-unprod`
18×	`pow1`
17×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`unpow-prod-down` `cube-prod` `pow-prod-down`
4×	`expm1-log1p-u` `pow-to-exp` `pow-exp` `log1p-expm1-u` `add-log-exp`
3×	`distribute-lft-neg-out` `distribute-lft-neg-in` `distribute-rgt-neg-in` `associate-r` `*-commutative` `distribute-rgt-neg-out`
1×	`cube-mult` `neg-mul-1` `unpow3` `fma-udef` `sqr-pow`

Counts

4 → 120

Calls

4 calls:

1.0ms	(fma 2.0 (fma x y (* z t)) (* (pow (sqrt (sqrt 2.0)) 3) (* (sqrt (sqrt 2.0)) (* (- (fma c b a)) (* c i)))))
10.0ms	(* (sqrt (sqrt 2.0)) (* (- (fma c b a)) (* c i)))
16.0ms	(* (pow (sqrt (sqrt 2.0)) 3) (* (sqrt (sqrt 2.0)) (* (- (fma c b a)) (* c i))))
6.0ms	(* (- (fma c b a)) (* c i))

series1.7s

Counts

4 → 12

Calls

4 calls:

1.1s	(fma 2.0 (fma x y (* z t)) (* (pow (sqrt (sqrt 2.0)) 3) (* (sqrt (sqrt 2.0)) (* (- (fma c b a)) (* c i)))))
251.0ms	(* (sqrt (sqrt 2.0)) (* (- (fma c b a)) (* c i)))
276.0ms	(* (pow (sqrt (sqrt 2.0)) 3) (* (sqrt (sqrt 2.0)) (* (- (fma c b a)) (* c i))))
62.0ms	(* (- (fma c b a)) (* c i))

simplify90.0ms

Algorithm

egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 2 (77.0ms)

Iter	Nodes	Cost
0	481	1304
1	2396	1071
2	5001	986

prune413.0ms

Filtered

132 candidates to 78 candidates (59.1%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	130	2	132
Fresh	2	3	5
Picked	0	1	1
Done	0	2	2
Total	132	8	140

Merged error: 0.3b

Counts

140 → 8

regimes859.0ms

Accuracy

31% (1.0b remaining)

Error of 1.3b against oracle of 0.2b and baseline of 1.7b

bsearch1.0ms

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	53	37
1	65	37
2	86	37
3	89	37
4	89	37

end0.0ms

sample1.4s

Algorithm

intervals

Results

719.0ms

15190×

body

valid