Details

sample54.0ms

Algorithm

intervals

Results

36.0ms

670×

body

valid

simplify81.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 2 (7.0ms)

Iter	Nodes	Cost
0	53	14
1	173	13
2	532	12
3	1681	12
4	4278	12
5	5001	12

prune6.0ms

Filtered

1 candidates to 1 candidates (100.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 0.2b

Counts

2 → 1

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))
0.1b	(* (* a a) (- 1.0 a))
0.3b	(pow (+ (* a a) (* b b)) 2.0)
0.6b	(* (* b b) (+ 3.0 a))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
26×	`*-un-lft-identity`
22×	`add-cube-cbrt`
18×	`associate-*r/` `prod-diff`
17×	`pow1` `add-exp-log`
16×	`add-cbrt-cube`
13×	`distribute-rgt-in` `distribute-lft-in`
12×	`associate-r`
7×	`pow-prod-down` `prod-exp` `cbrt-unprod`
5×	`associate-l`
4×	`expm1-log1p-u` `flip3-+` `frac-add` `flip-+` `log1p-expm1-u` `add-log-exp`
3×	`unpow-prod-down` `pow-unpow` `flip3--` `*-commutative` `flip--` `unswap-sqr`
2×	`sub-neg`
1×	`pow-to-exp` `pow-pow` `pow-exp` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares` `sqr-pow`

Counts

4 → 120

Calls

4 calls:

12.0ms	(* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))
9.0ms	(* (* a a) (- 1.0 a))
4.0ms	(pow (+ (* a a) (* b b)) 2.0)
8.0ms	(* (* b b) (+ 3.0 a))

series252.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))
56.0ms	(* (* a a) (- 1.0 a))
102.0ms	(pow (+ (* a a) (* b b)) 2.0)
36.0ms	(* (* b b) (+ 3.0 a))

simplify118.0ms

Algorithm

egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 1 (22.0ms)

Iter	Nodes	Cost
0	788	1033
1	4587	830
2	5001	830

prune353.0ms

Filtered

132 candidates to 83 candidates (62.9%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	126	6	132
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	127	6	133

Merged error: 0.1b

Counts

133 → 6

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))
0.1b	(* (* a a) (- 1.0 a))
0.3b	(* (pow (fma a a (* b b)) (/ 2.0 2)) (pow (fma a a (* b b)) (/ 2.0 2)))
0.6b	(* (* b b) (+ 3.0 a))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

46×	`add-sqr-sqrt`
32×	`*-un-lft-identity`
28×	`add-exp-log` `add-cube-cbrt`
19×	`associate-r`
18×	`unpow-prod-down` `associate-*r/` `prod-diff` `add-cbrt-cube`
16×	`pow1` `prod-exp`
13×	`distribute-rgt-in` `distribute-lft-in`
12×	`associate-l` `unswap-sqr`
10×	`sqr-pow`
8×	`pow-prod-down` `cbrt-unprod`
7×	`swap-sqr`
6×	`pow-to-exp` `pow-exp`
4×	`expm1-log1p-u` `flip3-+` `frac-add` `*-commutative` `flip-+` `log1p-expm1-u` `add-log-exp`
3×	`flip3--` `flip--`
2×	`sub-neg`
1×	`pow2` `pow-sqr` `pow-prod-up` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 155

Calls

4 calls:

12.0ms	(* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))
9.0ms	(* (* a a) (- 1.0 a))
11.0ms	(* (pow (fma a a (* b b)) (/ 2.0 2)) (pow (fma a a (* b b)) (/ 2.0 2)))
8.0ms	(* (* b b) (+ 3.0 a))

series301.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))
54.0ms	(* (* a a) (- 1.0 a))
157.0ms	(* (pow (fma a a (* b b)) (/ 2.0 2)) (pow (fma a a (* b b)) (/ 2.0 2)))
33.0ms	(* (* b b) (+ 3.0 a))

simplify134.0ms

Algorithm

egg-herbie

Counts

167 → 167

Iterations

Useful iterations: 1 (24.0ms)

Iter	Nodes	Cost
0	857	1475
1	4949	1213
2	5001	1213

prune453.0ms

Filtered

167 candidates to 97 candidates (58.1%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	163	4	167
Fresh	4	1	5
Picked	1	0	1
Done	0	0	0
Total	168	5	173

Merged error: 0.0b

Counts

173 → 5

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (pow (sqrt (pow (fma a a (* b b)) (/ 2.0 2))) 3) (sqrt (pow (fma a a (* b b)) (/ 2.0 2))))
0.6b	(* (* b b) (+ 3.0 a))
7.4b	(sqrt (pow (fma a a (* b b)) (/ 2.0 2)))
7.4b	(sqrt (pow (fma a a (* b b)) (/ 2.0 2)))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

89×	`sqrt-prod`
82×	`add-sqr-sqrt`
61×	`unpow-prod-down`
41×	`unswap-sqr`
30×	`sqr-pow`
27×	`associate-l`
26×	`cube-prod`
21×	`*-un-lft-identity`
19×	`add-cube-cbrt`
14×	`add-exp-log` `associate-r`
11×	`add-cbrt-cube`
10×	`pow1`
6×	`rem-sqrt-square` `prod-exp`
4×	`expm1-log1p-u` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
3×	`pow-prod-down`
2×	`sqrt-pow1` `pow1/2` `associate-r/` `-commutative`
1×	`distribute-rgt-in` `cube-mult` `pow-to-exp` `distribute-lft-in` `flip3-+` `pow-plus` `unpow3` `pow-exp` `pow-prod-up` `flip-+` `distribute-lft-out`

Counts

4 → 160

Calls

4 calls:

15.0ms	(* (pow (sqrt (pow (fma a a (* b b)) (/ 2.0 2))) 3) (sqrt (pow (fma a a (* b b)) (/ 2.0 2))))
8.0ms	(* (* b b) (+ 3.0 a))
3.0ms	(sqrt (pow (fma a a (* b b)) (/ 2.0 2)))
3.0ms	(sqrt (pow (fma a a (* b b)) (/ 2.0 2)))

series687.0ms

Counts

4 → 12

Calls

4 calls:

342.0ms	(* (pow (sqrt (pow (fma a a (* b b)) (/ 2.0 2))) 3) (sqrt (pow (fma a a (* b b)) (/ 2.0 2))))
31.0ms	(* (* b b) (+ 3.0 a))
158.0ms	(sqrt (pow (fma a a (* b b)) (/ 2.0 2)))
155.0ms	(sqrt (pow (fma a a (* b b)) (/ 2.0 2)))

simplify76.0ms

Algorithm

egg-herbie

Counts

172 → 172

Iterations

Useful iterations: 2 (56.0ms)

Iter	Nodes	Cost
0	455	1999
1	2241	1810
2	5002	1765

prune545.0ms

Filtered

172 candidates to 107 candidates (62.2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	170	2	172
Fresh	2	2	4
Picked	0	1	1
Done	0	0	0
Total	172	5	177

Merged error: 0b

Counts

177 → 5

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))
0.1b	(* (* a a) (- 1.0 a))
0.6b	(* (* b b) (+ 3.0 a))
7.4b	(sqrt (pow (fma a a (* b b)) (/ 2.0 2)))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt`
26×	`*-un-lft-identity`
22×	`add-cube-cbrt`
18×	`associate-*r/` `prod-diff`
16×	`pow1` `add-exp-log` `add-cbrt-cube`
13×	`distribute-rgt-in` `distribute-lft-in`
12×	`associate-r`
7×	`pow-prod-down` `prod-exp` `sqrt-prod` `cbrt-unprod`
5×	`associate-l`
4×	`expm1-log1p-u` `unpow-prod-down` `flip3-+` `frac-add` `flip-+` `log1p-expm1-u` `add-log-exp`
3×	`rem-sqrt-square` `flip3--` `*-commutative` `flip--` `unswap-sqr`
2×	`sub-neg` `sqr-pow`
1×	`sqrt-pow1` `pow1/2` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 122

Calls

4 calls:

12.0ms	(* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))
9.0ms	(* (* a a) (- 1.0 a))
8.0ms	(* (* b b) (+ 3.0 a))
3.0ms	(sqrt (pow (fma a a (* b b)) (/ 2.0 2)))

series305.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))
53.0ms	(* (* a a) (- 1.0 a))
32.0ms	(* (* b b) (+ 3.0 a))
157.0ms	(sqrt (pow (fma a a (* b b)) (/ 2.0 2)))

simplify117.0ms

Algorithm

egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 1 (22.0ms)

Iter	Nodes	Cost
0	797	1061
1	4470	861
2	5001	861

prune537.0ms

Filtered

134 candidates to 86 candidates (64.2%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	134	0	134
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	134	5	139

Merged error: 0b

Counts

139 → 5

regimes95.0ms

Accuracy

0% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 0.0b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	21
1	38	21

end0.0ms

sample1.4s

Algorithm

intervals

Results

1.0s

20277×

body

valid