Details

sample55.0ms

Algorithm

intervals

Results

37.0ms

668×

body

valid

simplify81.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	51	14
1	155	14
2	430	14
3	1195	14
4	2526	14
5	5001	14

prune3.0ms

Filtered

1 candidates to 0 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: 0.2b

Counts

2 → 1

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (pow (+ (* a a) (* b b)) 2.0) (* 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)
0.5b	(* (* b b) (+ 3.0 a))

rewrite131.0ms

Algorithm

rewrite-expression-head

Rules

44×	`add-sqr-sqrt`
41×	`associate-l`
38×	`*-un-lft-identity`
28×	`associate-+r+`
22×	`distribute-rgt-in` `distribute-lft-in`
18×	`add-cube-cbrt`
15×	`pow1` `add-exp-log` `associate-r`
14×	`add-cbrt-cube` `unswap-sqr`
10×	`swap-sqr`
9×	`+-commutative`
8×	`unpow-prod-down` `associate-+l+` `distribute-lft-out`
6×	`sub-neg` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `add-log-exp`
4×	`associate-*r/`
3×	`pow-unpow`
2×	`flip3-+` `flip-+`
1×	`pow-to-exp` `flip3--` `pow-pow` `pow-exp` `sum-log` `flip--` `distribute-lft-out--` `difference-of-squares` `sqr-pow`

Counts

4 → 144

Calls

4 calls:

87.0ms	(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a)))))
12.0ms	(* (* a a) (- 1.0 a))
16.0ms	(pow (+ (* a a) (* b b)) 2.0)
11.0ms	(* (* b b) (+ 3.0 a))

series316.0ms

Counts

4 → 12

Calls

4 calls:

118.0ms	(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a)))))
51.0ms	(* (* a a) (- 1.0 a))
112.0ms	(pow (+ (* a a) (* b b)) 2.0)
35.0ms	(* (* b b) (+ 3.0 a))

simplify99.0ms

Algorithm

egg-herbie

Counts

156 → 156

Iterations

Useful iterations: 1 (22.0ms)

Iter	Nodes	Cost
0	700	1025
1	3299	953
2	5001	953

prune320.0ms

Filtered

156 candidates to 101 candidates (35.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	152	4	156
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	152	5	157

Merged error: 0.0b

Counts

157 → 5

localize19.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (* b b) (+ 3.0 a))
0.5b	(* (* b b) (+ 3.0 a))
8.7b	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))
8.7b	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))

rewrite193.0ms

Algorithm

rewrite-expression-head

Rules

44×	`add-sqr-sqrt`
38×	`associate-l`
30×	`*-un-lft-identity`
18×	`add-cube-cbrt`
16×	`pow1`
14×	`add-exp-log` `associate-r` `add-cbrt-cube` `unswap-sqr`
10×	`sqrt-prod`
8×	`swap-sqr`
6×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `distribute-lft-out`
4×	`+-commutative` `distribute-rgt-in` `distribute-lft-in` `flip3-+` `sqrt-div` `associate-*r/` `flip-+` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 122

Calls

4 calls:

12.0ms	(* (* b b) (+ 3.0 a))
14.0ms	(* (* b b) (+ 3.0 a))
81.0ms	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))
82.0ms	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))

series439.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(* (* b b) (+ 3.0 a))
40.0ms	(* (* b b) (+ 3.0 a))
182.0ms	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))
183.0ms	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))

simplify66.0ms

Algorithm

egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	399	1146
1	1726	1072
2	5001	1066

prune382.0ms

Filtered

134 candidates to 84 candidates (37.3%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	132	2	134
Fresh	1	2	3
Picked	0	1	1
Done	0	1	1
Total	133	6	139

Merged error: 0.0b

Counts

139 → 6

localize28.0ms

Local error

Found 4 expressions with local error:

8.7b	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))
8.7b	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))
8.7b	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))
8.7b	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))

rewrite333.0ms

Algorithm

rewrite-expression-head

Rules

24×	`*-un-lft-identity`
20×	`sqrt-prod`
12×	`add-sqr-sqrt`
8×	`pow1` `add-cube-cbrt` `sqrt-div` `distribute-lft-out`
4×	`add-exp-log` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `associate-l` `add-cbrt-cube` `flip-+` `add-log-exp`

Counts

4 → 68

Calls

4 calls:

82.0ms	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))
83.0ms	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))
83.0ms	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))
83.0ms	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))

series732.0ms

Counts

4 → 12

Calls

4 calls:

187.0ms	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))
181.0ms	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))
181.0ms	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))
182.0ms	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))

simplify122.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 3 (106.0ms)

Iter	Nodes	Cost
0	175	1488
1	638	1424
2	3220	1420
3	5002	1408

prune293.0ms

Filtered

80 candidates to 56 candidates (30.0%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	80	0	80
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	80	6	86

Merged error: 0.0b

Counts

86 → 6

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))
0.0b	(* 2 (* (pow a 2) (pow b 2)))
1.6b	(* (pow a 2) (pow b 2))

rewrite74.0ms

Algorithm

rewrite-expression-head

Rules

81×	`add-sqr-sqrt`
65×	`unswap-sqr`
53×	`associate-r`
38×	`add-exp-log`
36×	`unpow-prod-down`
28×	`prod-exp` `unpow2` `sqr-pow`
21×	`*-un-lft-identity`
20×	`associate-l`
15×	`add-cube-cbrt`
12×	`pow1` `pow-to-exp` `pow-exp`
11×	`pow-prod-down`
10×	`add-cbrt-cube`
8×	`pow-unpow`
5×	`add-log-exp`
4×	`cbrt-unprod`
3×	`*-commutative`
2×	`pow-pow` `distribute-lft-out`
1×	`+-commutative` `flip3-+` `sum-log` `flip-+`

Counts

3 → 150

Calls

3 calls:

32.0ms	(+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))
25.0ms	(* 2 (* (pow a 2) (pow b 2)))
10.0ms	(* (pow a 2) (pow b 2))

series133.0ms

Counts

3 → 9

Calls

3 calls:

58.0ms	(+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))
37.0ms	(* 2 (* (pow a 2) (pow b 2)))
38.0ms	(* (pow a 2) (pow b 2))

simplify76.0ms

Algorithm

egg-herbie

Counts

159 → 159

Iterations

Useful iterations: 2 (63.0ms)

Iter	Nodes	Cost
0	484	862
1	2086	695
2	5001	688

prune276.0ms

Filtered

159 candidates to 86 candidates (45.9%)

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	159	0	159
Fresh	0	2	2
Picked	0	1	1
Done	0	3	3
Total	159	6	165

Merged error: 0.0b

Counts

165 → 6

regimes166.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	14
1	25	14

end0.0ms

sample1.4s

Algorithm

intervals

Results

1.1s

20764×

body

valid