Details

analyze217.0ms

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
15.6%	84.3%	0.1%	6
37.5%	62.4%	0.1%	7
46.8%	53.1%	0.1%	8
57.8%	39.8%	2.4%	9
64.6%	30.4%	5%	10
71.8%	20.3%	7.9%	11
74.1%	16.2%	9.7%	12
77.4%	10.7%	12%	13
78.6%	8.4%	13%	14

sample25.0ms

Algorithm

intervals

Results

17.0ms	256×	body	80	valid
1.0ms	15×	body	80	invalid

simplify14.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (12.0ms)

Iter	Nodes	Cost
0	5167	21

prune8.0ms

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: 13.4b

Counts

2 → 2

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
0.7b	(/ 1.0 (- (* b b) (* a a)))
4.2b	(- (* b b) (* a a))
8.3b	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

55×	`add-sqr-sqrt`
47×	`times-frac`
39×	`*-un-lft-identity`
36×	`add-exp-log` `add-cbrt-cube`
31×	`add-cube-cbrt`
30×	`associate-r`
14×	`frac-times` `associate-l`
13×	`prod-exp` `cbrt-unprod`
12×	`difference-of-squares`
11×	`pow1`
9×	`cbrt-undiv` `div-exp`
8×	`associate-r/` `associate-l/`
7×	`flip3--` `flip--`
6×	`add-log-exp`
5×	`div-inv` `distribute-lft-out--`
4×	`pow-prod-down` `associate-/r*` `associate-/r/` `frac-sub` `unswap-sqr`
3×	`sub-neg` `associate-/l*`
2×	`*-commutative`
1×	`distribute-rgt-in` `frac-2neg` `distribute-lft-in` `diff-log` `clear-num`

Counts

4 → 150

Calls

4 calls:

16.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
5.0ms	(/ 1.0 (- (* b b) (* a a)))
4.0ms	(- (* b b) (* a a))
23.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

series33.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
7.0ms	(/ 1.0 (- (* b b) (* a a)))
6.0ms	(- (* b b) (* a a))
13.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

simplify50.0ms

Algorithm

egg-herbie

Counts

162 → 162

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5018	2608

prune250.0ms

Filtered

119 candidates to 162 candidates (-36.1%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	152	10	162
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	154	10	164

Merged error: 8.2b

Counts

164 → 10

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (- b a))
0.1b	(* (/ PI (* (+ b a) 2.0)) (/ 1.0 (- b a)))
0.3b	(/ PI (* (+ b a) 2.0))
8.3b	(* (* (/ PI (* (+ b a) 2.0)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

61×	`add-exp-log` `add-sqr-sqrt` `add-cbrt-cube`
52×	`*-un-lft-identity`
47×	`times-frac`
33×	`associate-r`
30×	`add-cube-cbrt`
24×	`prod-exp` `cbrt-unprod`
17×	`cbrt-undiv` `div-exp`
14×	`frac-times`
12×	`associate-*l/` `distribute-lft-out--`
11×	`pow1` `difference-of-squares`
10×	`associate-l`
8×	`associate-*r/` `associate-/r/`
6×	`flip3--` `associate-/r` `flip--` `div-inv` `associate-/l`
4×	`pow-prod-down` `frac-sub` `add-log-exp`
2×	`sub-neg` `frac-2neg` `flip3-+` `clear-num` `*-commutative` `flip-+` `unswap-sqr`
1×	`distribute-rgt-in` `distribute-lft-in`

Counts

4 → 170

Calls

4 calls:

5.0ms	(/ 1.0 (- b a))
16.0ms	(* (/ PI (* (+ b a) 2.0)) (/ 1.0 (- b a)))
6.0ms	(/ PI (* (+ b a) 2.0))
28.0ms	(* (* (/ PI (* (+ b a) 2.0)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

series37.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(/ 1.0 (- b a))
12.0ms	(* (/ PI (* (+ b a) 2.0)) (/ 1.0 (- b a)))
7.0ms	(/ PI (* (+ b a) 2.0))
13.0ms	(* (* (/ PI (* (+ b a) 2.0)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

simplify41.0ms

Algorithm

egg-herbie

Counts

182 → 182

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	5608	2626

prune239.0ms

Filtered

122 candidates to 182 candidates (-49.2%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	173	9	182
Fresh	7	2	9
Picked	1	0	1
Done	0	0	0
Total	181	11	192

Merged error: 0.0b

Counts

192 → 11

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ 1.0 a) (/ 1.0 b))
0.1b	(/ (* (/ PI (* (+ b a) 2.0)) (* 1.0 (- (/ 1.0 a) (/ 1.0 b)))) (- b a))
0.3b	(/ PI (* (+ b a) 2.0))
0.3b	(* (/ PI (* (+ b a) 2.0)) (* 1.0 (- (/ 1.0 a) (/ 1.0 b))))

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

59×	`add-exp-log` `add-cbrt-cube`
28×	`add-sqr-sqrt`
24×	`*-un-lft-identity`
23×	`prod-exp` `cbrt-unprod`
21×	`times-frac`
18×	`associate-*r/`
17×	`cbrt-undiv` `div-exp`
12×	`add-cube-cbrt`
9×	`pow1` `associate-l`
7×	`associate-/l/` `distribute-lft-out--`
6×	`frac-times` `flip3--` `associate-l/` `associate-/r` `associate-/r/` `flip--` `add-log-exp` `difference-of-squares`
5×	`sub-neg` `frac-sub` `div-inv`
4×	`distribute-rgt-in` `distribute-lft-in` `associate-/l*`
3×	`pow-prod-down`
2×	`frac-2neg` `flip3-+` `clear-num` `flip-+`
1×	`diff-log` `associate-r` `*-commutative`

Counts

4 → 131

Calls

4 calls:

12.0ms	(- (/ 1.0 a) (/ 1.0 b))
25.0ms	(/ (* (/ PI (* (+ b a) 2.0)) (* 1.0 (- (/ 1.0 a) (/ 1.0 b)))) (- b a))
6.0ms	(/ PI (* (+ b a) 2.0))
21.0ms	(* (/ PI (* (+ b a) 2.0)) (* 1.0 (- (/ 1.0 a) (/ 1.0 b))))

series39.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(- (/ 1.0 a) (/ 1.0 b))
13.0ms	(/ (* (/ PI (* (+ b a) 2.0)) (* 1.0 (- (/ 1.0 a) (/ 1.0 b)))) (- b a))
7.0ms	(/ PI (* (+ b a) 2.0))
15.0ms	(* (/ PI (* (+ b a) 2.0)) (* 1.0 (- (/ 1.0 a) (/ 1.0 b))))

simplify37.0ms

Algorithm

egg-herbie

Counts

143 → 143

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	5023	2273

prune184.0ms

Filtered

93 candidates to 143 candidates (-53.8%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	139	4	143
Fresh	4	6	10
Picked	1	0	1
Done	0	0	0
Total	144	10	154

Merged error: 0b

Counts

154 → 10

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ 1.0 a) (/ 1.0 b))
0.2b	(/ (- (/ 1.0 a) (/ 1.0 b)) (- b a))
0.2b	(* (/ PI (* (+ b a) 2.0)) (* (/ (- (/ 1.0 a) (/ 1.0 b)) (- b a)) 1.0))
0.3b	(/ PI (* (+ b a) 2.0))

rewrite77.0ms

Algorithm

rewrite-expression-head

Rules

151×	`add-sqr-sqrt`
136×	`times-frac`
123×	`*-un-lft-identity`
48×	`distribute-lft-out--`
47×	`add-exp-log` `add-cbrt-cube`
41×	`add-cube-cbrt` `difference-of-squares`
19×	`prod-exp` `cbrt-unprod`
17×	`div-inv`
15×	`associate-/l*`
12×	`cbrt-undiv` `div-exp`
9×	`pow1` `associate-l`
7×	`associate-*l/`
6×	`associate-/r*` `associate-/r/` `add-log-exp`
3×	`flip3--` `pow-prod-down` `flip--` `associate-/l/`
2×	`frac-2neg` `flip3-+` `clear-num` `frac-sub` `flip-+`
1×	`frac-times` `sub-neg` `diff-log` `div-sub` `associate-r/` `associate-r` `-commutative`

Counts

4 → 180

Calls

4 calls:

12.0ms	(- (/ 1.0 a) (/ 1.0 b))
20.0ms	(/ (- (/ 1.0 a) (/ 1.0 b)) (- b a))
28.0ms	(* (/ PI (* (+ b a) 2.0)) (* (/ (- (/ 1.0 a) (/ 1.0 b)) (- b a)) 1.0))
6.0ms	(/ PI (* (+ b a) 2.0))

series32.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(- (/ 1.0 a) (/ 1.0 b))
7.0ms	(/ (- (/ 1.0 a) (/ 1.0 b)) (- b a))
13.0ms	(* (/ PI (* (+ b a) 2.0)) (* (/ (- (/ 1.0 a) (/ 1.0 b)) (- b a)) 1.0))
7.0ms	(/ PI (* (+ b a) 2.0))

simplify70.0ms

Algorithm

egg-herbie

Counts

192 → 192

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4983	3246
1	4983	3246

prune234.0ms

Filtered

130 candidates to 192 candidates (-47.7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	190	2	192
Fresh	3	6	9
Picked	1	0	1
Done	0	0	0
Total	194	8	202

Merged error: 0b

Counts

202 → 8

regimes107.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	15
1	17	15

end0.0ms

sample645.0ms

Algorithm

intervals

Results

473.0ms	8000×	body	80	valid
21.0ms	362×	body	80	invalid

Details

analyze217.0ms

sample25.0ms

simplify14.0ms

prune8.0ms

localize12.0ms

rewrite53.0ms

series33.0ms

simplify50.0ms

prune250.0ms

localize12.0ms

rewrite61.0ms

series37.0ms

simplify41.0ms

prune239.0ms

localize14.0ms

rewrite69.0ms

series39.0ms

simplify37.0ms

prune184.0ms

localize12.0ms

rewrite77.0ms

series32.0ms

simplify70.0ms

prune234.0ms

regimes107.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample645.0ms

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