Details

analyze216.0ms

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

sample23.0ms

Algorithm

intervals

Results

14.0ms	256×	body	80	valid
0.0ms	8×	body	80	invalid

simplify14.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (13.0ms)

Iter	Nodes	Cost
0	5167	21

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: 13.7b

Counts

2 → 2

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
0.6b	(/ 1.0 (- (* b b) (* a a)))
4.8b	(- (* b b) (* a a))
7.8b	(* (* (/ 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:

13.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
5.0ms	(/ 1.0 (- (* b b) (* a a)))
6.0ms	(- (* b b) (* a a))
22.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

series34.0ms

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 (36.0ms)

Iter	Nodes	Cost
0	5018	2608

prune243.0ms

Filtered

119 candidates to 162 candidates (-36.1%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	153	9	162
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	155	9	164

Merged error: 7.7b

Counts

164 → 9

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)))
0.2b	(/ PI (* (+ b a) 2.0))
7.8b	(* (* (/ 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)))

series38.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(/ 1.0 (- b a))
9.0ms	(* (/ PI (* (+ b a) 2.0)) (/ 1.0 (- b a)))
7.0ms	(/ PI (* (+ b a) 2.0))
17.0ms	(* (* (/ PI (* (+ b a) 2.0)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

simplify43.0ms

Algorithm

egg-herbie

Counts

182 → 182

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	5608	2626

prune236.0ms

Filtered

122 candidates to 182 candidates (-49.2%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	174	8	182
Fresh	6	2	8
Picked	1	0	1
Done	0	0	0
Total	181	10	191

Merged error: 0.0b

Counts

191 → 10

localize12.0ms

Local error

Found 4 expressions with local error:

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

rewrite83.0ms

Algorithm

rewrite-expression-head

Rules

58×	`add-sqr-sqrt`
52×	`add-exp-log` `add-cbrt-cube`
49×	`*-un-lft-identity`
42×	`times-frac`
27×	`add-cube-cbrt`
24×	`associate-l`
23×	`associate-*r/`
21×	`prod-exp` `cbrt-unprod`
13×	`cbrt-undiv` `div-exp` `associate-r`
12×	`distribute-lft-out--`
11×	`pow1` `difference-of-squares`
9×	`frac-times`
8×	`flip3--` `flip--`
7×	`associate-/l/`
6×	`sub-neg` `associate-/r*` `associate-/r/` `frac-sub`
5×	`distribute-rgt-in` `distribute-lft-in` `associate-*l/` `div-inv`
4×	`pow-prod-down` `associate-/l*` `add-log-exp`
2×	`frac-2neg` `clear-num` `*-commutative` `unswap-sqr`
1×	`flip3-+` `flip-+`

Counts

4 → 163

Calls

4 calls:

5.0ms	(/ 1.0 (- b a))
25.0ms	(/ (* PI (* (/ 1.0 (- b a)) (- (/ 1.0 a) (/ 1.0 b)))) (* (+ b a) 2.0))
20.0ms	(* PI (* (/ 1.0 (- b a)) (- (/ 1.0 a) (/ 1.0 b))))
25.0ms	(* (/ 1.0 (- b a)) (- (/ 1.0 a) (/ 1.0 b)))

series38.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(/ 1.0 (- b a))
13.0ms	(/ (* PI (* (/ 1.0 (- b a)) (- (/ 1.0 a) (/ 1.0 b)))) (* (+ b a) 2.0))
9.0ms	(* PI (* (/ 1.0 (- b a)) (- (/ 1.0 a) (/ 1.0 b))))
10.0ms	(* (/ 1.0 (- b a)) (- (/ 1.0 a) (/ 1.0 b)))

simplify41.0ms

Algorithm

egg-herbie

Counts

175 → 175

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	5363	2566

prune230.0ms

Filtered

119 candidates to 175 candidates (-47.1%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	172	3	175
Fresh	4	5	9
Picked	0	1	1
Done	0	0	0
Total	176	9	185

Merged error: 0.0b

Counts

185 → 9

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite94.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 169

Calls

4 calls:

14.0ms	(- (/ 1.0 a) (/ 1.0 b))
28.0ms	(/ (* PI (* 1.0 (/ (- (/ 1.0 a) (/ 1.0 b)) (- b a)))) (* (+ b a) 2.0))
19.0ms	(/ (- (/ 1.0 a) (/ 1.0 b)) (- b a))
22.0ms	(* PI (* 1.0 (/ (- (/ 1.0 a) (/ 1.0 b)) (- b a))))

series34.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(- (/ 1.0 a) (/ 1.0 b))
13.0ms	(/ (* PI (* 1.0 (/ (- (/ 1.0 a) (/ 1.0 b)) (- b a)))) (* (+ b a) 2.0))
7.0ms	(/ (- (/ 1.0 a) (/ 1.0 b)) (- b a))
9.0ms	(* PI (* 1.0 (/ (- (/ 1.0 a) (/ 1.0 b)) (- b a))))

simplify57.0ms

Algorithm

egg-herbie

Counts

181 → 181

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	4991	3214
1	4991	3214

prune215.0ms

Filtered

118 candidates to 181 candidates (-53.4%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	181	0	181
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	181	9	190

Merged error: 0.0b

Counts

190 → 9

regimes109.0ms

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 (1.0ms)

Iter	Nodes	Cost
0	44	21
1	44	21

end0.0ms

sample625.0ms

Algorithm

intervals

Results

459.0ms	8000×	body	80	valid
20.0ms	351×	body	80	invalid

Details

analyze216.0ms

sample23.0ms

simplify14.0ms

prune9.0ms

localize13.0ms

rewrite53.0ms

series34.0ms

simplify50.0ms

prune243.0ms

localize12.0ms

rewrite61.0ms

series38.0ms

simplify43.0ms

prune236.0ms

localize12.0ms

rewrite83.0ms

series38.0ms

simplify41.0ms

prune230.0ms

localize15.0ms

rewrite94.0ms

series34.0ms

simplify57.0ms

prune215.0ms

regimes109.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample625.0ms

Profiling