Details

analyze225.0ms

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
1.0ms	17×	body	80	invalid

simplify14.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (13.0ms)

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: 14.7b

Counts

2 → 2

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
0.6b	(/ 1.0 (- (* b b) (* a a)))
5.9b	(- (* b b) (* a a))
7.7b	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite79.0ms

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:

23.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
9.0ms	(/ 1.0 (- (* b b) (* a a)))
6.0ms	(- (* b b) (* a a))
35.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

series31.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
6.0ms	(/ 1.0 (- (* b b) (* a a)))
5.0ms	(- (* b b) (* a a))
12.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

simplify56.0ms

Algorithm

egg-herbie

Counts

162 → 162

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5018	2608

prune233.0ms

Filtered

119 candidates to 162 candidates (-36.1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	154	8	162
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	156	8	164

Merged error: 7.6b

Counts

164 → 8

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ 1.0 a) (/ 1.0 b))
0.2b	(* (/ PI (* (+ b a) 2.0)) (/ 1.0 (- b a)))
0.9b	(/ PI (* (+ b a) 2.0))
7.7b	(* (* (/ PI (* (+ b a) 2.0)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

59×	`add-exp-log` `add-cbrt-cube`
57×	`add-sqr-sqrt`
44×	`*-un-lft-identity`
42×	`times-frac`
33×	`associate-r`
24×	`prod-exp` `cbrt-unprod`
22×	`add-cube-cbrt`
16×	`cbrt-undiv` `div-exp`
14×	`frac-times`
13×	`distribute-lft-out--`
12×	`associate-*l/`
11×	`pow1` `difference-of-squares`
10×	`associate-l`
8×	`associate-*r/`
7×	`div-inv`
6×	`flip3--` `associate-/r/` `flip--` `add-log-exp`
5×	`frac-sub`
4×	`pow-prod-down`
3×	`sub-neg` `associate-/l*`
2×	`flip3-+` `*-commutative` `flip-+` `unswap-sqr`
1×	`distribute-rgt-in` `frac-2neg` `distribute-lft-in` `diff-log` `clear-num` `associate-/r*`

Counts

4 → 154

Calls

4 calls:

11.0ms	(- (/ 1.0 a) (/ 1.0 b))
15.0ms	(* (/ PI (* (+ b a) 2.0)) (/ 1.0 (- b a)))
6.0ms	(/ PI (* (+ b a) 2.0))
25.0ms	(* (* (/ PI (* (+ b a) 2.0)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

series35.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(- (/ 1.0 a) (/ 1.0 b))
8.0ms	(* (/ PI (* (+ b a) 2.0)) (/ 1.0 (- b a)))
6.0ms	(/ PI (* (+ b a) 2.0))
16.0ms	(* (* (/ PI (* (+ b a) 2.0)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

simplify41.0ms

Algorithm

egg-herbie

Counts

166 → 166

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	5614	2562

prune223.0ms

Filtered

112 candidates to 166 candidates (-48.2%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	157	9	166
Fresh	5	2	7
Picked	1	0	1
Done	0	0	0
Total	163	11	174

Merged error: 0.0b

Counts

174 → 11

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (- b a))
0.1b	(* (/ 1.0 (- b a)) (* 1.0 (- b a)))
0.2b	(/ (* (/ PI (* (+ b a) 2.0)) (* (/ 1.0 (- b a)) (* 1.0 (- b a)))) (* a b))
0.9b	(/ PI (* (+ b a) 2.0))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

211×	`add-exp-log` `add-cbrt-cube`
99×	`prod-exp` `cbrt-unprod`
69×	`cbrt-undiv` `div-exp`
39×	`add-sqr-sqrt` `*-un-lft-identity`
34×	`times-frac`
25×	`add-cube-cbrt`
23×	`associate-*r/`
21×	`associate-l`
11×	`frac-times` `associate-/l/`
9×	`pow1`
8×	`flip3--` `flip--`
7×	`associate-/r` `associate-/l` `distribute-lft-out--` `difference-of-squares`
6×	`associate-*l/` `associate-/r/`
4×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `div-inv` `add-log-exp`
3×	`frac-2neg` `pow-prod-down` `clear-num`
1×	`flip3-+` `associate-r` `*-commutative` `flip-+`

Counts

4 → 197

Calls

4 calls:

5.0ms	(/ 1.0 (- b a))
12.0ms	(* (/ 1.0 (- b a)) (* 1.0 (- b a)))
23.0ms	(/ (* (/ PI (* (+ b a) 2.0)) (* (/ 1.0 (- b a)) (* 1.0 (- b a)))) (* a b))
6.0ms	(/ PI (* (+ b a) 2.0))

series24.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(/ 1.0 (- b a))
1.0ms	(* (/ 1.0 (- b a)) (* 1.0 (- b a)))
11.0ms	(/ (* (/ PI (* (+ b a) 2.0)) (* (/ 1.0 (- b a)) (* 1.0 (- b a)))) (* a b))
7.0ms	(/ PI (* (+ b a) 2.0))

simplify79.0ms

Algorithm

egg-herbie

Counts

209 → 209

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	5021	2403

prune199.0ms

Filtered

107 candidates to 209 candidates (-95.3%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	206	3	209
Fresh	4	6	10
Picked	1	0	1
Done	0	0	0
Total	211	9	220

Merged error: 0b

Counts

220 → 9

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ 1.0 (- b a)) (* 1.0 (- b a)))
0.2b	(/ (* (/ 1 (/ (+ b a) (/ PI 2.0))) (* (/ 1.0 (- b a)) (* 1.0 (- b a)))) (* a b))
0.2b	(/ 1 (/ (+ b a) (/ PI 2.0)))
0.3b	(/ (+ b a) (/ PI 2.0))

rewrite155.0ms

Algorithm

rewrite-expression-head

Rules

677×	`add-exp-log`
636×	`times-frac`
426×	`*-un-lft-identity`
312×	`div-exp`
299×	`add-cbrt-cube`
294×	`add-sqr-sqrt`
288×	`add-cube-cbrt`
277×	`prod-exp`
129×	`cbrt-undiv`
115×	`cbrt-unprod`
71×	`associate-/r*`
66×	`distribute-lft-out`
33×	`rec-exp` `1-exp`
29×	`div-inv`
23×	`associate-*r/`
21×	`associate-l`
13×	`associate-/l/`
11×	`frac-times`
10×	`pow1`
8×	`associate-/r/` `associate-/l*`
7×	`flip3--` `flip--`
4×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `associate-*l/` `add-log-exp`
3×	`frac-2neg` `pow-prod-down` `clear-num` `distribute-lft-out--` `difference-of-squares`
1×	`pow-flip` `flip3-+` `associate-r` `*-commutative` `flip-+` `inv-pow`

Counts

4 → 559

Calls

4 calls:

12.0ms	(* (/ 1.0 (- b a)) (* 1.0 (- b a)))
59.0ms	(/ (* (/ 1 (/ (+ b a) (/ PI 2.0))) (* (/ 1.0 (- b a)) (* 1.0 (- b a)))) (* a b))
27.0ms	(/ 1 (/ (+ b a) (/ PI 2.0)))
8.0ms	(/ (+ b a) (/ PI 2.0))

series24.0ms

Counts

4 → 12

Calls

4 calls:

1.0ms	(* (/ 1.0 (- b a)) (* 1.0 (- b a)))
9.0ms	(/ (* (/ 1 (/ (+ b a) (/ PI 2.0))) (* (/ 1.0 (- b a)) (* 1.0 (- b a)))) (* a b))
7.0ms	(/ 1 (/ (+ b a) (/ PI 2.0)))
7.0ms	(/ (+ b a) (/ PI 2.0))

simplify138.0ms

Algorithm

egg-herbie

Counts

571 → 571

Iterations

Useful iterations: 0 (77.0ms)

Iter	Nodes	Cost
0	4956	8478
1	4956	8478

prune486.0ms

Filtered

252 candidates to 571 candidates (-126.6%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	571	0	571
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	571	9	580

Merged error: 0b

Counts

580 → 9

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 (1.0ms)

Iter	Nodes	Cost
0	32	25
1	32	25

end0.0ms

sample629.0ms

Algorithm

intervals

Results

465.0ms	8000×	body	80	valid
21.0ms	340×	body	80	invalid

Details

analyze225.0ms

sample23.0ms

simplify14.0ms

prune8.0ms

localize12.0ms

rewrite79.0ms

series31.0ms

simplify56.0ms

prune233.0ms

localize15.0ms

rewrite63.0ms

series35.0ms

simplify41.0ms

prune223.0ms

localize14.0ms

rewrite57.0ms

series24.0ms

simplify79.0ms

prune199.0ms

localize15.0ms

rewrite155.0ms

series24.0ms

simplify138.0ms

prune486.0ms

regimes107.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample629.0ms

Profiling