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

sample25.0ms

Algorithm

intervals

Results

15.0ms	256×	body	80	valid
1.0ms	16×	body	80	invalid

simplify30.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	5986	21

prune10.0ms

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: 15.4b

Counts

2 → 2

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
0.5b	(/ 1.0 (- (* b b) (* a a)))
3.9b	(- (* b b) (* a a))
10.8b	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite52.0ms

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:

14.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
5.0ms	(/ 1.0 (- (* b b) (* a a)))
4.0ms	(- (* b b) (* a a))
24.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

series36.0ms

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)))
9.0ms	(- (* b b) (* a a))
12.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

simplify45.0ms

Algorithm

egg-herbie

Counts

162 → 162

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	5671	2608

prune272.0ms

Filtered

122 candidates to 162 candidates (-32.8%)

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: 10.6b

Counts

164 → 8

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (+ b a))
0.1b	(/ (/ 1.0 (+ b a)) (- b a))
0.2b	(* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a)))
10.8b	(* (* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite111.0ms

Algorithm

rewrite-expression-head

Rules

352×	`times-frac`
305×	`*-un-lft-identity`
256×	`add-sqr-sqrt`
149×	`add-cube-cbrt`
108×	`associate-r`
61×	`add-exp-log` `add-cbrt-cube`
42×	`distribute-lft-out--`
41×	`difference-of-squares`
37×	`distribute-lft-out`
28×	`associate-/r/`
22×	`cbrt-undiv` `div-exp`
21×	`associate-/l*`
19×	`prod-exp` `cbrt-unprod`
17×	`div-inv`
14×	`frac-times` `associate-l`
12×	`flip3-+` `flip-+`
11×	`pow1`
9×	`associate-/r*`
8×	`associate-r/` `associate-l/`
6×	`flip3--` `flip--` `unswap-sqr`
4×	`pow-prod-down` `frac-sub` `add-log-exp`
2×	`sub-neg` `frac-2neg` `clear-num` `*-commutative`
1×	`distribute-rgt-in` `distribute-lft-in` `associate-/l/`

Counts

4 → 356

Calls

4 calls:

5.0ms	(/ 1.0 (+ b a))
11.0ms	(/ (/ 1.0 (+ b a)) (- b a))
42.0ms	(* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a)))
32.0ms	(* (* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

series37.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(/ 1.0 (+ b a))
7.0ms	(/ (/ 1.0 (+ b a)) (- b a))
9.0ms	(* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a)))
12.0ms	(* (* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

simplify55.0ms

Algorithm

egg-herbie

Counts

368 → 368

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	5643	6006

prune567.0ms

Filtered

239 candidates to 368 candidates (-54.0%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	363	5	368
Fresh	3	4	7
Picked	1	0	1
Done	0	0	0
Total	367	9	376

Merged error: 0.0b

Counts

376 → 9

localize12.0ms

Local error

Found 4 expressions with local error:

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

rewrite84.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 156

Calls

4 calls:

5.0ms	(/ 1.0 (+ b a))
26.0ms	(/ (* PI (* (/ 1.0 (+ b a)) (- (/ 1.0 a) (/ 1.0 b)))) (* 2.0 (- b a)))
23.0ms	(* PI (* (/ 1.0 (+ b a)) (- (/ 1.0 a) (/ 1.0 b))))
24.0ms	(* (/ 1.0 (+ b a)) (- (/ 1.0 a) (/ 1.0 b)))

series44.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(/ 1.0 (+ b a))
16.0ms	(/ (* PI (* (/ 1.0 (+ b a)) (- (/ 1.0 a) (/ 1.0 b)))) (* 2.0 (- b a)))
13.0ms	(* PI (* (/ 1.0 (+ b a)) (- (/ 1.0 a) (/ 1.0 b))))
10.0ms	(* (/ 1.0 (+ b a)) (- (/ 1.0 a) (/ 1.0 b)))

simplify60.0ms

Algorithm

egg-herbie

Counts

168 → 168

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4979	2462
1	4979	2462

prune246.0ms

Filtered

116 candidates to 168 candidates (-44.8%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	163	5	168
Fresh	4	4	8
Picked	1	0	1
Done	0	0	0
Total	168	9	177

Merged error: 0.0b

Counts

177 → 9

localize12.0ms

Local error

Found 4 expressions with local error:

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

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 146

Calls

4 calls:

5.0ms	(/ 1.0 (+ b a))
27.0ms	(/ (* (* (/ 1.0 (+ b a)) PI) (- (/ 1.0 a) (/ 1.0 b))) (* 2.0 (- b a)))
8.0ms	(* (/ 1.0 (+ b a)) PI)
21.0ms	(* (* (/ 1.0 (+ b a)) PI) (- (/ 1.0 a) (/ 1.0 b)))

series37.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify66.0ms

Algorithm

egg-herbie

Counts

158 → 158

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	5020	2056

prune193.0ms

Filtered

107 candidates to 158 candidates (-47.7%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	157	1	158
Fresh	1	7	8
Picked	0	1	1
Done	0	0	0
Total	158	9	167

Merged error: 0b

Counts

167 → 9

regimes120.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	90	21
1	90	21

end0.0ms

sample649.0ms

Algorithm

intervals

Results

471.0ms	8000×	body	80	valid
23.0ms	403×	body	80	invalid

Details

analyze216.0ms

sample25.0ms

simplify30.0ms

prune10.0ms

localize15.0ms

rewrite52.0ms

series36.0ms

simplify45.0ms

prune272.0ms

localize12.0ms

rewrite111.0ms

series37.0ms

simplify55.0ms

prune567.0ms

localize12.0ms

rewrite84.0ms

series44.0ms

simplify60.0ms

prune246.0ms

localize12.0ms

rewrite67.0ms

series37.0ms

simplify66.0ms

prune193.0ms

regimes120.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample649.0ms

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