Details

analyze234.0ms

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

15.0ms	256×	body	80	valid
0.0ms	8×	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: 15.1b

Counts

2 → 2

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
0.8b	(/ 1.0 (- (* b b) (* a a)))
4.0b	(- (* b b) (* a a))
10.1b	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite55.0ms

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))))
6.0ms	(/ 1.0 (- (* b b) (* a a)))
4.0ms	(- (* b b) (* a a))
26.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

series32.0ms

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

prune241.0ms

Filtered

119 candidates to 162 candidates (-36.1%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	154	8	162
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	155	9	164

Merged error: 10.0b

Counts

164 → 9

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (+ b a))
0.1b	(* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a)))
0.2b	(/ (/ 1.0 (+ b a)) (- b a))
10.1b	(* (* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite115.0ms

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))
44.0ms	(* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a)))
11.0ms	(/ (/ 1.0 (+ b a)) (- b a))
34.0ms	(* (* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

series33.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(/ 1.0 (+ b a))
9.0ms	(* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a)))
7.0ms	(/ (/ 1.0 (+ b a)) (- b a))
12.0ms	(* (* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

simplify71.0ms

Algorithm

egg-herbie

Counts

368 → 368

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5012	5968

prune470.0ms

Filtered

236 candidates to 368 candidates (-55.9%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	363	5	368
Fresh	3	5	8
Picked	1	0	1
Done	0	0	0
Total	367	10	377

Merged error: 0.1b

Counts

377 → 10

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)))
0.2b	(* 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))
28.0ms	(/ (* PI (* (/ 1.0 (+ b a)) (- (/ 1.0 a) (/ 1.0 b)))) (* 2.0 (- b a)))
21.0ms	(* PI (* (/ 1.0 (+ b a)) (- (/ 1.0 a) (/ 1.0 b))))
23.0ms	(* (/ 1.0 (+ b a)) (- (/ 1.0 a) (/ 1.0 b)))

series39.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(/ 1.0 (+ b a))
12.0ms	(/ (* PI (* (/ 1.0 (+ b a)) (- (/ 1.0 a) (/ 1.0 b)))) (* 2.0 (- b a)))
12.0ms	(* PI (* (/ 1.0 (+ b a)) (- (/ 1.0 a) (/ 1.0 b))))
10.0ms	(* (/ 1.0 (+ b a)) (- (/ 1.0 a) (/ 1.0 b)))

simplify44.0ms

Algorithm

egg-herbie

Counts

168 → 168

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	5377	2461

prune228.0ms

Filtered

113 candidates to 168 candidates (-48.7%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	162	6	168
Fresh	6	3	9
Picked	1	0	1
Done	0	0	0
Total	169	9	178

Merged error: 0.0b

Counts

178 → 9

localize13.0ms

Local error

Found 4 expressions with local error:

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

rewrite81.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 131

Calls

4 calls:

13.0ms	(- (/ 1.0 a) (/ 1.0 b))
24.0ms	(/ (/ (* 1.0 (* (- (/ 1.0 a) (/ 1.0 b)) PI)) (+ b a)) (* 2.0 (- b a)))
21.0ms	(/ (* 1.0 (* (- (/ 1.0 a) (/ 1.0 b)) PI)) (+ b a))
18.0ms	(* (- (/ 1.0 a) (/ 1.0 b)) PI)

series37.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(- (/ 1.0 a) (/ 1.0 b))
12.0ms	(/ (/ (* 1.0 (* (- (/ 1.0 a) (/ 1.0 b)) PI)) (+ b a)) (* 2.0 (- b a)))
15.0ms	(/ (* 1.0 (* (- (/ 1.0 a) (/ 1.0 b)) PI)) (+ b a))
6.0ms	(* (- (/ 1.0 a) (/ 1.0 b)) PI)

simplify36.0ms

Algorithm

egg-herbie

Counts

143 → 143

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	5332	2266

prune161.0ms

Filtered

98 candidates to 143 candidates (-45.9%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	140	3	143
Fresh	2	6	8
Picked	0	1	1
Done	0	0	0
Total	142	10	152

Merged error: 0b

Counts

152 → 10

regimes113.0ms

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	43	21
1	43	21

end0.0ms

sample634.0ms

Algorithm

intervals

Results

476.0ms	8000×	body	80	valid
20.0ms	345×	body	80	invalid

Details

analyze234.0ms

sample23.0ms

simplify14.0ms

prune8.0ms

localize12.0ms

rewrite55.0ms

series32.0ms

simplify56.0ms

prune241.0ms

localize12.0ms

rewrite115.0ms

series33.0ms

simplify71.0ms

prune470.0ms

localize12.0ms

rewrite84.0ms

series39.0ms

simplify44.0ms

prune228.0ms

localize13.0ms

rewrite81.0ms

series37.0ms

simplify36.0ms

prune161.0ms

regimes113.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample634.0ms

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