Details

analyze218.0ms

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

sample22.0ms

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 (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: 16.0b

Counts

2 → 2

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
0.7b	(/ 1.0 (- (* b b) (* a a)))
4.5b	(- (* b b) (* a a))
10.4b	(* (* (/ 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:

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))
25.0ms	(* (* (/ 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)))

simplify54.0ms

Algorithm

egg-herbie

Counts

162 → 162

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5018	2608

prune238.0ms

Filtered

119 candidates to 162 candidates (-36.1%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	155	7	162
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	157	7	164

Merged error: 10.2b

Counts

164 → 7

localize13.0ms

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 (- b a)))
0.5b	(/ PI (* (+ b a) 2.0))
10.4b	(* (* (/ PI (* (+ b a) 2.0)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite71.0ms

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:

12.0ms	(- (/ 1.0 a) (/ 1.0 b))
16.0ms	(* (/ PI (* (+ b a) 2.0)) (/ 1.0 (- b a)))
6.0ms	(/ PI (* (+ b a) 2.0))
30.0ms	(* (* (/ 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))
11.0ms	(* (/ PI (* (+ b a) 2.0)) (/ 1.0 (- b a)))
7.0ms	(/ PI (* (+ b a) 2.0))
12.0ms	(* (* (/ PI (* (+ b a) 2.0)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

simplify42.0ms

Algorithm

egg-herbie

Counts

166 → 166

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	5614	2562

prune218.0ms

Filtered

112 candidates to 166 candidates (-48.2%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	159	7	166
Fresh	3	3	6
Picked	1	0	1
Done	0	0	0
Total	163	10	173

Merged error: 0.0b

Counts

173 → 10

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (- b a))
0.2b	(* (/ 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))
0.5b	(/ PI (* (+ b a) 2.0))

rewrite62.0ms

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:

6.0ms	(/ 1.0 (- b a))
15.0ms	(* (/ 1.0 (- b a)) (* 1.0 (- b a)))
24.0ms	(/ (* (/ PI (* (+ b a) 2.0)) (* (/ 1.0 (- b a)) (* 1.0 (- b a)))) (* a b))
6.0ms	(/ PI (* (+ b a) 2.0))

series22.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify80.0ms

Algorithm

egg-herbie

Counts

209 → 209

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	5021	2403

prune183.0ms

Filtered

107 candidates to 209 candidates (-95.3%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	204	5	209
Fresh	6	3	9
Picked	1	0	1
Done	0	0	0
Total	211	8	219

Merged error: 0.0b

Counts

219 → 8

localize9.0ms

Local error

Found 3 expressions with local error:

0.2b	(/ (/ PI (* (+ b a) 2.0)) (/ b (/ (* 1.0 1.0) a)))
0.3b	(/ b (/ (* 1.0 1.0) a))
0.5b	(/ PI (* (+ b a) 2.0))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

651×	`times-frac`
215×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
74×	`div-inv`
71×	`add-exp-log` `add-cbrt-cube`
68×	`associate-/r/`
56×	`associate-*l/`
42×	`cbrt-undiv` `div-exp`
34×	`associate-/r*`
28×	`flip3-+` `flip-+`
15×	`associate-/l*`
9×	`prod-exp` `cbrt-unprod`
3×	`pow1` `frac-2neg` `clear-num` `add-log-exp`
1×	`associate-/l/`

Counts

3 → 376

Calls

3 calls:

18.0ms	(/ (/ PI (* (+ b a) 2.0)) (/ b (/ (* 1.0 1.0) a)))
6.0ms	(/ b (/ (* 1.0 1.0) a))
6.0ms	(/ PI (* (+ b a) 2.0))

series19.0ms

Counts

3 → 9

Calls

3 calls:

9.0ms	(/ (/ PI (* (+ b a) 2.0)) (/ b (/ (* 1.0 1.0) a)))
3.0ms	(/ b (/ (* 1.0 1.0) a))
7.0ms	(/ PI (* (+ b a) 2.0))

simplify72.0ms

Algorithm

egg-herbie

Counts

385 → 385

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	5308	8706

prune602.0ms

Filtered

329 candidates to 385 candidates (-17.0%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	381	4	385
Fresh	5	2	7
Picked	0	1	1
Done	0	0	0
Total	386	7	393

Merged error: 0b

Counts

393 → 7

regimes93.0ms

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

sample631.0ms

Algorithm

intervals

Results

462.0ms	8000×	body	80	valid
22.0ms	314×	body	80	invalid

Details

analyze218.0ms

sample22.0ms

simplify14.0ms

prune8.0ms

localize12.0ms

rewrite53.0ms

series32.0ms

simplify54.0ms

prune238.0ms

localize13.0ms

rewrite71.0ms

series35.0ms

simplify42.0ms

prune218.0ms

localize12.0ms

rewrite62.0ms

series22.0ms

simplify80.0ms

prune183.0ms

localize9.0ms

rewrite56.0ms

series19.0ms

simplify72.0ms

prune602.0ms

regimes93.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample631.0ms

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