Details

sample426.0ms

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 7.568359%

Guaranteed chance to sample good point: 96.005018%

Results

18.0ms	256×	body	80	valid
2.0ms	32×	body	80	invalid

simplify39.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	30	10
1	89	10
2	377	10
3	1779	10
4	5001	10

prune3.0ms

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: 13.4b

Counts

2 → 1

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
0.3b	(/ 1.0 (- (* b b) (* a a)))
4.7b	(- (* b b) (* a a))
8.0b	(* (* (/ 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×	`distribute-rgt-in` `distribute-lft-in` `*-commutative`
1×	`frac-2neg` `diff-log` `clear-num`

Counts

4 → 153

Calls

4 calls:

15.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
6.0ms	(/ 1.0 (- (* b b) (* a a)))
3.0ms	(- (* b b) (* a a))
24.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

series37.0ms

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

simplify109.0ms

Algorithm

egg-herbie

Counts

165 → 165

Iterations

Useful iterations: 1 (22.0ms)

Iter	Nodes	Cost
0	804	1567
1	4503	1342
2	5001	1342

prune244.0ms

Filtered

119 candidates to 165 candidates (-38.7%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	156	9	165
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	157	9	166

Merged error: 7.9b

Counts

166 → 9

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (- b a))
0.2b	(* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a)))
0.2b	(/ (/ PI 2.0) (+ b a))
8.0b	(* (* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite98.0ms

Algorithm

rewrite-expression-head

Rules

234×	`times-frac`
193×	`*-un-lft-identity`
164×	`add-sqr-sqrt`
117×	`add-cube-cbrt`
61×	`add-exp-log` `add-cbrt-cube`
59×	`associate-l`
33×	`associate-r`
27×	`distribute-lft-out`
22×	`cbrt-undiv` `div-exp`
19×	`prod-exp` `cbrt-unprod`
16×	`associate-/l*`
15×	`div-inv`
14×	`frac-times`
12×	`distribute-lft-out--`
11×	`pow1` `difference-of-squares`
9×	`associate-/r*`
8×	`associate-r/` `associate-l/` `associate-/r/`
6×	`flip3--` `flip--` `unswap-sqr`
4×	`pow-prod-down` `frac-sub` `add-log-exp`
2×	`distribute-rgt-in` `sub-neg` `frac-2neg` `distribute-lft-in` `flip3-+` `clear-num` `*-commutative` `flip-+`
1×	`associate-/l/`

Counts

4 → 288

Calls

4 calls:

5.0ms	(/ 1.0 (- b a))
35.0ms	(* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a)))
11.0ms	(/ (/ PI 2.0) (+ b a))
32.0ms	(* (* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

series37.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(/ 1.0 (- b a))
9.0ms	(* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a)))
7.0ms	(/ (/ PI 2.0) (+ b a))
16.0ms	(* (* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

simplify55.0ms

Algorithm

egg-herbie

Counts

300 → 300

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1260	2632
1	5001	2332

prune397.0ms

Filtered

204 candidates to 300 candidates (-47.1%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	295	5	300
Fresh	4	4	8
Picked	0	1	1
Done	0	0	0
Total	299	10	309

Merged error: 0.0b

Counts

309 → 10

localize12.0ms

Local error

Found 4 expressions with local error:

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

rewrite83.0ms

Algorithm

rewrite-expression-head

Rules

73×	`add-sqr-sqrt`
61×	`add-exp-log` `*-un-lft-identity` `add-cbrt-cube`
57×	`times-frac`
35×	`add-cube-cbrt`
33×	`associate-r`
27×	`frac-times`
22×	`prod-exp` `cbrt-unprod`
19×	`cbrt-undiv` `div-exp`
15×	`associate-r/` `associate-l/` `associate-/l/`
14×	`associate-l`
12×	`distribute-lft-out--`
11×	`pow1` `difference-of-squares`
10×	`flip3--` `flip--`
9×	`associate-/r*`
8×	`frac-sub`
6×	`associate-/r/` `div-inv`
4×	`pow-prod-down` `associate-/l*` `add-log-exp` `unswap-sqr`
2×	`distribute-rgt-in` `sub-neg` `frac-2neg` `distribute-lft-in` `clear-num` `*-commutative` `distribute-lft-out`
1×	`flip3-+` `flip-+`

Counts

4 → 195

Calls

4 calls:

5.0ms	(/ 1.0 (- b a))
28.0ms	(/ (* (* (/ PI 2.0) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b))) (+ b a))
26.0ms	(* (* (/ PI 2.0) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))
15.0ms	(* (/ PI 2.0) (/ 1.0 (- b a)))

series38.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(/ 1.0 (- b a))
16.0ms	(/ (* (* (/ PI 2.0) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b))) (+ b a))
9.0ms	(* (* (/ PI 2.0) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))
7.0ms	(* (/ PI 2.0) (/ 1.0 (- b a)))

simplify43.0ms

Algorithm

egg-herbie

Counts

207 → 207

Iterations

Useful iterations: 1 (24.0ms)

Iter	Nodes	Cost
0	965	1795
1	5001	1486

prune265.0ms

Filtered

142 candidates to 207 candidates (-45.8%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	202	5	207
Fresh	5	3	8
Picked	1	0	1
Done	0	1	1
Total	208	9	217

Merged error: 0b

Counts

217 → 9

localize7.0ms

Local error

Found 2 expressions with local error:

0.2b	(/ (* 0.5 (/ PI (* a b))) (+ b a))
0.6b	(/ PI (* a b))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-exp-log` `add-cbrt-cube`
10×	`*-un-lft-identity`
8×	`cbrt-undiv` `div-exp`
7×	`times-frac`
6×	`add-sqr-sqrt` `add-cube-cbrt`
5×	`prod-exp` `associate-/r*` `cbrt-unprod`
4×	`associate-/l*`
2×	`pow1` `frac-2neg` `clear-num` `associate-/r/` `div-inv` `distribute-lft-out` `add-log-exp`
1×	`flip3-+` `associate-*r/` `flip-+` `associate-/l/`

Counts

2 → 51

Calls

2 calls:

9.0ms	(/ (* 0.5 (/ PI (* a b))) (+ b a))
4.0ms	(/ PI (* a b))

series13.0ms

Counts

2 → 6

Calls

2 calls:

10.0ms	(/ (* 0.5 (/ PI (* a b))) (+ b a))
3.0ms	(/ PI (* a b))

simplify38.0ms

Algorithm

egg-herbie

Counts

57 → 57

Iterations

Useful iterations: 1 (8.0ms)

Iter	Nodes	Cost
0	295	316
1	1475	250
2	5002	250

prune51.0ms

Filtered

36 candidates to 57 candidates (-58.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	54	3	57
Fresh	3	4	7
Picked	1	0	1
Done	0	1	1
Total	58	8	66

Merged error: 0b

Counts

66 → 8

regimes98.0ms

Accuracy

0% (0.2b 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	6
1	17	6

end0.0ms

sample1.1s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 7.568359%

Guaranteed chance to sample good point: 96.005018%

Results

466.0ms	8000×	body	80	valid
52.0ms	915×	body	80	invalid

Details

sample426.0ms

simplify39.0ms

prune3.0ms

localize12.0ms

rewrite55.0ms

series37.0ms

simplify109.0ms

prune244.0ms

localize13.0ms

rewrite98.0ms

series37.0ms

simplify55.0ms

prune397.0ms

localize12.0ms

rewrite83.0ms

series38.0ms

simplify43.0ms

prune265.0ms

localize7.0ms

rewrite15.0ms

series13.0ms

simplify38.0ms

prune51.0ms

regimes98.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample1.1s

Profiling