Details

sample493.0ms

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 14.709473%

Guaranteed chance to sample good point: 95.005009%

Results

14.0ms	256×	body	80	valid
0.0ms	6×	body	80	invalid

simplify40.0ms

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: 15.8b

Counts

2 → 1

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
0.6b	(/ 1.0 (- (* b b) (* a a)))
4.3b	(- (* b b) (* a a))
10.7b	(* (* (/ 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×	`distribute-rgt-in` `distribute-lft-in` `*-commutative`
1×	`frac-2neg` `diff-log` `clear-num`

Counts

4 → 153

Calls

4 calls:

13.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
5.0ms	(/ 1.0 (- (* b b) (* a a)))
3.0ms	(- (* b b) (* a a))
25.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

series33.0ms

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))
13.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

simplify114.0ms

Algorithm

egg-herbie

Counts

165 → 165

Iterations

Useful iterations: 1 (22.0ms)

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

prune245.0ms

Filtered

119 candidates to 165 candidates (-38.7%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	158	7	165
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	159	7	166

Merged error: 10.6b

Counts

166 → 7

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ 1.0 a) (/ 1.0 b))
0.2b	(* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a)))
0.3b	(/ (/ PI 2.0) (+ b a))
10.7b	(* (* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite105.0ms

Algorithm

rewrite-expression-head

Rules

229×	`times-frac`
185×	`*-un-lft-identity`
160×	`add-sqr-sqrt`
109×	`add-cube-cbrt`
59×	`add-exp-log` `associate-l` `add-cbrt-cube`
33×	`associate-r`
27×	`distribute-lft-out`
21×	`cbrt-undiv` `div-exp`
19×	`prod-exp` `cbrt-unprod`
16×	`div-inv`
14×	`frac-times`
13×	`associate-/l*` `distribute-lft-out--`
11×	`pow1` `difference-of-squares`
8×	`associate-r/` `associate-l/`
6×	`flip3--` `associate-/r/` `flip--` `add-log-exp` `unswap-sqr`
5×	`frac-sub`
4×	`pow-prod-down` `associate-/r*`
3×	`sub-neg`
2×	`distribute-rgt-in` `distribute-lft-in` `flip3-+` `*-commutative` `flip-+`
1×	`frac-2neg` `diff-log` `clear-num` `associate-/l/`

Counts

4 → 273

Calls

4 calls:

14.0ms	(- (/ 1.0 a) (/ 1.0 b))
29.0ms	(* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a)))
7.0ms	(/ (/ PI 2.0) (+ b a))
41.0ms	(* (* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

series31.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(- (/ 1.0 a) (/ 1.0 b))
8.0ms	(* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a)))
6.0ms	(/ (/ PI 2.0) (+ b a))
12.0ms	(* (* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

simplify57.0ms

Algorithm

egg-herbie

Counts

285 → 285

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1270	2599
1	5001	2298

prune378.0ms

Filtered

194 candidates to 285 candidates (-46.9%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	281	4	285
Fresh	3	3	6
Picked	1	0	1
Done	0	0	0
Total	285	7	292

Merged error: 0.0b

Counts

292 → 7

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ 1.0 a) (/ 1.0 b))
0.1b	(* (/ (/ PI 2.0) (+ b a)) (* (/ 1.0 (- b a)) (- (/ 1.0 a) (/ 1.0 b))))
0.3b	(/ (/ PI 2.0) (+ b a))
0.3b	(* (/ 1.0 (- b a)) (- (/ 1.0 a) (/ 1.0 b)))

rewrite89.0ms

Algorithm

rewrite-expression-head

Rules

221×	`times-frac`
185×	`*-un-lft-identity`
144×	`add-sqr-sqrt`
109×	`add-cube-cbrt`
79×	`associate-l`
50×	`add-exp-log` `add-cbrt-cube`
27×	`distribute-lft-out`
17×	`prod-exp` `cbrt-unprod`
16×	`cbrt-undiv` `frac-times` `associate-*r/` `div-exp` `div-inv`
13×	`associate-r` `associate-/l*` `distribute-lft-out--`
11×	`pow1` `difference-of-squares`
10×	`distribute-rgt-in` `distribute-lft-in`
8×	`flip3--` `flip--`
7×	`sub-neg` `frac-sub`
6×	`associate-/r/` `add-log-exp`
4×	`pow-prod-down` `associate-l/` `associate-/r`
2×	`flip3-+` `*-commutative` `flip-+` `unswap-sqr`
1×	`frac-2neg` `diff-log` `clear-num` `associate-/l/`

Counts

4 → 277

Calls

4 calls:

11.0ms	(- (/ 1.0 a) (/ 1.0 b))
30.0ms	(* (/ (/ PI 2.0) (+ b a)) (* (/ 1.0 (- b a)) (- (/ 1.0 a) (/ 1.0 b))))
7.0ms	(/ (/ PI 2.0) (+ b a))
24.0ms	(* (/ 1.0 (- b a)) (- (/ 1.0 a) (/ 1.0 b)))

series29.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(- (/ 1.0 a) (/ 1.0 b))
12.0ms	(* (/ (/ PI 2.0) (+ b a)) (* (/ 1.0 (- b a)) (- (/ 1.0 a) (/ 1.0 b))))
6.0ms	(/ (/ PI 2.0) (+ b a))
7.0ms	(* (/ 1.0 (- b a)) (- (/ 1.0 a) (/ 1.0 b)))

simplify54.0ms

Algorithm

egg-herbie

Counts

289 → 289

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1236	2823
1	5001	2532

prune370.0ms

Filtered

196 candidates to 289 candidates (-47.4%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	283	6	289
Fresh	4	2	6
Picked	1	0	1
Done	0	0	0
Total	288	8	296

Merged error: 0b

Counts

296 → 8

localize10.0ms

Local error

Found 3 expressions with local error:

0.1b	(* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (* a b)))
0.3b	(/ (/ PI 2.0) (+ b a))
0.5b	(/ 1.0 (* a b))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

194×	`times-frac`
152×	`*-un-lft-identity`
107×	`add-sqr-sqrt`
98×	`add-cube-cbrt`
58×	`associate-l`
49×	`add-exp-log` `add-cbrt-cube`
27×	`distribute-lft-out`
20×	`cbrt-undiv` `div-exp`
16×	`associate-/l*`
13×	`prod-exp` `cbrt-unprod` `div-inv`
7×	`associate-r`
5×	`pow1` `associate-/r*`
4×	`associate-/r/`
3×	`add-log-exp` `unswap-sqr`
2×	`frac-2neg` `flip3-+` `clear-num` `flip-+`
1×	`frac-times` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative` `associate-/l/`

Counts

3 → 205

Calls

3 calls:

19.0ms	(* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (* a b)))
7.0ms	(/ (/ PI 2.0) (+ b a))
4.0ms	(/ 1.0 (* a b))

series18.0ms

Counts

3 → 9

Calls

3 calls:

9.0ms	(* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (* a b)))
6.0ms	(/ (/ PI 2.0) (+ b a))
3.0ms	(/ 1.0 (* a b))

simplify90.0ms

Algorithm

egg-herbie

Counts

214 → 214

Iterations

Useful iterations: 1 (21.0ms)

Iter	Nodes	Cost
0	846	1599
1	4094	1433
2	5003	1433

prune214.0ms

Filtered

143 candidates to 214 candidates (-49.7%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	211	3	214
Fresh	4	3	7
Picked	1	0	1
Done	0	0	0
Total	216	6	222

Merged error: 0b

Counts

222 → 6

regimes90.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	6
1	14	6

end0.0ms

sample1.1s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 14.709473%

Guaranteed chance to sample good point: 95.005009%

Results

450.0ms	8000×	body	80	valid
10.0ms	178×	body	80	invalid

Details

sample493.0ms

simplify40.0ms

prune3.0ms

localize12.0ms

rewrite52.0ms

series33.0ms

simplify114.0ms

prune245.0ms

localize23.0ms

rewrite105.0ms

series31.0ms

simplify57.0ms

prune378.0ms

localize12.0ms

rewrite89.0ms

series29.0ms

simplify54.0ms

prune370.0ms

localize10.0ms

rewrite40.0ms

series18.0ms

simplify90.0ms

prune214.0ms

regimes90.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample1.1s

Profiling