Details

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

14.0ms	256×	body	80	valid
0.0ms	7×	body	80	invalid

simplify41.0ms

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: 15.5b

Counts

2 → 1

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
0.9b	(/ 1.0 (- (* b b) (* a a)))
5.9b	(- (* b b) (* a a))
8.1b	(* (* (/ 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)))

series34.0ms

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)))
6.0ms	(- (* b b) (* a a))
13.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

simplify112.0ms

Algorithm

egg-herbie

Counts

165 → 165

Iterations

Useful iterations: 1 (21.0ms)

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

prune241.0ms

Filtered

119 candidates to 165 candidates (-38.7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	157	8	165
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	158	8	166

Merged error: 7.9b

Counts

166 → 8

localize15.0ms

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)))
0.3b	(/ (/ PI 2.0) (+ b a))
8.1b	(* (* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite95.0ms

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:

12.0ms	(- (/ 1.0 a) (/ 1.0 b))
33.0ms	(* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a)))
8.0ms	(/ (/ PI 2.0) (+ b a))
28.0ms	(* (* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

series35.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(- (/ 1.0 a) (/ 1.0 b))
9.0ms	(* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a)))
7.0ms	(/ (/ PI 2.0) (+ b a))
13.0ms	(* (* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

simplify65.0ms

Algorithm

egg-herbie

Counts

285 → 285

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1270	2599
1	5001	2298

prune398.0ms

Filtered

194 candidates to 285 candidates (-46.9%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	278	7	285
Fresh	4	3	7
Picked	0	1	1
Done	0	0	0
Total	282	11	293

Merged error: 0.0b

Counts

293 → 11

localize13.0ms

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)) (- (/ 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)))

rewrite88.0ms

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:

12.0ms	(- (/ 1.0 a) (/ 1.0 b))
33.0ms	(* (/ (/ PI 2.0) (+ b a)) (* (/ 1.0 (- b a)) (- (/ 1.0 a) (/ 1.0 b))))
7.0ms	(/ (/ PI 2.0) (+ b a))
22.0ms	(* (/ 1.0 (- b a)) (- (/ 1.0 a) (/ 1.0 b)))

series36.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(- (/ 1.0 a) (/ 1.0 b))
17.0ms	(* (/ (/ PI 2.0) (+ b a)) (* (/ 1.0 (- b a)) (- (/ 1.0 a) (/ 1.0 b))))
7.0ms	(/ (/ PI 2.0) (+ b a))
8.0ms	(* (/ 1.0 (- b a)) (- (/ 1.0 a) (/ 1.0 b)))

simplify55.0ms

Algorithm

egg-herbie

Counts

289 → 289

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1236	2823
1	5001	2529

prune384.0ms

Filtered

194 candidates to 289 candidates (-49.0%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	285	4	289
Fresh	4	5	9
Picked	1	0	1
Done	0	1	1
Total	290	10	300

Merged error: 0.0b

Counts

300 → 10

localize13.0ms

Local error

Found 4 expressions with local error:

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

rewrite94.0ms

Algorithm

rewrite-expression-head

Rules

62×	`add-sqr-sqrt`
59×	`add-exp-log` `add-cbrt-cube`
53×	`*-un-lft-identity`
49×	`times-frac`
34×	`associate-l`
29×	`frac-times` `associate-*r/`
27×	`add-cube-cbrt`
22×	`prod-exp` `cbrt-unprod`
18×	`cbrt-undiv` `div-exp`
15×	`associate-/l/`
13×	`associate-r` `distribute-lft-out--`
12×	`flip3--` `flip--`
11×	`pow1` `frac-sub` `difference-of-squares`
10×	`distribute-rgt-in` `distribute-lft-in`
7×	`sub-neg` `associate-*l/` `div-inv`
6×	`add-log-exp`
4×	`pow-prod-down` `associate-/r*` `associate-/r/`
2×	`*-commutative` `distribute-lft-out` `unswap-sqr`
1×	`frac-2neg` `flip3-+` `diff-log` `clear-num` `flip-+` `associate-/l*`

Counts

4 → 190

Calls

4 calls:

12.0ms	(- (/ 1.0 a) (/ 1.0 b))
26.0ms	(/ (* (/ PI 2.0) (* (/ 1.0 (- b a)) (- (/ 1.0 a) (/ 1.0 b)))) (+ b a))
25.0ms	(* (/ PI 2.0) (* (/ 1.0 (- b a)) (- (/ 1.0 a) (/ 1.0 b))))
23.0ms	(* (/ 1.0 (- b a)) (- (/ 1.0 a) (/ 1.0 b)))

series37.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(- (/ 1.0 a) (/ 1.0 b))
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))))
8.0ms	(* (/ 1.0 (- b a)) (- (/ 1.0 a) (/ 1.0 b)))

simplify42.0ms

Algorithm

egg-herbie

Counts

202 → 202

Iterations

Useful iterations: 1 (22.0ms)

Iter	Nodes	Cost
0	952	2019
1	5001	1674

prune229.0ms

Filtered

136 candidates to 202 candidates (-48.5%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	199	3	202
Fresh	3	5	8
Picked	1	0	1
Done	0	1	1
Total	203	9	212

Merged error: 0b

Counts

212 → 9

regimes108.0ms

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	14	6
1	14	6

end0.0ms

sample1.8s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 14.709473%

Guaranteed chance to sample good point: 95.005009%

Results

446.0ms	8000×	body	80	valid
10.0ms	178×	body	80	invalid

Details

sample1.1s

simplify41.0ms

prune3.0ms

localize13.0ms

rewrite52.0ms

series34.0ms

simplify112.0ms

prune241.0ms

localize15.0ms

rewrite95.0ms

series35.0ms

simplify65.0ms

prune398.0ms

localize13.0ms

rewrite88.0ms

series36.0ms

simplify55.0ms

prune384.0ms

localize13.0ms

rewrite94.0ms

series37.0ms

simplify42.0ms

prune229.0ms

regimes108.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample1.8s

Profiling