Details

sample432.0ms

Algorithm

intervals

sampling

Space saved by range analysis: 14.792744%

Space saved by search: 0.097632%

Guaranteed chance to sample good point: 0%

Results

14.0ms	256×	body	80	valid
0.0ms	4×	body	80	invalid

simplify38.0ms

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: 15.4b

Counts

2 → 1

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
0.8b	(/ 1.0 (- (* b b) (* a a)))
4.3b	(- (* b b) (* a a))
9.9b	(* (* (/ 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))
23.0ms	(* (* (/ 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))
17.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

simplify110.0ms

Algorithm

egg-herbie

Counts

165 → 165

Iterations

Useful iterations: 1 (21.0ms)

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

prune243.0ms

Filtered

119 candidates to 165 candidates (-38.7%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	155	10	165
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	156	10	166

Merged error: 9.7b

Counts

166 → 10

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ 1.0 a) (/ 1.0 b))
0.2b	(* (* (/ PI 2.0) (/ (sqrt 1.0) (+ b a))) (/ (sqrt 1.0) (- b a)))
0.3b	(* (/ PI 2.0) (/ (sqrt 1.0) (+ b a)))
9.9b	(* (* (* (/ PI 2.0) (/ (sqrt 1.0) (+ b a))) (/ (sqrt 1.0) (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite99.0ms

Algorithm

rewrite-expression-head

Rules

110×	`add-exp-log` `add-cbrt-cube`
103×	`add-sqr-sqrt`
90×	`times-frac`
88×	`*-un-lft-identity`
78×	`associate-r`
51×	`prod-exp` `cbrt-unprod`
48×	`add-cube-cbrt`
47×	`frac-times`
33×	`associate-*l/`
30×	`cbrt-undiv` `div-exp`
29×	`sqrt-prod`
20×	`pow1`
19×	`associate-*r/`
16×	`distribute-lft-out--`
15×	`associate-l`
14×	`difference-of-squares`
10×	`flip3--` `pow-prod-down` `flip--`
9×	`frac-sub`
7×	`div-inv`
6×	`distribute-lft-out` `add-log-exp` `unswap-sqr`
4×	`associate-/r/`
3×	`sub-neg` `*-commutative`
2×	`distribute-rgt-in` `distribute-lft-in`
1×	`flip3-+` `diff-log` `flip-+`

Counts

4 → 246

Calls

4 calls:

13.0ms	(- (/ 1.0 a) (/ 1.0 b))
20.0ms	(* (* (/ PI 2.0) (/ (sqrt 1.0) (+ b a))) (/ (sqrt 1.0) (- b a)))
19.0ms	(* (/ PI 2.0) (/ (sqrt 1.0) (+ b a)))
34.0ms	(* (* (* (/ PI 2.0) (/ (sqrt 1.0) (+ b a))) (/ (sqrt 1.0) (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

series68.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(- (/ 1.0 a) (/ 1.0 b))
19.0ms	(* (* (/ PI 2.0) (/ (sqrt 1.0) (+ b a))) (/ (sqrt 1.0) (- b a)))
13.0ms	(* (/ PI 2.0) (/ (sqrt 1.0) (+ b a)))
31.0ms	(* (* (* (/ PI 2.0) (/ (sqrt 1.0) (+ b a))) (/ (sqrt 1.0) (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

simplify60.0ms

Algorithm

egg-herbie

Counts

258 → 258

Iterations

Useful iterations: 1 (30.0ms)

Iter	Nodes	Cost
0	1344	3063
1	5001	2608

prune425.0ms

Filtered

164 candidates to 258 candidates (-57.3%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	251	7	258
Fresh	5	4	9
Picked	1	0	1
Done	0	0	0
Total	257	11	268

Merged error: 0.0b

Counts

268 → 11

localize12.0ms

Local error

Found 4 expressions with local error:

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

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 133

Calls

4 calls:

12.0ms	(- (/ 1.0 a) (/ 1.0 b))
26.0ms	(/ (* (- (/ 1.0 a) (/ 1.0 b)) (/ (* PI 1.0) (- b a))) (* 2.0 (+ b a)))
6.0ms	(/ (* PI 1.0) (- b a))
23.0ms	(* (- (/ 1.0 a) (/ 1.0 b)) (/ (* PI 1.0) (- b a)))

series33.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(- (/ 1.0 a) (/ 1.0 b))
13.0ms	(/ (* (- (/ 1.0 a) (/ 1.0 b)) (/ (* PI 1.0) (- b a))) (* 2.0 (+ b a)))
7.0ms	(/ (* PI 1.0) (- b a))
9.0ms	(* (- (/ 1.0 a) (/ 1.0 b)) (/ (* PI 1.0) (- b a)))

simplify92.0ms

Algorithm

egg-herbie

Counts

145 → 145

Iterations

Useful iterations: 1 (18.0ms)

Iter	Nodes	Cost
0	695	1331
1	4083	1048
2	5002	1048

prune189.0ms

Filtered

97 candidates to 145 candidates (-49.5%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	139	6	145
Fresh	4	6	10
Picked	1	0	1
Done	0	0	0
Total	144	12	156

Merged error: 0.0b

Counts

156 → 12

localize8.0ms

Local error

Found 2 expressions with local error:

0.2b	(/ (* 1.0 (/ PI (* a b))) (* 2.0 (+ b a)))
0.8b	(/ PI (* a b))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

39×	`add-exp-log` `add-cbrt-cube`
14×	`cbrt-undiv` `div-exp`
13×	`prod-exp` `cbrt-unprod`
4×	`add-sqr-sqrt` `add-cube-cbrt` `-un-lft-identity` `times-frac` `associate-/l`
3×	`associate-*r/`
2×	`pow1` `frac-2neg` `clear-num` `associate-/r*` `associate-/r/` `div-inv` `add-log-exp`
1×	`flip3-+` `flip-+` `associate-/l/`

Counts

2 → 53

Calls

2 calls:

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

series12.0ms

Counts

2 → 6

Calls

2 calls:

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

simplify49.0ms

Algorithm

egg-herbie

Counts

59 → 59

Iterations

Useful iterations: 1 (10.0ms)

Iter	Nodes	Cost
0	390	416
1	2377	290
2	5003	290

prune50.0ms

Filtered

33 candidates to 59 candidates (-78.8%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	55	4	59
Fresh	5	6	11
Picked	1	0	1
Done	0	0	0
Total	61	10	71

Merged error: 0b

Counts

71 → 10

regimes116.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	7
1	19	7

end0.0ms

sample967.0ms

Algorithm

intervals

sampling

Space saved by range analysis: 14.792744%

Space saved by search: 0.097632%

Guaranteed chance to sample good point: 0%

Results

444.0ms	8000×	body	80	valid
10.0ms	195×	body	80	invalid

Details

sample432.0ms

simplify38.0ms

prune3.0ms

localize12.0ms

rewrite52.0ms

series37.0ms

simplify110.0ms

prune243.0ms

localize15.0ms

rewrite99.0ms

series68.0ms

simplify60.0ms

prune425.0ms

localize12.0ms

rewrite72.0ms

series33.0ms

simplify92.0ms

prune189.0ms

localize8.0ms

rewrite19.0ms

series12.0ms

simplify49.0ms

prune50.0ms

regimes116.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample967.0ms

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