Details

analyze414.0ms

Algorithm

sampling

Space saved by range analysis: 0.097632%

Space saved by search: 14.792744%

Guaranteed chance to sample good point: 95.005009%

sample22.0ms

Algorithm

intervals

Results

14.0ms	256×	body	80	valid
0.0ms	7×	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: 15.5b

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)))
4.2b	(- (* b b) (* a a))
10.1b	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite50.0ms

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))))
5.0ms	(/ 1.0 (- (* b b) (* a a)))
3.0ms	(- (* b b) (* a a))
21.0ms	(* (* (/ 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))))
7.0ms	(/ 1.0 (- (* b b) (* a a)))
6.0ms	(- (* b b) (* a a))
12.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

simplify105.0ms

Algorithm

egg-herbie

Counts

165 → 165

Iterations

Useful iterations: 1 (20.0ms)

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

prune233.0ms

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: 9.9b

Counts

166 → 8

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)))
0.3b	(/ (/ PI 2.0) (+ b a))
10.1b	(* (* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite90.0ms

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))
30.0ms	(* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a)))
8.0ms	(/ (/ PI 2.0) (+ b a))
31.0ms	(* (* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

series38.0ms

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

simplify54.0ms

Algorithm

egg-herbie

Counts

300 → 300

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1260	2632
1	5001	2332

prune399.0ms

Filtered

204 candidates to 300 candidates (-47.1%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	296	4	300
Fresh	2	5	7
Picked	1	0	1
Done	0	0	0
Total	299	9	308

Merged error: 0.0b

Counts

308 → 9

localize13.0ms

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

rewrite81.0ms

Algorithm

rewrite-expression-head

Rules

122×	`times-frac`
108×	`*-un-lft-identity`
88×	`add-sqr-sqrt`
60×	`add-cube-cbrt`
43×	`add-exp-log` `add-cbrt-cube`
14×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `distribute-lft-out` `associate-/l*`
12×	`associate-r` `distribute-lft-out--`
11×	`div-inv`
10×	`associate-*l/` `difference-of-squares`
9×	`pow1` `associate-/r*`
8×	`associate-/l/`
6×	`frac-times` `flip3--` `associate-*r/` `flip--` `add-log-exp`
5×	`frac-sub`
4×	`associate-/r/`
3×	`sub-neg` `pow-prod-down`
2×	`distribute-rgt-in` `frac-2neg` `distribute-lft-in` `clear-num`
1×	`flip3-+` `diff-log` `associate-l` `*-commutative` `flip-+`

Counts

4 → 190

Calls

4 calls:

12.0ms	(- (/ 1.0 a) (/ 1.0 b))
26.0ms	(/ (* (* (/ (/ PI 2.0) (+ b a)) 1.0) (- (/ 1.0 a) (/ 1.0 b))) (- b a))
8.0ms	(/ (/ PI 2.0) (+ b a))
26.0ms	(* (* (/ (/ PI 2.0) (+ b a)) 1.0) (- (/ 1.0 a) (/ 1.0 b)))

series41.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(- (/ 1.0 a) (/ 1.0 b))
13.0ms	(/ (* (* (/ (/ PI 2.0) (+ b a)) 1.0) (- (/ 1.0 a) (/ 1.0 b))) (- b a))
7.0ms	(/ (/ PI 2.0) (+ b a))
16.0ms	(* (* (/ (/ PI 2.0) (+ b a)) 1.0) (- (/ 1.0 a) (/ 1.0 b)))

simplify110.0ms

Algorithm

egg-herbie

Counts

202 → 202

Iterations

Useful iterations: 1 (22.0ms)

Iter	Nodes	Cost
0	931	1844
1	4583	1596
2	5002	1596

prune265.0ms

Filtered

137 candidates to 202 candidates (-47.4%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	198	4	202
Fresh	3	5	8
Picked	1	0	1
Done	0	0	0
Total	202	9	211

Merged error: 0b

Counts

211 → 9

localize12.0ms

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

rewrite98.0ms

Algorithm

rewrite-expression-head

Rules

514×	`times-frac`
420×	`add-sqr-sqrt`
380×	`*-un-lft-identity`
142×	`add-cube-cbrt`
122×	`distribute-lft-out--`
105×	`difference-of-squares`
83×	`associate-/r*`
44×	`div-inv`
43×	`add-exp-log` `add-cbrt-cube`
22×	`cbrt-undiv` `div-exp`
19×	`associate-/l*`
14×	`distribute-lft-out`
12×	`associate-/r/`
6×	`prod-exp` `cbrt-unprod` `add-log-exp`
5×	`flip3--` `flip--`
4×	`pow1` `frac-sub` `associate-/l/`
3×	`frac-2neg` `clear-num`
1×	`sub-neg` `flip3-+` `diff-log` `div-sub` `associate-*l/` `flip-+`

Counts

4 → 366

Calls

4 calls:

12.0ms	(- (/ 1.0 a) (/ 1.0 b))
32.0ms	(/ (* (/ (/ PI 2.0) (+ b a)) 1.0) (/ (- b a) (- (/ 1.0 a) (/ 1.0 b))))
16.0ms	(/ (- b a) (- (/ 1.0 a) (/ 1.0 b)))
8.0ms	(/ (/ PI 2.0) (+ b a))

series31.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify70.0ms

Algorithm

egg-herbie

Counts

378 → 378

Iterations

Useful iterations: 1 (30.0ms)

Iter	Nodes	Cost
0	1498	4278
1	5002	4025

prune543.0ms

Filtered

254 candidates to 378 candidates (-48.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	377	1	378
Fresh	1	7	8
Picked	1	0	1
Done	0	0	0
Total	379	8	387

Merged error: 0b

Counts

387 → 8

regimes104.0ms

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	18	10
1	18	10

end0.0ms

analyze407.0ms

Algorithm

sampling

Space saved by range analysis: 0.097632%

Space saved by search: 14.792744%

Guaranteed chance to sample good point: 95.005009%

sample616.0ms

Algorithm

intervals

Results

466.0ms	8000×	body	80	valid
9.0ms	160×	body	80	invalid

Details

analyze414.0ms

sample22.0ms

simplify39.0ms

prune3.0ms

localize12.0ms

rewrite50.0ms

series33.0ms

simplify105.0ms

prune233.0ms

localize13.0ms

rewrite90.0ms

series38.0ms

simplify54.0ms

prune399.0ms

localize13.0ms

rewrite81.0ms

series41.0ms

simplify110.0ms

prune265.0ms

localize12.0ms

rewrite98.0ms

series31.0ms

simplify70.0ms

prune543.0ms

regimes104.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

analyze407.0ms

sample616.0ms

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