Details

sample276.0ms

Algorithm

intervals

sampling

Space saved by range analysis: 71.884159%

Space saved by search: 71.884159%

Guaranteed chance to sample good point: 97.259521%

Results

11.0ms	200×	body	80	valid
6.0ms	256×	pre	80	true
5.0ms	17×	body	1280	valid
4.0ms	17×	body	640	valid
2.0ms	12×	body	320	valid
1.0ms	10×	body	160	valid

simplify51.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	31	14
1	103	14
2	454	14
3	2127	14
4	5001	14

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: 24.2b

Counts

2 → 1

localize13.0ms

Local error

Found 3 expressions with local error:

0.1b

(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))

2.0b

(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

20.0b

(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

54×	`times-frac`
47×	`*-un-lft-identity`
25×	`add-sqr-sqrt` `add-cube-cbrt`
17×	`add-exp-log` `add-cbrt-cube`
14×	`associate-/r/`
11×	`flip3-+` `flip-+` `distribute-lft-out`
10×	`associate-/l*`
9×	`associate-/l/`
7×	`cbrt-undiv` `div-exp` `associate-/r*` `div-inv`
5×	`add-log-exp`
4×	`frac-times`
3×	`pow1` `flip3--` `flip--`
2×	`frac-2neg` `associate-r/` `associate-l/` `prod-exp` `clear-num` `cbrt-unprod`
1×	`+-commutative` `sum-log`

Counts

3 → 111

Calls

3 calls:

19.0ms

(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))

30.0ms

(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

13.0ms

(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

series170.0ms

Counts

3 → 9

Calls

3 calls:

67.0ms

(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))

85.0ms

(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

18.0ms

(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

simplify91.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 1 (17.0ms)

Iter	Nodes	Cost
0	681	1905
1	3622	1789
2	5001	1789

prune253.0ms

Filtered

89 candidates to 120 candidates (-34.8%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	110	10	120
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	111	10	121

Merged error: 6.3b

Counts

121 → 10

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
0.1b	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
3.0b	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
4.0b	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

rewrite109.0ms

Algorithm

rewrite-expression-head

Rules

321×	`times-frac`
290×	`*-un-lft-identity`
211×	`add-sqr-sqrt`
140×	`add-cube-cbrt`
90×	`associate-r`
44×	`distribute-lft-out`
31×	`distribute-lft-out--` `difference-of-squares`
26×	`associate-/l*`
24×	`associate-/r/`
20×	`add-exp-log` `add-cbrt-cube`
15×	`flip3-+` `flip-+`
12×	`div-inv`
7×	`cbrt-undiv` `div-exp` `associate-/r*`
6×	`pow1` `add-log-exp`
4×	`associate-l`
3×	`div-sub` `prod-exp` `cbrt-unprod` `associate-/l/` `unswap-sqr`
2×	`frac-times` `frac-2neg` `associate-*l/` `clear-num`
1×	`+-commutative` `flip3--` `associate-r/` `pow-prod-down` `sum-log` `-commutative` `flip--`

Counts

4 → 295

Calls

4 calls:

12.0ms	(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
18.0ms	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
36.0ms	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
27.0ms	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

series204.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
38.0ms	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
66.0ms	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
85.0ms	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

simplify74.0ms

Algorithm

egg-herbie

Counts

307 → 307

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1080	4781
1	5001	4605

prune562.0ms

Filtered

198 candidates to 307 candidates (-55.1%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	302	5	307
Fresh	5	4	9
Picked	1	0	1
Done	0	0	0
Total	308	9	317

Merged error: 6.3b

Counts

317 → 9

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0) 3)
0.1b	(cbrt (pow (+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0) 3))
3.0b	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
4.0b	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

rewrite127.0ms

Algorithm

rewrite-expression-head

Rules

147×	`times-frac`
137×	`*-un-lft-identity`
102×	`add-sqr-sqrt`
90×	`associate-r`
69×	`add-cube-cbrt`
22×	`distribute-lft-out`
14×	`add-exp-log` `add-cbrt-cube`
12×	`cbrt-prod` `distribute-lft-out--` `difference-of-squares`
10×	`flip3-+` `associate-/r/` `flip-+`
7×	`pow1`
6×	`unpow-prod-down` `cube-prod` `add-log-exp`
5×	`div-inv`
4×	`cube-div` `associate-l`
3×	`cbrt-undiv` `pow-unpow` `div-exp` `prod-exp` `cbrt-unprod` `unswap-sqr`
2×	`cube-mult` `frac-times` `cbrt-div` `unpow3` `associate-*l/` `sqr-pow`
1×	`+-commutative` `pow-to-exp` `pow-pow` `pow1/3` `associate-r/` `pow-prod-down` `pow-exp` `sum-log` `-commutative` `rem-cbrt-cube` `rem-cube-cbrt`

Counts

4 → 176

Calls

4 calls:

26.0ms	(pow (+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0) 3)
25.0ms	(cbrt (pow (+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0) 3))
38.0ms	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
25.0ms	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

series455.0ms

Counts

4 → 12

Calls

4 calls:

229.0ms	(pow (+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0) 3)
82.0ms	(cbrt (pow (+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0) 3))
62.0ms	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
81.0ms	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

simplify59.0ms

Algorithm

egg-herbie

Counts

188 → 188

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	976	3078
1	5002	2920

prune412.0ms

Filtered

118 candidates to 188 candidates (-59.3%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	183	5	188
Fresh	2	6	8
Picked	1	0	1
Done	0	0	0
Total	186	11	197

Merged error: 6.3b

Counts

197 → 11

localize26.0ms

Local error

Found 4 expressions with local error:

3.0b	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
3.0b	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
3.0b	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
3.9b	(+ (pow (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 3) (pow 1.0 3))

rewrite150.0ms

Algorithm

rewrite-expression-head

Rules

441×	`times-frac`
387×	`*-un-lft-identity`
280×	`add-sqr-sqrt`
270×	`associate-r`
181×	`add-cube-cbrt`
67×	`distribute-lft-out`
36×	`distribute-lft-out--` `difference-of-squares`
31×	`add-exp-log` `add-cbrt-cube`
30×	`associate-/r/`
22×	`flip3-+` `flip-+`
15×	`div-inv`
12×	`associate-l`
10×	`pow1`
9×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `unswap-sqr`
6×	`frac-times` `associate-*l/` `add-log-exp`
3×	`associate-r/` `pow-prod-down` `-commutative`
1×	`+-commutative` `sum-log` `sum-cubes`

Counts

4 → 364

Calls

4 calls:

37.0ms	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
42.0ms	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
38.0ms	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
10.0ms	(+ (pow (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 3) (pow 1.0 3))

series3.1s

Counts

4 → 12

Calls

4 calls:

66.0ms	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
67.0ms	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
66.0ms	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
2.9s	(+ (pow (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 3) (pow 1.0 3))

simplify73.0ms

Algorithm

egg-herbie

Counts

376 → 376

Iterations

Useful iterations: 1 (25.0ms)

Iter	Nodes	Cost
0	852	5278
1	5002	5022

prune2.6s

Filtered

238 candidates to 376 candidates (-58.0%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	373	3	376
Fresh	1	9	10
Picked	1	0	1
Done	0	0	0
Total	375	12	387

Merged error: 6.3b

Counts

387 → 12

regimes425.0ms

Accuracy

16.8% (5.2b remaining)

Error of 11.2b against oracle of 6.0b and baseline of 12.3b

bsearch46.0ms

Steps

Iters	Range		Point
9	1.0693022609506356e+195	8.125945092645044e+201	1.0739346921458221e+198

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	60	73
1	60	73

end0.0ms

sample1.4s

Algorithm

intervals

sampling

Space saved by range analysis: 71.884159%

Space saved by search: 71.884159%

Guaranteed chance to sample good point: 97.259521%

Results

362.0ms	6361×	body	80	valid
176.0ms	8000×	pre	80	true
152.0ms	505×	body	1280	valid
131.0ms	583×	body	640	valid
59.0ms	354×	body	320	valid
24.0ms	197×	body	160	valid

Details

sample276.0ms

simplify51.0ms

prune3.0ms

localize13.0ms

rewrite67.0ms

series170.0ms

simplify91.0ms

prune253.0ms

localize12.0ms

rewrite109.0ms

series204.0ms

simplify74.0ms

prune562.0ms

localize15.0ms

rewrite127.0ms

series455.0ms

simplify59.0ms

prune412.0ms

localize26.0ms

rewrite150.0ms

series3.1s

simplify73.0ms

prune2.6s

regimes425.0ms

bsearch46.0ms

simplify2.0ms

end0.0ms

sample1.4s

Profiling