Details

sample831.0ms

Algorithm

intervals

sampling

Space saved by range analysis: 71.884159%

Space saved by search: 71.884159%

Guaranteed chance to sample good point: 91.107178%

Results

10.0ms	194×	body	80	valid
6.0ms	23×	body	1280	valid
5.0ms	256×	pre	80	true
4.0ms	19×	body	640	valid
3.0ms	17×	body	320	valid
0.0ms	3×	body	160	valid

simplify53.0ms

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

prune4.0ms

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: 23.1b

Counts

2 → 1

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (+ (+ alpha beta) (* 2.0 i)) 2.0)
0.0b	(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
1.7b	(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
18.8b	(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

rewrite75.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 126

Calls

4 calls:

7.0ms	(+ (+ (+ alpha beta) (* 2.0 i)) 2.0)
19.0ms	(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
28.0ms	(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
16.0ms	(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

series170.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(+ (+ (+ alpha beta) (* 2.0 i)) 2.0)
64.0ms	(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
83.0ms	(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
17.0ms	(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

simplify108.0ms

Algorithm

egg-herbie

Counts

138 → 138

Iterations

Useful iterations: 1 (19.0ms)

Iter	Nodes	Cost
0	732	2016
1	4108	1891
2	5002	1891

prune286.0ms

Filtered

102 candidates to 138 candidates (-35.3%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	129	9	138
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	130	9	139

Merged error: 6.0b

Counts

139 → 9

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (+ (+ alpha beta) (* 2.0 i)) 2.0)
0.0b	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
1.1b	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
3.1b	(+ (* (+ 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

306×	`times-frac`
274×	`*-un-lft-identity`
193×	`add-sqr-sqrt`
130×	`add-cube-cbrt`
90×	`associate-r`
45×	`distribute-lft-out`
27×	`distribute-lft-out--` `difference-of-squares`
22×	`associate-/r/`
21×	`associate-/l*`
18×	`add-exp-log` `add-cbrt-cube`
15×	`flip3-+` `flip-+` `add-log-exp`
11×	`div-inv`
7×	`sum-log`
6×	`pow1` `cbrt-undiv` `div-exp`
4×	`associate-l` `associate-/r*`
3×	`prod-exp` `cbrt-unprod` `unswap-sqr`
2×	`+-commutative` `frac-times` `div-sub` `associate-*l/`
1×	`associate-+l+` `frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `-commutative` `associate-/l/`

Counts

4 → 270

Calls

4 calls:

8.0ms	(+ (+ (+ alpha beta) (* 2.0 i)) 2.0)
18.0ms	(/ (/ (- 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)))
24.0ms	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

series184.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(+ (+ (+ alpha beta) (* 2.0 i)) 2.0)
37.0ms	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
60.0ms	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
80.0ms	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

simplify66.0ms

Algorithm

egg-herbie

Counts

282 → 282

Iterations

Useful iterations: 1 (26.0ms)

Iter	Nodes	Cost
0	1095	4515
1	5001	4346

prune512.0ms

Filtered

181 candidates to 282 candidates (-55.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	279	3	282
Fresh	3	5	8
Picked	1	0	1
Done	0	0	0
Total	283	8	291

Merged error: 6.0b

Counts

291 → 8

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
0.1b	(cbrt (pow (+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0) 3))
1.1b	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
3.1b	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

rewrite126.0ms

Algorithm

rewrite-expression-head

Rules

306×	`times-frac`
275×	`*-un-lft-identity`
196×	`add-sqr-sqrt`
133×	`add-cube-cbrt`
90×	`associate-r`
44×	`distribute-lft-out`
27×	`distribute-lft-out--` `difference-of-squares`
22×	`associate-/r/`
21×	`associate-/l*`
18×	`add-exp-log` `add-cbrt-cube`
15×	`flip3-+` `flip-+`
12×	`cbrt-prod`
11×	`div-inv`
6×	`pow1` `cbrt-undiv` `div-exp` `add-log-exp`
4×	`associate-l` `associate-/r*`
3×	`unpow-prod-down` `cube-prod` `prod-exp` `cbrt-unprod` `unswap-sqr`
2×	`cube-div` `frac-times` `cbrt-div` `div-sub` `associate-*l/`
1×	`+-commutative` `cube-mult` `frac-2neg` `pow1/3` `unpow3` `associate-r/` `pow-prod-down` `clear-num` `sum-log` `-commutative` `rem-cbrt-cube` `associate-/l/` `sqr-pow`

Counts

4 → 278

Calls

4 calls:

19.0ms	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
25.0ms	(cbrt (pow (+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0) 3))
41.0ms	(* (+ 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)

series470.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
82.0ms	(cbrt (pow (+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0) 3))
266.0ms	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
83.0ms	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

simplify74.0ms

Algorithm

egg-herbie

Counts

290 → 290

Iterations

Useful iterations: 1 (30.0ms)

Iter	Nodes	Cost
0	1124	4978
1	5001	4845

prune672.0ms

Filtered

186 candidates to 290 candidates (-55.9%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	283	7	290
Fresh	4	3	7
Picked	1	0	1
Done	0	0	0
Total	288	10	298

Merged error: 6.0b

Counts

298 → 10

localize23.0ms

Local error

Found 4 expressions with local error:

3.4b	(cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
3.4b	(cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
3.4b	(cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
8.9b	(+ (* (* (+ alpha beta) (/ (* (cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) (/ (cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) 1.0)

rewrite92.0ms

Algorithm

rewrite-expression-head

Rules

63×	`cbrt-prod`
49×	`add-sqr-sqrt` `*-un-lft-identity`
45×	`times-frac`
31×	`add-cube-cbrt`
9×	`distribute-lft-out--` `difference-of-squares`
6×	`associate-/r/` `add-log-exp`
4×	`pow1` `add-exp-log` `flip3-+` `add-cbrt-cube` `flip-+`
3×	`cbrt-div` `pow1/3` `div-inv`
1×	`+-commutative` `sum-log`

Counts

4 → 101

Calls

4 calls:

9.0ms	(cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
8.0ms	(cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
8.0ms	(cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
63.0ms	(+ (* (* (+ alpha beta) (/ (* (cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) (/ (cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) 1.0)

series320.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
76.0ms	(cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
77.0ms	(cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
90.0ms	(+ (* (* (+ alpha beta) (/ (* (cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) (/ (cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) 1.0)

simplify52.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	360	1874
1	1194	1757
2	5002	1749

prune444.0ms

Filtered

93 candidates to 113 candidates (-21.5%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	112	1	113
Fresh	1	8	9
Picked	0	1	1
Done	0	0	0
Total	113	10	123

Merged error: 6.0b

Counts

123 → 10

regimes541.0ms

Accuracy

76% (1.6b remaining)

Error of 7.6b against oracle of 6.0b and baseline of 12.6b

bsearch1.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	58	61
1	58	61

end0.0ms

sample1.9s

Algorithm

intervals

sampling

Space saved by range analysis: 71.884159%

Space saved by search: 71.884159%

Guaranteed chance to sample good point: 91.107178%

Results

347.0ms	6322×	body	80	valid
170.0ms	8000×	pre	80	true
160.0ms	561×	body	1280	valid
126.0ms	547×	body	640	valid
56.0ms	349×	body	320	valid
28.0ms	221×	body	160	valid

Details

sample831.0ms

simplify53.0ms

prune4.0ms

localize13.0ms

rewrite75.0ms

series170.0ms

simplify108.0ms

prune286.0ms

localize13.0ms

rewrite109.0ms

series184.0ms

simplify66.0ms

prune512.0ms

localize16.0ms

rewrite126.0ms

series470.0ms

simplify74.0ms

prune672.0ms

localize23.0ms

rewrite92.0ms

series320.0ms

simplify52.0ms

prune444.0ms

regimes541.0ms

bsearch1.0ms

simplify2.0ms

end0.0ms

sample1.9s

Profiling