Details

sample906.0ms

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
7.0ms	24×	body	1280	valid
5.0ms	256×	pre	80	true
3.0ms	14×	body	640	valid
2.0ms	12×	body	320	valid
1.0ms	6×	body	160	valid

simplify48.0ms

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: 24.7b

Counts

2 → 1

localize12.0ms

Local error

Found 3 expressions with local error:

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)

21.7b

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

rewrite66.0ms

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)))

series163.0ms

Counts

3 → 9

Calls

3 calls:

64.0ms

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

82.0ms

(+ (/ (/ (* (+ 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)))

simplify93.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 1 (17.0ms)

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

prune231.0ms

Filtered

89 candidates to 120 candidates (-34.8%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	113	7	120
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	114	7	121

Merged error: 5.7b

Counts

121 → 7

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))
1.7b	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
2.6b	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

rewrite107.0ms

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:

9.0ms	(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
18.0ms	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
40.0ms	(* (+ 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)

series204.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
37.0ms	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
65.0ms	(* (+ 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)

simplify71.0ms

Algorithm

egg-herbie

Counts

307 → 307

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1080	4781
1	5001	4605

prune571.0ms

Filtered

199 candidates to 307 candidates (-54.3%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	302	5	307
Fresh	3	3	6
Picked	0	1	1
Done	0	0	0
Total	305	9	314

Merged error: 5.7b

Counts

314 → 9

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b	(cbrt (pow (+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0) 3))
0.1b	(/ (/ (- 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)))
2.6b	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

rewrite124.0ms

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:

26.0ms	(cbrt (pow (+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0) 3))
21.0ms	(/ (/ (- 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)))
25.0ms	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

series265.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(cbrt (pow (+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0) 3))
36.0ms	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ 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)))
85.0ms	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

simplify78.0ms

Algorithm

egg-herbie

Counts

290 → 290

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1121	4976
1	5001	4843

prune704.0ms

Filtered

185 candidates to 290 candidates (-56.8%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	285	5	290
Fresh	4	3	7
Picked	1	0	1
Done	0	1	1
Total	290	9	299

Merged error: 5.7b

Counts

299 → 9

localize25.0ms

Local error

Found 4 expressions with local error:

6.2b	(cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
6.2b	(cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
6.2b	(cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
8.7b	(+ (* (* (+ 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)

rewrite95.0ms

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:

10.0ms	(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))))
65.0ms	(+ (* (* (+ 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)

series313.0ms

Counts

4 → 12

Calls

4 calls:

75.0ms	(cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
73.0ms	(cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
75.0ms	(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 (33.0ms)

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

prune442.0ms

Filtered

93 candidates to 113 candidates (-21.5%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	113	0	113
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	113	9	122

Merged error: 5.7b

Counts

122 → 9

regimes338.0ms

Accuracy

7% (6.2b remaining)

Error of 12.4b against oracle of 6.1b and baseline of 12.8b

bsearch144.0ms

Steps

Iters	Range		Point
6	9.488198067665015e+265	4.73281547695331e+266	2.15583876401463e+266
8	3.064208509337496e+191	3.360157688383856e+195	3.1283799594316206e+194
6	1.6029283204595071e+119	8.571106273708597e+119	7.980694016064676e+119

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	69	74
1	69	74

end0.0ms

sample2.1s

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

343.0ms	6285×	body	80	valid
176.0ms	8000×	pre	80	true
160.0ms	560×	body	1280	valid
129.0ms	593×	body	640	valid
63.0ms	359×	body	320	valid
24.0ms	203×	body	160	valid

Details

sample906.0ms

simplify48.0ms

prune3.0ms

localize12.0ms

rewrite66.0ms

series163.0ms

simplify93.0ms

prune231.0ms

localize12.0ms

rewrite107.0ms

series204.0ms

simplify71.0ms

prune571.0ms

localize19.0ms

rewrite124.0ms

series265.0ms

simplify78.0ms

prune704.0ms

localize25.0ms

rewrite95.0ms

series313.0ms

simplify52.0ms

prune442.0ms

regimes338.0ms

bsearch144.0ms

simplify3.0ms

end0.0ms

sample2.1s

Profiling