Details

sample840.0ms

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

14.0ms	203×	body	80	valid
6.0ms	256×	pre	80	true
5.0ms	21×	body	640	valid
4.0ms	16×	body	1280	valid
1.0ms	8×	body	320	valid
1.0ms	8×	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: 20.4b

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))
2.2b	(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
17.0b	(/ (* (+ 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:

8.0ms	(+ (+ (+ 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))
31.0ms	(+ (/ (/ (* (+ 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)))

series169.0ms

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))
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)))

simplify99.0ms

Algorithm

egg-herbie

Counts

138 → 138

Iterations

Useful iterations: 1 (18.0ms)

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

prune292.0ms

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: 6.6b

Counts

139 → 9

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
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)))
3.2b	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

rewrite115.0ms

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:

10.0ms	(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
19.0ms	(/ (/ (- 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)))
26.0ms	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

series209.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
39.0ms	(/ (/ (- 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)))
89.0ms	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

simplify66.0ms

Algorithm

egg-herbie

Counts

307 → 307

Iterations

Useful iterations: 1 (25.0ms)

Iter	Nodes	Cost
0	1080	4781
1	5001	4605

prune569.0ms

Filtered

200 candidates to 307 candidates (-53.5%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	300	7	307
Fresh	6	2	8
Picked	1	0	1
Done	0	0	0
Total	307	9	316

Merged error: 6.6b

Counts

316 → 9

localize22.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
0.6b	(cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
1.1b	(* (+ alpha beta) (* (/ (/ (* (cbrt (- beta alpha)) (cbrt (- beta alpha))) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (cbrt (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))))
5.8b	(+ (* (+ alpha beta) (* (/ (/ (* (cbrt (- beta alpha)) (cbrt (- beta alpha))) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (cbrt (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))) 1.0)

rewrite149.0ms

Algorithm

rewrite-expression-head

Rules

72×	`add-exp-log`
39×	`add-cbrt-cube`
28×	`prod-exp` `cbrt-unprod`
27×	`cbrt-undiv` `div-exp`
13×	`*-un-lft-identity`
9×	`pow1` `frac-times`
8×	`cbrt-prod`
7×	`add-sqr-sqrt` `add-cube-cbrt` `flip3-+` `flip-+`
6×	`associate-*r/` `add-log-exp`
5×	`associate-*l/`
4×	`cbrt-div` `associate-l`
3×	`pow-prod-down` `distribute-lft-out`
2×	`pow1/3`
1×	`+-commutative` `associate-r` `sum-log` `*-commutative`

Counts

4 → 91

Calls

4 calls:

7.0ms	(cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
7.0ms	(cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
68.0ms	(* (+ alpha beta) (* (/ (/ (* (cbrt (- beta alpha)) (cbrt (- beta alpha))) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (cbrt (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))))
64.0ms	(+ (* (+ alpha beta) (* (/ (/ (* (cbrt (- beta alpha)) (cbrt (- beta alpha))) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (cbrt (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))) 1.0)

series247.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
39.0ms	(cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
65.0ms	(* (+ alpha beta) (* (/ (/ (* (cbrt (- beta alpha)) (cbrt (- beta alpha))) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (cbrt (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))))
103.0ms	(+ (* (+ alpha beta) (* (/ (/ (* (cbrt (- beta alpha)) (cbrt (- beta alpha))) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (cbrt (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))) 1.0)

simplify100.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 2 (74.0ms)

Iter	Nodes	Cost
0	804	3182
1	3484	2530
2	5002	2456

prune245.0ms

Filtered

60 candidates to 103 candidates (-71.7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	102	1	103
Fresh	1	7	8
Picked	1	0	1
Done	0	0	0
Total	104	8	112

Merged error: 6.6b

Counts

112 → 8

localize26.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
0.6b	(cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
1.1b	(* (+ alpha beta) (* (/ (/ (* (cbrt (- beta alpha)) (cbrt (- beta alpha))) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (cbrt (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))))
5.8b	(+ (* (+ alpha beta) (* (/ (/ (* (cbrt (- beta alpha)) (cbrt (- beta alpha))) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (cbrt (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))) 1.0)

rewrite159.0ms

Algorithm

rewrite-expression-head

Rules

72×	`add-exp-log`
39×	`add-cbrt-cube`
28×	`prod-exp` `cbrt-unprod`
27×	`cbrt-undiv` `div-exp`
13×	`*-un-lft-identity`
9×	`pow1` `frac-times`
8×	`cbrt-prod`
7×	`add-sqr-sqrt` `add-cube-cbrt` `flip3-+` `flip-+`
6×	`associate-*r/` `add-log-exp`
5×	`associate-*l/`
4×	`cbrt-div` `associate-l`
3×	`pow-prod-down` `distribute-lft-out`
2×	`pow1/3`
1×	`+-commutative` `associate-r` `sum-log` `*-commutative`

Counts

4 → 91

Calls

4 calls:

7.0ms	(cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
7.0ms	(cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
74.0ms	(* (+ alpha beta) (* (/ (/ (* (cbrt (- beta alpha)) (cbrt (- beta alpha))) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (cbrt (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))))
68.0ms	(+ (* (+ alpha beta) (* (/ (/ (* (cbrt (- beta alpha)) (cbrt (- beta alpha))) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (cbrt (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))) 1.0)

series233.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
39.0ms	(cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
66.0ms	(* (+ alpha beta) (* (/ (/ (* (cbrt (- beta alpha)) (cbrt (- beta alpha))) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (cbrt (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))))
88.0ms	(+ (* (+ alpha beta) (* (/ (/ (* (cbrt (- beta alpha)) (cbrt (- beta alpha))) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (cbrt (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))) 1.0)

simplify97.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 2 (73.0ms)

Iter	Nodes	Cost
0	804	3182
1	3484	2530
2	5002	2456

prune259.0ms

Filtered

61 candidates to 103 candidates (-68.9%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	97	6	103
Fresh	2	5	7
Picked	0	1	1
Done	0	0	0
Total	99	12	111

Merged error: 6.6b

Counts

111 → 12

regimes414.0ms

Accuracy

17.2% (5.3b remaining)

Error of 11.2b against oracle of 5.9b and baseline of 12.4b

bsearch37.0ms

Steps

Iters	Range		Point
7	3.436894675436117e+176	7.544018811387455e+177	7.187494738699348e+177

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	48	27
1	48	27

end0.0ms

sample2.0s

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

358.0ms	6360×	body	80	valid
178.0ms	8000×	pre	80	true
153.0ms	523×	body	1280	valid
133.0ms	562×	body	640	valid
60.0ms	346×	body	320	valid
23.0ms	209×	body	160	valid

Details

sample840.0ms

simplify51.0ms

prune3.0ms

localize13.0ms

rewrite75.0ms

series169.0ms

simplify99.0ms

prune292.0ms

localize14.0ms

rewrite115.0ms

series209.0ms

simplify66.0ms

prune569.0ms

localize22.0ms

rewrite149.0ms

series247.0ms

simplify100.0ms

prune245.0ms

localize26.0ms

rewrite159.0ms

series233.0ms

simplify97.0ms

prune259.0ms

regimes414.0ms

bsearch37.0ms

simplify2.0ms

end0.0ms

sample2.0s

Profiling