Details

sample32.0ms

Algorithm

intervals

sampling

Space saved by range analysis: 43.768318%

Space saved by search: 43.768318%

Guaranteed chance to sample good point: 100%

Results

15.0ms	256×	body	80	valid
4.0ms	256×	pre	80	true

simplify82.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	33	17
1	114	17
2	563	17
3	4164	17
4	5002	17

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: 4.1b

Counts

2 → 1

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (+ alpha beta) (* beta alpha))
0.0b	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
0.1b	(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
3.9b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite120.0ms

Algorithm

rewrite-expression-head

Rules

804×	`times-frac`
584×	`*-un-lft-identity`
340×	`add-sqr-sqrt` `add-cube-cbrt`
122×	`distribute-lft-out`
82×	`associate-/l*`
54×	`associate-/r/`
29×	`flip3-+` `flip-+`
27×	`div-inv`
20×	`add-exp-log` `add-cbrt-cube`
10×	`cbrt-undiv` `div-exp` `associate-/r*`
9×	`add-log-exp`
4×	`pow1` `associate-/l/`
3×	`frac-2neg` `clear-num` `sum-log`
1×	`+-commutative` `associate-+l+`

Counts

4 → 463

Calls

4 calls:

6.0ms	(+ (+ alpha beta) (* beta alpha))
21.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
40.0ms	(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
19.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series67.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(+ (+ alpha beta) (* beta alpha))
21.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
24.0ms	(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
13.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify145.0ms

Algorithm

egg-herbie

Counts

475 → 475

Iterations

Useful iterations: 1 (33.0ms)

Iter	Nodes	Cost
0	1512	13008
1	5001	12540

prune1.3s

Filtered

280 candidates to 475 candidates (-69.6%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	468	7	475
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	469	7	476

Merged error: 1.4b

Counts

476 → 7

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))))
0.1b	(* (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))) (/ (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
3.9b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
3.9b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite380.0ms

Algorithm

rewrite-expression-head

Rules

862×	`times-frac`
599×	`*-un-lft-identity`
438×	`add-sqr-sqrt`
387×	`sqrt-prod`
349×	`add-cube-cbrt`
258×	`associate-r`
125×	`distribute-lft-out`
63×	`associate-l`
54×	`associate-/r/`
29×	`flip3-+` `flip-+`
27×	`div-inv`
20×	`unswap-sqr`
13×	`add-exp-log` `add-cbrt-cube`
8×	`associate-/l*`
7×	`pow1`
6×	`associate-/r*`
4×	`associate-/l/` `add-log-exp`
3×	`cbrt-undiv` `rem-sqrt-square` `sqrt-div` `div-exp`
2×	`frac-2neg` `prod-exp` `clear-num` `cbrt-unprod`
1×	`frac-times` `sqrt-pow1` `pow1/2` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative`

Counts

4 → 500

Calls

4 calls:

25.0ms	(sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))))
284.0ms	(* (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))) (/ (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
14.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
14.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series107.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))))
24.0ms	(* (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))) (/ (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
12.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
21.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify166.0ms

Algorithm

egg-herbie

Counts

512 → 512

Iterations

Useful iterations: 1 (37.0ms)

Iter	Nodes	Cost
0	1819	15509
1	5001	14700

prune2.6s

Filtered

341 candidates to 512 candidates (-50.1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	512	0	512
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	512	7	519

Merged error: 1.4b

Counts

519 → 7

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)))
0.5b	(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
3.8b	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
3.8b	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

98×	`*-un-lft-identity`
80×	`sqrt-prod`
70×	`times-frac`
56×	`add-sqr-sqrt`
54×	`add-cube-cbrt`
22×	`distribute-lft-out`
13×	`associate-/r*`
11×	`associate-/l*`
10×	`sqrt-div`
8×	`add-exp-log` `add-cbrt-cube`
6×	`pow1` `flip3-+` `flip-+`
4×	`associate-/r/` `associate-/l/` `add-log-exp`
2×	`cbrt-undiv` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `clear-num` `div-inv`
1×	`sqrt-undiv`

Counts

4 → 159

Calls

4 calls:

17.0ms	(/ (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)))
18.0ms	(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
7.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
7.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

series113.0ms

Counts

4 → 12

Calls

4 calls:

75.0ms	(/ (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)))
18.0ms	(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
10.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
10.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

simplify72.0ms

Algorithm

egg-herbie

Counts

171 → 171

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	551	2625
1	2087	2476
2	5001	2422

prune435.0ms

Filtered

103 candidates to 171 candidates (-66.0%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	171	0	171
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	171	7	178

Merged error: 1.4b

Counts

178 → 7

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (+ alpha beta) (* beta alpha))
0.0b	(* (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
2.8b	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (* (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))))
3.9b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

54×	`times-frac`
53×	`*-un-lft-identity`
33×	`add-sqr-sqrt`
31×	`add-cube-cbrt`
22×	`associate-/l*`
20×	`add-exp-log` `add-cbrt-cube`
17×	`flip3-+` `flip-+`
14×	`associate-/r/`
11×	`distribute-lft-out`
9×	`add-log-exp`
8×	`frac-times`
7×	`cbrt-undiv` `div-exp`
6×	`pow1`
4×	`associate-r/` `associate-l` `associate-l/` `associate-/r*` `div-inv`
3×	`associate-r` `prod-exp` `sum-log` `cbrt-unprod` `associate-/l/`
2×	`frac-2neg` `clear-num`
1×	`+-commutative` `distribute-rgt-in` `associate-+l+` `distribute-lft-in` `pow-prod-down` `*-commutative` `unswap-sqr`

Counts

4 → 141

Calls

4 calls:

6.0ms	(+ (+ alpha beta) (* beta alpha))
14.0ms	(* (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
31.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (* (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))))
14.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series47.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(+ (+ alpha beta) (* beta alpha))
7.0ms	(* (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
24.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (* (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))))
13.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify121.0ms

Algorithm

egg-herbie

Counts

153 → 153

Iterations

Useful iterations: 1 (21.0ms)

Iter	Nodes	Cost
0	765	2456
1	4241	2233
2	5001	2233

prune264.0ms

Filtered

111 candidates to 153 candidates (-37.8%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	152	1	153
Fresh	1	3	4
Picked	0	1	1
Done	0	2	2
Total	153	7	160

Merged error: 1.4b

Counts

160 → 7

regimes118.0ms

Accuracy

53.3% (1.1b remaining)

Error of 2.3b against oracle of 1.2b and baseline of 3.6b

bsearch31.0ms

Steps

Iters	Range		Point
8	4.588062755452424e+156	5.495788214791645e+159	5.425582402344228e+159

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	43
1	42	43

end0.0ms

sample819.0ms

Algorithm

intervals

sampling

Space saved by range analysis: 43.768318%

Space saved by search: 43.768318%

Guaranteed chance to sample good point: 100%

Results

482.0ms	8000×	body	80	valid
131.0ms	8000×	pre	80	true

Details

sample32.0ms

simplify82.0ms

prune3.0ms

localize12.0ms

rewrite120.0ms

series67.0ms

simplify145.0ms

prune1.3s

localize18.0ms

rewrite380.0ms

series107.0ms

simplify166.0ms

prune2.6s

localize16.0ms

rewrite56.0ms

series113.0ms

simplify72.0ms

prune435.0ms

localize12.0ms

rewrite70.0ms

series47.0ms

simplify121.0ms

prune264.0ms

regimes118.0ms

bsearch31.0ms

simplify2.0ms

end0.0ms

sample819.0ms

Profiling