Details

sample407.0ms

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 77.355957%

Guaranteed chance to sample good point: 94.67655%

Results

14.0ms	256×	body	80	valid
0.0ms	5×	body	80	invalid
0.0ms	2×	body	80	nan

simplify94.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	27	10
1	72	10
2	192	10
3	437	10
4	816	10
5	1578	10
6	2764	10
7	5002	10

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: 0.2b

Counts

2 → 1

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)))
0.2b	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
0.2b	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
0.4b	(sqrt (* 9.0 (- a (/ 1.0 3.0))))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

36×	`add-sqr-sqrt`
26×	`*-un-lft-identity` `times-frac`
24×	`add-cube-cbrt` `associate-l`
13×	`add-exp-log` `add-cbrt-cube`
11×	`pow1`
8×	`associate-*r/` `sqrt-prod`
6×	`flip3--` `sqrt-div` `associate-r` `flip--`
4×	`frac-times` `associate-/r*` `associate-/r/` `add-log-exp`
3×	`flip3-+` `pow-prod-down` `associate-l/` `prod-exp` `cbrt-unprod` `flip-+` `associate-/l` `unswap-sqr`
2×	`cbrt-undiv` `sqrt-pow1` `div-exp` `*-commutative` `div-inv` `difference-of-squares`
1×	`distribute-rgt-in` `frac-2neg` `distribute-lft-in` `pow1/2` `clear-num` `distribute-lft-out--`

Counts

4 → 114

Calls

4 calls:

10.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)))
9.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
16.0ms	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
7.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))

series49.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)))
9.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
19.0ms	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
6.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))

simplify103.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 1 (21.0ms)

Iter	Nodes	Cost
0	1008	1422
1	4619	1341
2	5001	1341

prune351.0ms

Filtered

105 candidates to 126 candidates (-20.0%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	117	9	126
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	118	9	127

Merged error: 0.0b

Counts

127 → 9

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (- a (/ 1.0 3.0)))
0.1b	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ (/ 1.0 (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0)))) rand)))
0.2b	(* (/ (/ 1.0 (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0)))) rand)
0.4b	(/ (/ 1.0 (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0))))

rewrite122.0ms

Algorithm

rewrite-expression-head

Rules

795×	`times-frac`
608×	`add-sqr-sqrt`
452×	`sqrt-prod`
440×	`*-un-lft-identity`
346×	`add-cube-cbrt`
210×	`associate-l`
94×	`difference-of-squares`
47×	`distribute-lft-out--`
22×	`associate-/l*`
21×	`div-inv`
20×	`add-exp-log` `add-cbrt-cube`
9×	`pow1` `associate-/r*`
8×	`unswap-sqr`
6×	`cbrt-undiv` `flip3--` `sqrt-div` `div-exp` `associate-r` `flip--`
4×	`frac-times` `prod-exp` `associate-/r/` `cbrt-unprod` `add-log-exp`
3×	`flip3-+` `associate-*l/` `flip-+`
2×	`associate-r/` `pow-prod-down` `-commutative`
1×	`distribute-rgt-in` `rem-sqrt-square` `frac-2neg` `distribute-lft-in` `sqrt-pow1` `pow1/2` `clear-num` `associate-/l/`

Counts

4 → 525

Calls

4 calls:

7.0ms	(sqrt (- a (/ 1.0 3.0)))
10.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ (/ 1.0 (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0)))) rand)))
44.0ms	(* (/ (/ 1.0 (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0)))) rand)
18.0ms	(/ (/ 1.0 (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0))))

series59.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(sqrt (- a (/ 1.0 3.0)))
22.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ (/ 1.0 (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0)))) rand)))
22.0ms	(* (/ (/ 1.0 (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0)))) rand)
11.0ms	(/ (/ 1.0 (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0))))

simplify100.0ms

Algorithm

egg-herbie

Counts

537 → 537

Iterations

Useful iterations: 1 (34.0ms)

Iter	Nodes	Cost
0	1838	6805
1	5001	6554

prune1.7s

Filtered

326 candidates to 537 candidates (-64.7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	535	2	537
Fresh	2	6	8
Picked	1	0	1
Done	0	0	0
Total	538	8	546

Merged error: 0b

Counts

546 → 8

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1 (sqrt 9.0)) (* (/ 1.0 (sqrt (- a (/ 1.0 3.0)))) rand))))
0.2b	(* (/ 1.0 (sqrt (- a (/ 1.0 3.0)))) rand)
0.3b	(/ 1.0 (sqrt (- a (/ 1.0 3.0))))
0.3b	(* (/ 1 (sqrt 9.0)) (* (/ 1.0 (sqrt (- a (/ 1.0 3.0)))) rand))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

104×	`add-sqr-sqrt`
82×	`times-frac`
70×	`*-un-lft-identity`
61×	`associate-l`
54×	`add-cube-cbrt`
52×	`add-exp-log` `sqrt-prod`
34×	`add-cbrt-cube`
23×	`prod-exp`
16×	`difference-of-squares`
13×	`pow1` `cbrt-unprod`
12×	`div-exp`
9×	`associate-/r*`
8×	`distribute-lft-out--`
7×	`cbrt-undiv` `associate-r`
6×	`associate-*l/`
5×	`frac-times` `flip3--` `pow-prod-down` `flip--`
4×	`sqrt-div` `associate-/r/` `add-log-exp` `unswap-sqr`
3×	`rec-exp` `flip3-+` `1-exp` `associate-r/` `-commutative` `flip-+` `div-inv` `associate-/l*`
1×	`distribute-rgt-in` `frac-2neg` `distribute-lft-in` `clear-num`

Counts

4 → 191

Calls

4 calls:

11.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1 (sqrt 9.0)) (* (/ 1.0 (sqrt (- a (/ 1.0 3.0)))) rand))))
14.0ms	(* (/ 1.0 (sqrt (- a (/ 1.0 3.0)))) rand)
9.0ms	(/ 1.0 (sqrt (- a (/ 1.0 3.0))))
18.0ms	(* (/ 1 (sqrt 9.0)) (* (/ 1.0 (sqrt (- a (/ 1.0 3.0)))) rand))

series67.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1 (sqrt 9.0)) (* (/ 1.0 (sqrt (- a (/ 1.0 3.0)))) rand))))
18.0ms	(* (/ 1.0 (sqrt (- a (/ 1.0 3.0)))) rand)
6.0ms	(/ 1.0 (sqrt (- a (/ 1.0 3.0))))
27.0ms	(* (/ 1 (sqrt 9.0)) (* (/ 1.0 (sqrt (- a (/ 1.0 3.0)))) rand))

simplify53.0ms

Algorithm

egg-herbie

Counts

203 → 203

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1259	2249
1	5001	2036

prune513.0ms

Filtered

144 candidates to 203 candidates (-41.0%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	202	1	203
Fresh	1	6	7
Picked	0	1	1
Done	0	0	0
Total	203	8	211

Merged error: 0b

Counts

211 → 8

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ 1.0 (sqrt (- a (/ 1.0 3.0)))) rand)
0.2b	(/ (* (- a (/ 1.0 3.0)) (* (/ 1.0 (sqrt (- a (/ 1.0 3.0)))) rand)) (sqrt 9.0))
0.3b	(/ 1.0 (sqrt (- a (/ 1.0 3.0))))
6.1b	(* (- a (/ 1.0 3.0)) (* (/ 1.0 (sqrt (- a (/ 1.0 3.0)))) rand))

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

92×	`add-sqr-sqrt`
70×	`times-frac`
60×	`*-un-lft-identity`
49×	`sqrt-prod`
44×	`add-cube-cbrt`
39×	`associate-l`
34×	`add-exp-log` `add-cbrt-cube`
16×	`difference-of-squares`
15×	`associate-/r*`
12×	`prod-exp` `cbrt-unprod`
11×	`pow1` `associate-*l/`
8×	`cbrt-undiv` `div-exp` `distribute-lft-out--`
6×	`flip3--` `flip--`
5×	`associate-/l/`
4×	`frac-times` `sqrt-div` `associate-r` `pow-prod-down` `associate-/r/` `associate-/l*` `add-log-exp`
3×	`div-inv` `unswap-sqr`
2×	`frac-2neg` `associate-r/` `clear-num` `-commutative`

Counts

4 → 170

Calls

4 calls:

14.0ms	(* (/ 1.0 (sqrt (- a (/ 1.0 3.0)))) rand)
20.0ms	(/ (* (- a (/ 1.0 3.0)) (* (/ 1.0 (sqrt (- a (/ 1.0 3.0)))) rand)) (sqrt 9.0))
9.0ms	(/ 1.0 (sqrt (- a (/ 1.0 3.0))))
18.0ms	(* (- a (/ 1.0 3.0)) (* (/ 1.0 (sqrt (- a (/ 1.0 3.0)))) rand))

series58.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(* (/ 1.0 (sqrt (- a (/ 1.0 3.0)))) rand)
20.0ms	(/ (* (- a (/ 1.0 3.0)) (* (/ 1.0 (sqrt (- a (/ 1.0 3.0)))) rand)) (sqrt 9.0))
6.0ms	(/ 1.0 (sqrt (- a (/ 1.0 3.0))))
15.0ms	(* (- a (/ 1.0 3.0)) (* (/ 1.0 (sqrt (- a (/ 1.0 3.0)))) rand))

simplify154.0ms

Algorithm

egg-herbie

Counts

182 → 182

Iterations

Useful iterations: 1 (38.0ms)

Iter	Nodes	Cost
0	1066	1924
1	4717	1720
2	5002	1720

prune464.0ms

Filtered

134 candidates to 182 candidates (-35.8%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	180	2	182
Fresh	3	3	6
Picked	0	1	1
Done	0	1	1
Total	183	7	190

Merged error: 0b

Counts

190 → 7

regimes162.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	12
1	22	12

end0.0ms

sample1.0s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 77.355957%

Guaranteed chance to sample good point: 94.67655%

Results

458.0ms	8000×	body	80	valid
7.0ms	126×	body	80	invalid
6.0ms	125×	body	80	nan

Details

sample407.0ms

simplify94.0ms

prune3.0ms

localize10.0ms

rewrite46.0ms

series49.0ms

simplify103.0ms

prune351.0ms

localize12.0ms

rewrite122.0ms

series59.0ms

simplify100.0ms

prune1.7s

localize17.0ms

rewrite61.0ms

series67.0ms

simplify53.0ms

prune513.0ms

localize15.0ms

rewrite71.0ms

series58.0ms

simplify154.0ms

prune464.0ms

regimes162.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample1.0s

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