Details

sample223.0ms

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 77.264404%

Guaranteed chance to sample good point: 93.66443%

Results

18.0ms	256×	body	80	valid
0.0ms	5×	body	80	invalid
0.0ms	5×	body	80	nan

simplify104.0ms

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: 0.1b

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))))) rand)
0.3b	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
0.4b	(sqrt (* 9.0 (- a (/ 1.0 3.0))))

rewrite43.0ms

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)))
14.0ms	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
9.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
7.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))

series57.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)))
21.0ms	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
10.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
9.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))

simplify108.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 1 (23.0ms)

Iter	Nodes	Cost
0	1008	1422
1	4617	1341
2	5001	1341

prune358.0ms

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

localize11.0ms

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)
0.3b	(/ (/ 1.0 (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0))))

rewrite120.0ms

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:

6.0ms	(sqrt (- a (/ 1.0 3.0)))
9.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ (/ 1.0 (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0)))) rand)))
41.0ms	(* (/ (/ 1.0 (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0)))) rand)
16.0ms	(/ (/ 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)))
17.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ (/ 1.0 (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0)))) rand)))
24.0ms	(* (/ (/ 1.0 (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0)))) rand)
13.0ms	(/ (/ 1.0 (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0))))

simplify107.0ms

Algorithm

egg-herbie

Counts

537 → 537

Iterations

Useful iterations: 1 (38.0ms)

Iter	Nodes	Cost
0	1838	6805
1	5001	6554

prune1.7s

Filtered

326 candidates to 537 candidates (-64.7%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	535	2	537
Fresh	3	5	8
Picked	0	1	1
Done	0	0	0
Total	538	8	546

Merged error: 0.0b

Counts

546 → 8

localize11.0ms

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

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

56×	`add-sqr-sqrt`
35×	`*-un-lft-identity`
33×	`times-frac`
28×	`associate-l` `sqrt-prod`
25×	`add-cube-cbrt`
20×	`add-exp-log` `add-cbrt-cube`
9×	`pow1` `associate-/r*`
8×	`difference-of-squares`
7×	`associate-r`
5×	`cbrt-undiv` `flip3--` `div-exp` `prod-exp` `flip--` `cbrt-unprod`
4×	`frac-times` `sqrt-div` `associate-*l/` `distribute-lft-out--` `add-log-exp` `unswap-sqr`
3×	`flip3-+` `flip-+`
2×	`associate-r/` `pow-prod-down` `associate-/r/` `-commutative` `div-inv`
1×	`distribute-rgt-in` `rem-sqrt-square` `frac-2neg` `distribute-lft-in` `sqrt-pow1` `pow1/2` `clear-num` `associate-/l/` `distribute-lft-out` `associate-/l*`

Counts

4 → 130

Calls

4 calls:

6.0ms	(sqrt (- a (/ 1.0 3.0)))
20.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (/ (* (/ 1.0 (sqrt 9.0)) rand) (sqrt (- a (/ 1.0 3.0))))))
12.0ms	(/ (* (/ 1.0 (sqrt 9.0)) rand) (sqrt (- a (/ 1.0 3.0))))
7.0ms	(* (/ 1.0 (sqrt 9.0)) rand)

series47.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(sqrt (- a (/ 1.0 3.0)))
17.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (/ (* (/ 1.0 (sqrt 9.0)) rand) (sqrt (- a (/ 1.0 3.0))))))
20.0ms	(/ (* (/ 1.0 (sqrt 9.0)) rand) (sqrt (- a (/ 1.0 3.0))))
6.0ms	(* (/ 1.0 (sqrt 9.0)) rand)

simplify115.0ms

Algorithm

egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 2 (97.0ms)

Iter	Nodes	Cost
0	926	1411
1	4538	1315
2	5001	1305

prune327.0ms

Filtered

103 candidates to 142 candidates (-37.9%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	140	2	142
Fresh	1	5	6
Picked	1	0	1
Done	0	1	1
Total	142	8	150

Merged error: 0.0b

Counts

150 → 8

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (- a (/ 1.0 3.0)))
0.3b	(/ (* (/ 1.0 (sqrt 9.0)) rand) (sqrt (- a (/ 1.0 3.0))))
0.3b	(* (/ 1.0 (sqrt 9.0)) rand)
8.5b	(* (- a (/ 1.0 3.0)) (/ (* (/ 1.0 (sqrt 9.0)) rand) (sqrt (- a (/ 1.0 3.0)))))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

63×	`add-sqr-sqrt`
43×	`times-frac`
37×	`*-un-lft-identity`
34×	`sqrt-prod`
32×	`add-exp-log` `add-cbrt-cube`
28×	`associate-l`
27×	`add-cube-cbrt`
18×	`associate-r`
10×	`prod-exp` `cbrt-unprod` `difference-of-squares`
9×	`pow1` `cbrt-undiv` `div-exp` `associate-/r*`
6×	`sqrt-div`
5×	`flip3--` `flip--` `distribute-lft-out--`
4×	`associate-*l/` `associate-/r/` `add-log-exp` `unswap-sqr`
3×	`div-inv`
2×	`frac-times` `pow-prod-down` `*-commutative`
1×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `associate-r/` `clear-num` `associate-/l/` `associate-/l`

Counts

4 → 142

Calls

4 calls:

6.0ms	(sqrt (- a (/ 1.0 3.0)))
12.0ms	(/ (* (/ 1.0 (sqrt 9.0)) rand) (sqrt (- a (/ 1.0 3.0))))
7.0ms	(* (/ 1.0 (sqrt 9.0)) rand)
23.0ms	(* (- a (/ 1.0 3.0)) (/ (* (/ 1.0 (sqrt 9.0)) rand) (sqrt (- a (/ 1.0 3.0)))))

series56.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(sqrt (- a (/ 1.0 3.0)))
24.0ms	(/ (* (/ 1.0 (sqrt 9.0)) rand) (sqrt (- a (/ 1.0 3.0))))
6.0ms	(* (/ 1.0 (sqrt 9.0)) rand)
22.0ms	(* (- a (/ 1.0 3.0)) (/ (* (/ 1.0 (sqrt 9.0)) rand) (sqrt (- a (/ 1.0 3.0)))))

simplify118.0ms

Algorithm

egg-herbie

Counts

154 → 154

Iterations

Useful iterations: 1 (23.0ms)

Iter	Nodes	Cost
0	916	1506
1	4689	1354
2	5002	1354

prune355.0ms

Filtered

112 candidates to 154 candidates (-37.5%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	150	4	154
Fresh	5	1	6
Picked	0	1	1
Done	0	1	1
Total	155	7	162

Merged error: 0b

Counts

162 → 7

regimes166.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	14
1	19	14

end0.0ms

sample882.0ms

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 77.264404%

Guaranteed chance to sample good point: 93.66443%

Results

462.0ms	8000×	body	80	valid
11.0ms	190×	body	80	invalid
7.0ms	123×	body	80	nan

Details

sample223.0ms

simplify104.0ms

prune3.0ms

localize10.0ms

rewrite43.0ms

series57.0ms

simplify108.0ms

prune358.0ms

localize11.0ms

rewrite120.0ms

series59.0ms

simplify107.0ms

prune1.7s

localize11.0ms

rewrite50.0ms

series47.0ms

simplify115.0ms

prune327.0ms

localize12.0ms

rewrite54.0ms

series56.0ms

simplify118.0ms

prune355.0ms

regimes166.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample882.0ms

Profiling