Details

sample82.0ms

Algorithm

intervals

Results

40.0ms	875×	body	80	nan
16.0ms	286×	body	80	valid

simplify96.0ms

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

prune2.0ms

Filtered

1 candidates to 0 candidates (0.0%)

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

localize11.0ms

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)))
0.1b	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
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)))))

rewrite45.0ms

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)))
7.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
13.0ms	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
10.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))

series512.0ms

Counts

4 → 12

Calls

4 calls:

117.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)))
72.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
182.0ms	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
140.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))

simplify91.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 1 (18.0ms)

Iter	Nodes	Cost
0	823	1338
1	3607	1238
2	5002	1238

prune362.0ms

Filtered

126 candidates to 105 candidates (83.3%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	119	7	126
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	120	7	127

Merged error: 0b

Counts

127 → 7

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
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)))))
6.7b	(* (- a (/ 1.0 3.0)) (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
26×	`times-frac`
25×	`*-un-lft-identity`
24×	`associate-l`
23×	`add-cube-cbrt`
20×	`add-exp-log` `add-cbrt-cube`
14×	`pow1`
8×	`sqrt-prod`
7×	`associate-*r/` `prod-exp` `cbrt-unprod`
6×	`sqrt-div` `associate-*l/`
5×	`flip3--` `pow-prod-down` `flip--`
4×	`associate-r` `associate-/r*` `associate-/r/` `add-log-exp`
3×	`cbrt-undiv` `div-exp` `associate-/l*`
2×	`frac-times` `sqrt-pow1` `*-commutative` `div-inv` `difference-of-squares` `unswap-sqr`
1×	`frac-2neg` `pow1/2` `clear-num` `distribute-lft-out--`

Counts

4 → 111

Calls

4 calls:

7.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
15.0ms	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
10.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
18.0ms	(* (- a (/ 1.0 3.0)) (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand))

series550.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
178.0ms	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
142.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
158.0ms	(* (- a (/ 1.0 3.0)) (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand))

simplify74.0ms

Algorithm

egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 1 (16.0ms)

Iter	Nodes	Cost
0	754	1232
1	3049	1085
2	5002	1085

prune302.0ms

Filtered

123 candidates to 99 candidates (80.5%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	122	1	123
Fresh	1	5	6
Picked	0	1	1
Done	0	0	0
Total	123	7	130

Merged error: 0b

Counts

130 → 7

localize12.0ms

Local error

Found 4 expressions with local error:

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

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 118

Calls

4 calls:

10.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1.0 (* (sqrt 9.0) (sqrt (- a (/ 1.0 3.0))))) rand)))
14.0ms	(* (/ 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)))))
11.0ms	(* (sqrt 9.0) (sqrt (- a (/ 1.0 3.0))))

series638.0ms

Counts

4 → 12

Calls

4 calls:

157.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1.0 (* (sqrt 9.0) (sqrt (- a (/ 1.0 3.0))))) rand)))
216.0ms	(* (/ 1.0 (* (sqrt 9.0) (sqrt (- a (/ 1.0 3.0))))) rand)
177.0ms	(/ 1.0 (* (sqrt 9.0) (sqrt (- a (/ 1.0 3.0)))))
88.0ms	(* (sqrt 9.0) (sqrt (- a (/ 1.0 3.0))))

simplify108.0ms

Algorithm

egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 1 (21.0ms)

Iter	Nodes	Cost
0	846	1427
1	4127	1300
2	5001	1300

prune322.0ms

Filtered

130 candidates to 96 candidates (73.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	128	2	130
Fresh	3	2	5
Picked	1	0	1
Done	0	1	1
Total	132	5	137

Merged error: 0b

Counts

137 → 5

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

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

441×	`times-frac`
343×	`add-sqr-sqrt`
259×	`*-un-lft-identity`
258×	`sqrt-prod`
205×	`add-cube-cbrt`
54×	`difference-of-squares`
36×	`associate-/l*`
27×	`distribute-lft-out--`
18×	`sqrt-div`
16×	`associate-/r/`
15×	`associate-/r*`
13×	`add-exp-log` `add-cbrt-cube`
12×	`flip3--` `flip--`
9×	`div-inv`
7×	`pow1`
6×	`associate-l`
4×	`cbrt-undiv` `frac-times` `div-exp` `add-log-exp`
3×	`flip3-+` `associate-r` `flip-+`
2×	`frac-2neg` `associate-r/` `associate-l/` `clear-num`
1×	`distribute-rgt-in` `rem-sqrt-square` `distribute-lft-in` `sqrt-pow1` `pow1/2` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `associate-/l/` `unswap-sqr`

Counts

4 → 354

Calls

4 calls:

6.0ms	(sqrt (- a (/ 1.0 3.0)))
10.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* 1.0 (/ (/ rand (sqrt (- a (/ 1.0 3.0)))) (sqrt 9.0)))))
21.0ms	(/ (/ rand (sqrt (- a (/ 1.0 3.0)))) (sqrt 9.0))
9.0ms	(/ rand (sqrt (- a (/ 1.0 3.0))))

series678.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(sqrt (- a (/ 1.0 3.0)))
153.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* 1.0 (/ (/ rand (sqrt (- a (/ 1.0 3.0)))) (sqrt 9.0)))))
400.0ms	(/ (/ rand (sqrt (- a (/ 1.0 3.0)))) (sqrt 9.0))
87.0ms	(/ rand (sqrt (- a (/ 1.0 3.0))))

simplify79.0ms

Algorithm

egg-herbie

Counts

366 → 366

Iterations

Useful iterations: 1 (30.0ms)

Iter	Nodes	Cost
0	1354	5061
1	5001	4787

prune766.0ms

Filtered

366 candidates to 215 candidates (58.7%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	366	0	366
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	366	5	371

Merged error: 0b

Counts

371 → 5

regimes70.0ms

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	13
1	19	13

end0.0ms

sample2.4s

Algorithm

intervals

Results

1.3s	28093×	body	80	nan
440.0ms	9142×	body	80	valid

Details

sample82.0ms

simplify96.0ms

prune2.0ms

localize11.0ms

rewrite45.0ms

series512.0ms

simplify91.0ms

prune362.0ms

localize13.0ms

rewrite54.0ms

series550.0ms

simplify74.0ms

prune302.0ms

localize12.0ms

rewrite51.0ms

series638.0ms

simplify108.0ms

prune322.0ms

localize12.0ms

rewrite69.0ms

series678.0ms

simplify79.0ms

prune766.0ms

regimes70.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample2.4s

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