Details

sample80.0ms

Algorithm

intervals

Results

38.0ms	845×	body	80	nan
16.0ms	300×	body	80	valid

simplify91.0ms

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: 0.2b

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

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

series523.0ms

Counts

4 → 12

Calls

4 calls:

124.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)))
75.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
140.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
183.0ms	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)

simplify88.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 1 (18.0ms)

Iter	Nodes	Cost
0	823	1338
1	3609	1238
2	5001	1238

prune331.0ms

Filtered

126 candidates to 105 candidates (83.3%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	118	8	126
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	119	8	127

Merged error: 0b

Counts

127 → 8

localize11.0ms

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

rewrite53.0ms

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)))
12.0ms	(* (sqrt 9.0) (sqrt (- a (/ 1.0 3.0))))
12.0ms	(/ 1.0 (* (sqrt 9.0) (sqrt (- a (/ 1.0 3.0)))))
15.0ms	(* (/ 1.0 (* (sqrt 9.0) (sqrt (- a (/ 1.0 3.0))))) rand)

series659.0ms

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)))
91.0ms	(* (sqrt 9.0) (sqrt (- a (/ 1.0 3.0))))
184.0ms	(/ 1.0 (* (sqrt 9.0) (sqrt (- a (/ 1.0 3.0)))))
226.0ms	(* (/ 1.0 (* (sqrt 9.0) (sqrt (- a (/ 1.0 3.0))))) rand)

simplify106.0ms

Algorithm

egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 2 (92.0ms)

Iter	Nodes	Cost
0	846	1427
1	4130	1300
2	5002	1296

prune304.0ms

Filtered

130 candidates to 95 candidates (73.1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	129	1	130
Fresh	2	5	7
Picked	0	1	1
Done	0	0	0
Total	131	7	138

Merged error: 0b

Counts

138 → 7

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

rewrite73.0ms

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

series493.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(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)))))
89.0ms	(/ rand (sqrt (- a (/ 1.0 3.0))))
207.0ms	(/ (/ rand (sqrt (- a (/ 1.0 3.0)))) (sqrt 9.0))

simplify81.0ms

Algorithm

egg-herbie

Counts

366 → 366

Iterations

Useful iterations: 1 (30.0ms)

Iter	Nodes	Cost
0	1354	5061
1	5001	4790

prune745.0ms

Filtered

366 candidates to 215 candidates (58.7%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	365	1	366
Fresh	2	3	5
Picked	0	1	1
Done	0	1	1
Total	367	6	373

Merged error: 0b

Counts

373 → 6

localize12.0ms

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)
0.2b	(/ 1.0 (sqrt (- a (/ 1.0 3.0))))
0.4b	(* (/ 1 (sqrt 9.0)) (* (/ 1.0 (sqrt (- a (/ 1.0 3.0)))) rand))

rewrite67.0ms

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:

10.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1 (sqrt 9.0)) (* (/ 1.0 (sqrt (- a (/ 1.0 3.0)))) rand))))
15.0ms	(* (/ 1.0 (sqrt (- a (/ 1.0 3.0)))) rand)
9.0ms	(/ 1.0 (sqrt (- a (/ 1.0 3.0))))
23.0ms	(* (/ 1 (sqrt 9.0)) (* (/ 1.0 (sqrt (- a (/ 1.0 3.0)))) rand))

series629.0ms

Counts

4 → 12

Calls

4 calls:

168.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1 (sqrt 9.0)) (* (/ 1.0 (sqrt (- a (/ 1.0 3.0)))) rand))))
156.0ms	(* (/ 1.0 (sqrt (- a (/ 1.0 3.0)))) rand)
80.0ms	(/ 1.0 (sqrt (- a (/ 1.0 3.0))))
224.0ms	(* (/ 1 (sqrt 9.0)) (* (/ 1.0 (sqrt (- a (/ 1.0 3.0)))) rand))

simplify46.0ms

Algorithm

egg-herbie

Counts

203 → 203

Iterations

Useful iterations: 1 (25.0ms)

Iter	Nodes	Cost
0	1086	2160
1	5001	1926

prune441.0ms

Filtered

203 candidates to 144 candidates (70.9%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	202	1	203
Fresh	1	2	3
Picked	0	1	1
Done	0	2	2
Total	203	6	209

Merged error: 0b

Counts

209 → 6

regimes199.0ms

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	17	11
1	17	11

end0.0ms

sample2.3s

Algorithm

intervals

Results

1.2s	27100×	body	80	nan
440.0ms	9169×	body	80	valid