Details

analyze128.0ms

Algorithm: search

sample27.0ms

Algorithm

intervals

Results

17.0ms	256×	body	80	valid
0.0ms	7×	body	80	nan
0.0ms	4×	body	80	invalid

simplify92.0ms

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

series50.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)))
6.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
20.0ms	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
10.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))

simplify124.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 1 (21.0ms)

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

prune417.0ms

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

localize10.0ms

Local error

Found 4 expressions with local error:

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

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 97

Calls

4 calls:

10.0ms	(* 9.0 (- a (/ 1.0 3.0)))
13.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))))
7.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
11.0ms	(/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))

series40.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(* 9.0 (- a (/ 1.0 3.0)))
14.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))))
5.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
17.0ms	(/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))

simplify89.0ms

Algorithm

egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 1 (19.0ms)

Iter	Nodes	Cost
0	870	1101
1	4263	1027
2	5001	1027

prune240.0ms

Filtered

83 candidates to 109 candidates (-31.3%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	106	3	109
Fresh	4	4	8
Picked	1	0	1
Done	0	0	0
Total	111	7	118

Merged error: 0.0b

Counts

118 → 7

localize11.0ms

Local error

Found 2 expressions with local error:

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

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 160

Calls

2 calls:

33.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (/ (/ (* 1.0 rand) (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0))))))
14.0ms	(/ (/ (* 1.0 rand) (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0))))

series34.0ms

Counts

2 → 6

Calls

2 calls:

15.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (/ (/ (* 1.0 rand) (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0))))))
19.0ms	(/ (/ (* 1.0 rand) (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0))))

simplify111.0ms

Algorithm

egg-herbie

Counts

166 → 166

Iterations

Useful iterations: 1 (22.0ms)

Iter	Nodes	Cost
0	1042	2425
1	4911	2278
2	5001	2278

prune373.0ms

Filtered

102 candidates to 166 candidates (-62.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	165	1	166
Fresh	1	5	6
Picked	0	1	1
Done	0	0	0
Total	166	7	173

Merged error: 0.0b

Counts

173 → 7

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	(/ (sqrt (* 9.0 (- a (/ 1.0 3.0)))) rand)
0.8b	(/ 1.0 (/ (sqrt (* 9.0 (- a (/ 1.0 3.0)))) rand))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 160

Calls

4 calls:

22.0ms	(* (- 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	(/ (sqrt (* 9.0 (- a (/ 1.0 3.0)))) rand)
15.0ms	(/ 1.0 (/ (sqrt (* 9.0 (- a (/ 1.0 3.0)))) rand))

series66.0ms

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))))
6.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
25.0ms	(/ (sqrt (* 9.0 (- a (/ 1.0 3.0)))) rand)
21.0ms	(/ 1.0 (/ (sqrt (* 9.0 (- a (/ 1.0 3.0)))) rand))

simplify49.0ms

Algorithm

egg-herbie

Counts

172 → 172

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1172	2120
1	5001	2032

prune435.0ms

Filtered

146 candidates to 172 candidates (-17.8%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	172	0	172
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	172	7	179

Merged error: 0.0b

Counts

179 → 7

regimes158.0ms

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

analyze73.0ms

Algorithm: search

sample605.0ms

Algorithm

intervals

Results

440.0ms	8000×	body	80	valid
14.0ms	258×	body	80	invalid
11.0ms	226×	body	80	nan

Details

analyze128.0ms

sample27.0ms

simplify92.0ms

prune3.0ms

localize10.0ms

rewrite45.0ms

series50.0ms

simplify124.0ms

prune417.0ms

localize10.0ms

rewrite44.0ms

series40.0ms

simplify89.0ms

prune240.0ms

localize11.0ms

rewrite57.0ms

series34.0ms

simplify111.0ms

prune373.0ms

localize11.0ms

rewrite60.0ms

series66.0ms

simplify49.0ms

prune435.0ms

regimes158.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

analyze73.0ms

sample605.0ms

Profiling