Details

analyze80.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	50%	50%	2
0%	50%	50%	3
0%	50%	50%	4
6.2%	43.7%	50%	5
9.4%	28.1%	62.5%	6
12.5%	25%	62.5%	7
15.6%	15.6%	68.8%	8
16.8%	14.4%	68.8%	9
18.5%	8.8%	72.7%	10
19.2%	7.7%	73.1%	11
20.1%	4.6%	75.2%	12
20.5%	4%	75.5%	13
21%	2.4%	76.6%	14

sample30.0ms

Algorithm

intervals

Results

15.0ms	256×	body	80	valid
0.0ms	9×	body	80	invalid
0.0ms	2×	body	80	nan

simplify118.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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

prune6.0ms

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

localize14.0ms

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))))

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)))
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))))

series53.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)))
22.0ms	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
9.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
5.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))

simplify101.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 1 (21.0ms)

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

prune376.0ms

Filtered

105 candidates to 126 candidates (-20.0%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	116	10	126
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	117	10	127

Merged error: 0.0b

Counts

127 → 10

localize11.0ms

Local error

Found 4 expressions with local error:

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

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 85

Calls

4 calls:

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

series71.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(- a (/ 1.0 3.0))
25.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))))
29.0ms	(/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
13.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))

simplify100.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	807	1043
1	3859	978
2	5001	978

prune214.0ms

Filtered

77 candidates to 97 candidates (-26.0%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	95	2	97
Fresh	4	5	9
Picked	1	0	1
Done	0	0	0
Total	100	7	107

Merged error: 0.0b

Counts

107 → 7

localize12.0ms

Local error

Found 4 expressions with local error:

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))))
7.5b	(* (- a (/ 1.0 3.0)) (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand))

rewrite53.0ms

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:

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)))))
9.0ms	(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))

series85.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
15.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
9.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
27.0ms	(* (- a (/ 1.0 3.0)) (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand))

simplify105.0ms

Algorithm

egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 1 (21.0ms)

Iter	Nodes	Cost
0	973	1339
1	4224	1216
2	5001	1216

prune323.0ms

Filtered

99 candidates to 123 candidates (-24.2%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	122	1	123
Fresh	1	5	6
Picked	1	0	1
Done	0	0	0
Total	124	6	130

Merged error: 0.0b

Counts

130 → 6

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(- 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)))))))
0.2b	(/ rand (sqrt (- a (/ 1.0 3.0))))
0.3b	(* (/ 1.0 (sqrt 9.0)) (/ rand (sqrt (- a (/ 1.0 3.0)))))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

130×	`add-sqr-sqrt`
93×	`times-frac`
71×	`*-un-lft-identity`
57×	`sqrt-prod`
53×	`add-cube-cbrt`
36×	`associate-r`
28×	`associate-l`
20×	`add-exp-log` `add-cbrt-cube`
18×	`difference-of-squares`
10×	`unswap-sqr`
9×	`associate-/r*` `distribute-lft-out--`
8×	`pow1`
6×	`flip3--` `flip--` `add-log-exp`
5×	`cbrt-undiv` `frac-times` `div-exp` `prod-exp` `cbrt-unprod`
4×	`sqrt-div` `associate-/r/`
3×	`flip3-+` `associate-r/` `associate-l/` `flip-+` `div-inv` `associate-/l*`
2×	`pow-prod-down` `*-commutative`
1×	`distribute-rgt-in` `sub-neg` `frac-2neg` `distribute-lft-in` `diff-log` `clear-num`

Counts

4 → 183

Calls

4 calls:

6.0ms	(- a (/ 1.0 3.0))
10.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1.0 (sqrt 9.0)) (/ rand (sqrt (- a (/ 1.0 3.0)))))))
10.0ms	(/ rand (sqrt (- a (/ 1.0 3.0))))
26.0ms	(* (/ 1.0 (sqrt 9.0)) (/ rand (sqrt (- a (/ 1.0 3.0)))))

series50.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(- a (/ 1.0 3.0))
19.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1.0 (sqrt 9.0)) (/ rand (sqrt (- a (/ 1.0 3.0)))))))
10.0ms	(/ rand (sqrt (- a (/ 1.0 3.0))))
19.0ms	(* (/ 1.0 (sqrt 9.0)) (/ rand (sqrt (- a (/ 1.0 3.0)))))

simplify46.0ms

Algorithm

egg-herbie

Counts

195 → 195

Iterations

Useful iterations: 1 (25.0ms)

Iter	Nodes	Cost
0	1120	2137
1	5001	2028

prune432.0ms

Filtered

144 candidates to 195 candidates (-35.4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	195	0	195
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	195	6	201

Merged error: 0.0b

Counts

201 → 6

regimes417.0ms

Accuracy

0% (0.1b 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	17	11
1	17	11

end0.0ms

analyze78.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	50%	50%	2
0%	50%	50%	3
0%	50%	50%	4
6.2%	43.7%	50%	5
9.4%	28.1%	62.5%	6
12.5%	25%	62.5%	7
15.6%	15.6%	68.8%	8
16.8%	14.4%	68.8%	9
18.5%	8.8%	72.7%	10
19.2%	7.7%	73.1%	11
20.1%	4.6%	75.2%	12
20.5%	4%	75.5%	13
21%	2.4%	76.6%	14

sample634.0ms

Algorithm

intervals

Results

466.0ms	8000×	body	80	valid
16.0ms	281×	body	80	invalid
13.0ms	238×	body	80	nan

Details

analyze80.0ms

sample30.0ms

simplify118.0ms

prune6.0ms

localize14.0ms

rewrite46.0ms

series53.0ms

simplify101.0ms

prune376.0ms

localize11.0ms

rewrite46.0ms

series71.0ms

simplify100.0ms

prune214.0ms

localize12.0ms

rewrite53.0ms

series85.0ms

simplify105.0ms

prune323.0ms

localize11.0ms

rewrite60.0ms

series50.0ms

simplify46.0ms

prune432.0ms

regimes417.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

analyze78.0ms

sample634.0ms

Profiling