Details

sample167.0ms

Algorithm

intervals

sampling

Space saved by range analysis: 77.378065%

Space saved by search: 0.097632%

Guaranteed chance to sample good point: 0%

Results

17.0ms	256×	body	80	valid
0.0ms	5×	body	80	nan
0.0ms	4×	body	80	invalid

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

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

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)))
0.2b	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
0.3b	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
0.6b	(sqrt (* 9.0 (- a (/ 1.0 3.0))))

rewrite44.0ms

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

series52.0ms

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

simplify105.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 1 (22.0ms)

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

prune341.0ms

Filtered

105 candidates to 126 candidates (-20.0%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	120	6	126
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	121	6	127

Merged error: 0.0b

Counts

127 → 6

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)))))))
0.3b	(/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
0.6b	(sqrt (* 9.0 (- a (/ 1.0 3.0))))

rewrite45.0ms

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:

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

series41.0ms

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

simplify93.0ms

Algorithm

egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 1 (20.0ms)

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

prune219.0ms

Filtered

83 candidates to 109 candidates (-31.3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	107	2	109
Fresh	2	3	5
Picked	0	1	1
Done	0	0	0
Total	109	6	115

Merged error: 0.0b

Counts

115 → 6

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	(/ (sqrt (* 9.0 (- a (/ 1.0 3.0)))) rand)
0.6b	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
0.8b	(/ 1.0 (/ (sqrt (* 9.0 (- a (/ 1.0 3.0)))) rand))

rewrite58.0ms

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))))
10.0ms	(/ (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))

series65.0ms

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))))
21.0ms	(/ (sqrt (* 9.0 (- a (/ 1.0 3.0)))) rand)
6.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
23.0ms	(/ 1.0 (/ (sqrt (* 9.0 (- a (/ 1.0 3.0)))) rand))

simplify48.0ms

Algorithm

egg-herbie

Counts

172 → 172

Iterations

Useful iterations: 1 (26.0ms)

Iter	Nodes	Cost
0	1172	2120
1	5001	2032

prune424.0ms

Filtered

146 candidates to 172 candidates (-17.8%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	171	1	172
Fresh	0	4	4
Picked	0	1	1
Done	1	0	1
Total	172	6	178

Merged error: 0.0b

Counts

178 → 6

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(- a (/ 1.0 3.0))
0.0b	(sqrt (- a (/ 1.0 3.0)))
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))))

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

164×	`times-frac`
132×	`add-sqr-sqrt`
102×	`sqrt-prod`
89×	`*-un-lft-identity`
59×	`add-cube-cbrt`
28×	`difference-of-squares`
15×	`add-exp-log` `add-cbrt-cube`
14×	`distribute-lft-out--`
11×	`div-inv`
10×	`associate-/l*`
9×	`associate-/r*`
7×	`pow1`
6×	`flip3--` `associate-l` `flip--` `add-log-exp`
5×	`cbrt-undiv` `div-exp`
4×	`frac-times` `sqrt-div` `associate-r`
3×	`flip3-+` `flip-+`
2×	`associate-r/` `associate-l/` `prod-exp` `associate-/r/` `cbrt-unprod`
1×	`distribute-rgt-in` `sub-neg` `rem-sqrt-square` `frac-2neg` `distribute-lft-in` `sqrt-pow1` `pow1/2` `diff-log` `pow-prod-down` `clear-num` `*-commutative` `associate-/l/` `distribute-lft-out` `unswap-sqr`

Counts

4 → 193

Calls

4 calls:

6.0ms	(- a (/ 1.0 3.0))
6.0ms	(sqrt (- a (/ 1.0 3.0)))
35.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (/ (/ (* 1.0 rand) (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0))))))
17.0ms	(/ (/ (* 1.0 rand) (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0))))

series44.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(- a (/ 1.0 3.0))
4.0ms	(sqrt (- a (/ 1.0 3.0)))
16.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (/ (/ (* 1.0 rand) (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0))))))
23.0ms	(/ (/ (* 1.0 rand) (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0))))

simplify51.0ms

Algorithm

egg-herbie

Counts

205 → 205

Iterations

Useful iterations: 1 (25.0ms)

Iter	Nodes	Cost
0	1119	2653
1	5001	2497

prune413.0ms

Filtered

132 candidates to 205 candidates (-55.3%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	205	0	205
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	205	6	211

Merged error: 0.0b

Counts

211 → 6

regimes149.0ms

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	16	10
1	16	10

end0.0ms

sample745.0ms

Algorithm

intervals

sampling

Space saved by range analysis: 77.378065%

Space saved by search: 0.097632%

Guaranteed chance to sample good point: 0%

Results

459.0ms	8000×	body	80	valid
7.0ms	134×	body	80	nan
7.0ms	120×	body	80	invalid

Details

sample167.0ms

simplify96.0ms

prune3.0ms

localize11.0ms

rewrite44.0ms

series52.0ms

simplify105.0ms

prune341.0ms

localize10.0ms

rewrite45.0ms

series41.0ms

simplify93.0ms

prune219.0ms

localize10.0ms

rewrite58.0ms

series65.0ms

simplify48.0ms

prune424.0ms

localize11.0ms

rewrite73.0ms

series44.0ms

simplify51.0ms

prune413.0ms

regimes149.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample745.0ms

Profiling