Details

analyze143.0ms

Algorithm

sampling

Space saved by range analysis: 0.097632%

Space saved by search: 77.378065%

Guaranteed chance to sample good point: 94.67655%

sample25.0ms

Algorithm

intervals

Results

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

simplify97.0ms

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: 0.2b

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

rewrite43.0ms

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:

14.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)))
5.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
19.0ms	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
11.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))

simplify108.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 1 (23.0ms)

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

prune362.0ms

Filtered

105 candidates to 126 candidates (-20.0%)

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

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))))
0.3b	(/ (* 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:

9.0ms	(* 9.0 (- a (/ 1.0 3.0)))
15.0ms	(* (- 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)))))

simplify91.0ms

Algorithm

egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 1 (19.0ms)

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

prune247.0ms

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	3	4	7
Picked	1	0	1
Done	0	0	0
Total	110	7	117

Merged error: 0b

Counts

117 → 7

localize11.0ms

Local error

Found 3 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 9.0)) (sqrt (- a (/ 1.0 3.0))))))
0.3b	(/ (/ (* 1.0 rand) (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0))))

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

163×	`times-frac`
126×	`add-sqr-sqrt`
102×	`sqrt-prod`
86×	`*-un-lft-identity`
58×	`add-cube-cbrt`
26×	`difference-of-squares`
14×	`add-exp-log` `add-cbrt-cube`
13×	`distribute-lft-out--`
11×	`div-inv`
10×	`associate-/l*`
9×	`associate-/r*`
6×	`pow1` `associate-l`
5×	`cbrt-undiv` `flip3--` `div-exp` `flip--`
4×	`frac-times` `sqrt-div` `associate-r`
3×	`flip3-+` `flip-+` `add-log-exp`
2×	`associate-r/` `associate-l/` `prod-exp` `associate-/r/` `cbrt-unprod`
1×	`distribute-rgt-in` `rem-sqrt-square` `frac-2neg` `distribute-lft-in` `sqrt-pow1` `pow1/2` `pow-prod-down` `clear-num` `*-commutative` `associate-/l/` `distribute-lft-out` `unswap-sqr`

Counts

3 → 178

Calls

3 calls:

8.0ms	(sqrt (- a (/ 1.0 3.0)))
34.0ms	(* (- 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))))

series39.0ms

Counts

3 → 9

Calls

3 calls:

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

simplify53.0ms

Algorithm

egg-herbie

Counts

187 → 187

Iterations

Useful iterations: 1 (25.0ms)

Iter	Nodes	Cost
0	1112	2575
1	5001	2425

prune411.0ms

Filtered

119 candidates to 187 candidates (-57.1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	187	0	187
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	187	7	194

Merged error: 0b

Counts

194 → 7

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	(/ (sqrt (* 9.0 (- a (/ 1.0 3.0)))) rand)
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))))
7.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
12.0ms	(/ (sqrt (* 9.0 (- a (/ 1.0 3.0)))) rand)
11.0ms	(/ 1.0 (/ (sqrt (* 9.0 (- a (/ 1.0 3.0)))) rand))

series62.0ms

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))))
5.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
23.0ms	(/ (sqrt (* 9.0 (- a (/ 1.0 3.0)))) rand)
19.0ms	(/ 1.0 (/ (sqrt (* 9.0 (- a (/ 1.0 3.0)))) rand))

simplify46.0ms

Algorithm

egg-herbie

Counts

172 → 172

Iterations

Useful iterations: 1 (26.0ms)

Iter	Nodes	Cost
0	1172	2120
1	5001	2032

prune420.0ms

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: 0b

Counts

179 → 7

regimes239.0ms

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

analyze142.0ms

Algorithm

sampling

Space saved by range analysis: 0.097632%

Space saved by search: 77.378065%

Guaranteed chance to sample good point: 94.67655%

sample621.0ms

Algorithm

intervals

Results

468.0ms	8000×	body	80	valid
10.0ms	139×	body	80	nan
9.0ms	156×	body	80	invalid

Details

analyze143.0ms

sample25.0ms

simplify97.0ms

prune3.0ms

localize10.0ms

rewrite43.0ms

series50.0ms

simplify108.0ms

prune362.0ms

localize10.0ms

rewrite44.0ms

series40.0ms

simplify91.0ms

prune247.0ms

localize11.0ms

rewrite64.0ms

series39.0ms

simplify53.0ms

prune411.0ms

localize10.0ms

rewrite58.0ms

series62.0ms

simplify46.0ms

prune420.0ms

regimes239.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

analyze142.0ms

sample621.0ms

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