Details

sample67.0ms

Algorithm

intervals

Results

29.0ms	883×	body	80	nan
13.0ms	288×	body	80	valid

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

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: 0.1b

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)))
0.2b	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
0.2b	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
0.3b	(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)))
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)
7.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))

series541.0ms

Counts

4 → 12

Calls

4 calls:

122.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)))
151.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
192.0ms	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
75.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))

simplify86.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 1 (18.0ms)

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

prune562.0ms

Filtered

126 candidates to 105 candidates (83.3%)

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

rewrite48.0ms

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)))
17.0ms	(* (- 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))))

series452.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(* 9.0 (- a (/ 1.0 3.0)))
129.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))))
202.0ms	(/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
79.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))

simplify78.0ms

Algorithm

egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 1 (16.0ms)

Iter	Nodes	Cost
0	744	1044
1	3484	958
2	5001	958

prune290.0ms

Filtered

109 candidates to 83 candidates (76.1%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	105	4	109
Fresh	4	1	5
Picked	1	0	1
Done	0	0	0
Total	110	5	115

Merged error: 0b

Counts

115 → 5

localize14.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sqrt 9.0) (sqrt (- a (/ 1.0 3.0))))
0.3b	(* (sqrt 9.0) (sqrt (- a (/ 1.0 3.0))))
0.3b	(sqrt (* (* (sqrt 9.0) (sqrt (- a (/ 1.0 3.0)))) (* (sqrt 9.0) (sqrt (- a (/ 1.0 3.0))))))
0.4b	(* (* (sqrt 9.0) (sqrt (- a (/ 1.0 3.0)))) (* (sqrt 9.0) (sqrt (- a (/ 1.0 3.0)))))

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

123×	`pow1`
76×	`pow-prod-down`
60×	`sqrt-pow1`
38×	`add-sqr-sqrt`
37×	`pow1/2`
36×	`sqrt-div`
32×	`associate-*r/`
27×	`sqrt-prod`
20×	`add-exp-log` `add-cbrt-cube`
19×	`associate-r`
16×	`*-un-lft-identity` `pow-prod-up`
14×	`flip3--` `flip--`
13×	`associate-l`
12×	`add-cube-cbrt` `pow-sqr`
10×	`prod-exp` `cbrt-unprod`
8×	`frac-times` `unswap-sqr`
7×	`sqrt-unprod`
4×	`pow-plus` `associate-*l/` `add-log-exp` `difference-of-squares`
3×	`*-commutative`
2×	`pow2` `times-frac` `distribute-lft-out--`
1×	`rem-sqrt-square` `swap-sqr` `rem-square-sqrt`

Counts

4 → 164

Calls

4 calls:

11.0ms	(* (sqrt 9.0) (sqrt (- a (/ 1.0 3.0))))
14.0ms	(* (sqrt 9.0) (sqrt (- a (/ 1.0 3.0))))
21.0ms	(sqrt (* (* (sqrt 9.0) (sqrt (- a (/ 1.0 3.0)))) (* (sqrt 9.0) (sqrt (- a (/ 1.0 3.0))))))
21.0ms	(* (* (sqrt 9.0) (sqrt (- a (/ 1.0 3.0)))) (* (sqrt 9.0) (sqrt (- a (/ 1.0 3.0)))))

series396.0ms

Counts

4 → 12

Calls

4 calls:

96.0ms	(* (sqrt 9.0) (sqrt (- a (/ 1.0 3.0))))
95.0ms	(* (sqrt 9.0) (sqrt (- a (/ 1.0 3.0))))
96.0ms	(sqrt (* (* (sqrt 9.0) (sqrt (- a (/ 1.0 3.0)))) (* (sqrt 9.0) (sqrt (- a (/ 1.0 3.0))))))
110.0ms	(* (* (sqrt 9.0) (sqrt (- a (/ 1.0 3.0)))) (* (sqrt 9.0) (sqrt (- a (/ 1.0 3.0)))))

simplify65.0ms

Algorithm

egg-herbie

Counts

176 → 176

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	428	1302
1	1769	1143
2	5002	1127

prune386.0ms

Filtered

176 candidates to 92 candidates (52.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	176	0	176
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	176	5	181

Merged error: 0b

Counts

181 → 5

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

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 186

Calls

4 calls:

6.0ms	(sqrt (- 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)))))))
9.0ms	(/ rand (sqrt (- a (/ 1.0 3.0))))
29.0ms	(* (/ 1.0 (sqrt 9.0)) (/ rand (sqrt (- a (/ 1.0 3.0)))))

series552.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(sqrt (- a (/ 1.0 3.0)))
164.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1.0 (sqrt 9.0)) (/ rand (sqrt (- a (/ 1.0 3.0)))))))
100.0ms	(/ rand (sqrt (- a (/ 1.0 3.0))))
248.0ms	(* (/ 1.0 (sqrt 9.0)) (/ rand (sqrt (- a (/ 1.0 3.0)))))

simplify123.0ms

Algorithm

egg-herbie

Counts

198 → 198

Iterations

Useful iterations: 1 (23.0ms)

Iter	Nodes	Cost
0	1033	2135
1	4807	2003
2	5001	2003

prune574.0ms

Filtered

198 candidates to 148 candidates (74.7%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	196	2	198
Fresh	2	1	3
Picked	0	1	1
Done	0	1	1
Total	198	5	203

Merged error: 0b

Counts

203 → 5

regimes77.0ms

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	20	18
1	20	18

end0.0ms

sample1.8s

Algorithm

intervals

Results

915.0ms	27376×	body	80	nan
326.0ms	9087×	body	80	valid