Details

sample78.0ms

Algorithm

intervals

Results

38.0ms	845×	body	80	nan
14.0ms	300×	body	80	valid

simplify99.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	27	10
1	76	10
2	211	10
3	530	10
4	1065	10
5	2198	10
6	3794	10
7	5001	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: 0.2b

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

rewrite58.0ms

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×	`expm1-log1p-u` `frac-times` `associate-/r*` `associate-/r/` `log1p-expm1-u` `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 → 122

Calls

4 calls:

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

series536.0ms

Counts

4 → 12

Calls

4 calls:

127.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)))
75.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
144.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
189.0ms	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)

simplify95.0ms

Algorithm

egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 2 (81.0ms)

Iter	Nodes	Cost
0	860	1389
1	3776	1282
2	5002	1276

prune386.0ms

Filtered

134 candidates to 115 candidates (85.8%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	127	7	134
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	128	7	135

Merged error: 0.0b

Counts

135 → 7

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1.0 (* (sqrt 9.0) (sqrt (- a (/ 1.0 3.0))))) rand)))
0.2b	(* (sqrt 9.0) (sqrt (- a (/ 1.0 3.0))))
0.3b	(/ 1.0 (* (sqrt 9.0) (sqrt (- a (/ 1.0 3.0)))))
0.3b	(* (/ 1.0 (* (sqrt 9.0) (sqrt (- a (/ 1.0 3.0))))) rand)

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

37×	`add-sqr-sqrt`
22×	`add-exp-log` `add-cbrt-cube`
21×	`associate-l`
19×	`*-un-lft-identity`
15×	`add-cube-cbrt` `associate-r`
13×	`sqrt-prod`
12×	`pow1`
8×	`times-frac` `associate-*r/`
7×	`prod-exp` `cbrt-unprod`
6×	`flip3--` `sqrt-div` `flip--` `unswap-sqr`
5×	`pow-prod-down`
4×	`cbrt-undiv` `expm1-log1p-u` `frac-times` `div-exp` `associate-/r/` `log1p-expm1-u` `add-log-exp` `difference-of-squares`
3×	`flip3-+` `associate-l/` `-commutative` `flip-+` `associate-/l*`
2×	`sqrt-pow1` `pow1/2` `div-inv` `distribute-lft-out--`
1×	`distribute-rgt-in` `frac-2neg` `distribute-lft-in` `sqrt-unprod` `clear-num` `associate-/r*`

Counts

4 → 126

Calls

4 calls:

11.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1.0 (* (sqrt 9.0) (sqrt (- a (/ 1.0 3.0))))) rand)))
16.0ms	(* (sqrt 9.0) (sqrt (- a (/ 1.0 3.0))))
12.0ms	(/ 1.0 (* (sqrt 9.0) (sqrt (- a (/ 1.0 3.0)))))
15.0ms	(* (/ 1.0 (* (sqrt 9.0) (sqrt (- a (/ 1.0 3.0))))) rand)

series673.0ms

Counts

4 → 12

Calls

4 calls:

160.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1.0 (* (sqrt 9.0) (sqrt (- a (/ 1.0 3.0))))) rand)))
94.0ms	(* (sqrt 9.0) (sqrt (- a (/ 1.0 3.0))))
192.0ms	(/ 1.0 (* (sqrt 9.0) (sqrt (- a (/ 1.0 3.0)))))
226.0ms	(* (/ 1.0 (* (sqrt 9.0) (sqrt (- a (/ 1.0 3.0))))) rand)

simplify117.0ms

Algorithm

egg-herbie

Counts

138 → 138

Iterations

Useful iterations: 2 (102.0ms)

Iter	Nodes	Cost
0	883	1486
1	4285	1354
2	5001	1346

prune345.0ms

Filtered

138 candidates to 106 candidates (76.8%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	136	2	138
Fresh	2	4	6
Picked	1	0	1
Done	0	0	0
Total	139	6	145

Merged error: 0b

Counts

145 → 6

localize12.0ms

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

rewrite79.0ms

Algorithm

rewrite-expression-head

Rules

441×	`times-frac`
343×	`add-sqr-sqrt`
259×	`*-un-lft-identity`
258×	`sqrt-prod`
205×	`add-cube-cbrt`
54×	`difference-of-squares`
36×	`associate-/l*`
27×	`distribute-lft-out--`
18×	`sqrt-div`
16×	`associate-/r/`
15×	`associate-/r*`
13×	`add-exp-log` `add-cbrt-cube`
12×	`flip3--` `flip--`
9×	`div-inv`
7×	`pow1`
6×	`associate-l`
4×	`cbrt-undiv` `expm1-log1p-u` `frac-times` `div-exp` `log1p-expm1-u` `add-log-exp`
3×	`flip3-+` `associate-r` `flip-+`
2×	`frac-2neg` `associate-r/` `associate-l/` `clear-num`
1×	`distribute-rgt-in` `rem-sqrt-square` `distribute-lft-in` `sqrt-pow1` `pow1/2` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `associate-/l/` `unswap-sqr`

Counts

4 → 362

Calls

4 calls:

10.0ms	(sqrt (- a (/ 1.0 3.0)))
11.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* 1.0 (/ (/ rand (sqrt (- a (/ 1.0 3.0)))) (sqrt 9.0)))))
13.0ms	(/ rand (sqrt (- a (/ 1.0 3.0))))
20.0ms	(/ (/ rand (sqrt (- a (/ 1.0 3.0)))) (sqrt 9.0))

series502.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(sqrt (- a (/ 1.0 3.0)))
162.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* 1.0 (/ (/ rand (sqrt (- a (/ 1.0 3.0)))) (sqrt 9.0)))))
88.0ms	(/ rand (sqrt (- a (/ 1.0 3.0))))
211.0ms	(/ (/ rand (sqrt (- a (/ 1.0 3.0)))) (sqrt 9.0))

simplify89.0ms

Algorithm

egg-herbie

Counts

374 → 374

Iterations

Useful iterations: 1 (33.0ms)

Iter	Nodes	Cost
0	1390	5110
1	5001	4841

prune780.0ms

Filtered

374 candidates to 225 candidates (60.2%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	374	0	374
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	374	6	380

Merged error: 0b

Counts

380 → 6

localize13.0ms

Local error

Found 4 expressions with local error:

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

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

52×	`sqrt-prod`
49×	`times-frac`
48×	`add-sqr-sqrt`
42×	`associate-l`
41×	`add-cube-cbrt` `*-un-lft-identity`
15×	`add-exp-log` `add-cbrt-cube`
13×	`sqrt-div`
11×	`pow1`
9×	`associate-*r/`
8×	`associate-/r*` `associate-/r/`
6×	`associate-/l*`
4×	`expm1-log1p-u` `flip3--` `associate-r` `pow-prod-down` `associate-*l/` `prod-exp` `flip--` `cbrt-unprod` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`unswap-sqr`
2×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `*-commutative`
1×	`frac-times`

Counts

4 → 152

Calls

4 calls:

15.0ms	(* (sqrt (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))) rand)
14.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
10.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
28.0ms	(* (sqrt (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))) (* (sqrt (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))) rand))

series1.3s

Counts

4 → 12

Calls

4 calls:

637.0ms	(* (sqrt (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))) rand)
157.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
148.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
324.0ms	(* (sqrt (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))) (* (sqrt (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))) rand))

simplify101.0ms

Algorithm

egg-herbie

Counts

164 → 164

Iterations

Useful iterations: 2 (82.0ms)

Iter	Nodes	Cost
0	858	1836
1	3714	1662
2	5002	1652

prune545.0ms

Filtered

164 candidates to 140 candidates (85.4%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	164	0	164
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	164	6	170

Merged error: 0b

Counts

170 → 6

regimes98.0ms

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

sample2.4s

Algorithm

intervals

Results

1.3s	27100×	body	80	nan
460.0ms	9169×	body	80	valid