Details

sample66.0ms

Algorithm

intervals

Results

29.0ms	917×	body	80	nan
10.0ms	298×	body	80	valid

simplify102.0ms

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

prune3.0ms

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

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

rewrite54.0ms

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

series512.0ms

Counts

4 → 12

Calls

4 calls:

119.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)))
68.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
181.0ms	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
144.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))

simplify94.0ms

Algorithm

egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 2 (79.0ms)

Iter	Nodes	Cost
0	860	1389
1	3774	1282
2	5001	1276

prune384.0ms

Filtered

134 candidates to 115 candidates (85.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	126	8	134
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	127	8	135

Merged error: 0.0b

Counts

135 → 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))))
0.2b	(/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

92×	`add-sqr-sqrt`
84×	`*-un-lft-identity`
78×	`add-cube-cbrt` `prod-diff`
60×	`times-frac`
42×	`distribute-rgt-in` `distribute-lft-in`
13×	`add-exp-log` `add-cbrt-cube`
11×	`pow1`
10×	`associate-r`
9×	`associate-l`
8×	`associate-*r/`
7×	`div-inv`
6×	`flip3--` `flip--`
4×	`expm1-log1p-u` `frac-times` `sqrt-div` `associate-/r*` `log1p-expm1-u` `add-log-exp` `difference-of-squares`
3×	`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` `distribute-lft-out` `associate-/l*`

Counts

4 → 183

Calls

4 calls:

12.0ms	(* 9.0 (- a (/ 1.0 3.0)))
13.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))))
17.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
14.0ms	(/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))

series435.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(* 9.0 (- a (/ 1.0 3.0)))
120.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))))
76.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
195.0ms	(/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))

simplify57.0ms

Algorithm

egg-herbie

Counts

195 → 195

Iterations

Useful iterations: 1 (30.0ms)

Iter	Nodes	Cost
0	1157	3007
1	5001	2366

prune335.0ms

Filtered

195 candidates to 103 candidates (52.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	193	2	195
Fresh	1	6	7
Picked	1	0	1
Done	0	0	0
Total	195	8	203

Merged error: 0.0b

Counts

203 → 8

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1 (sqrt 9.0)) (* (/ 1.0 (sqrt (- a (/ 1.0 3.0)))) rand))))
0.2b	(* (/ 1.0 (sqrt (- a (/ 1.0 3.0)))) rand)
0.3b	(/ 1.0 (sqrt (- a (/ 1.0 3.0))))
0.3b	(* (/ 1 (sqrt 9.0)) (* (/ 1.0 (sqrt (- a (/ 1.0 3.0)))) rand))

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

104×	`add-sqr-sqrt`
82×	`times-frac`
70×	`*-un-lft-identity`
61×	`associate-l`
54×	`add-cube-cbrt`
52×	`add-exp-log` `sqrt-prod`
34×	`add-cbrt-cube`
23×	`prod-exp`
16×	`difference-of-squares`
13×	`pow1` `cbrt-unprod`
12×	`div-exp`
9×	`associate-/r*`
8×	`distribute-lft-out--`
7×	`cbrt-undiv` `associate-r`
6×	`associate-*l/`
5×	`frac-times` `flip3--` `pow-prod-down` `flip--`
4×	`expm1-log1p-u` `sqrt-div` `associate-/r/` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`rec-exp` `flip3-+` `1-exp` `associate-r/` `-commutative` `flip-+` `div-inv` `associate-/l*`
1×	`distribute-rgt-in` `frac-2neg` `distribute-lft-in` `clear-num`

Counts

4 → 199

Calls

4 calls:

10.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1 (sqrt 9.0)) (* (/ 1.0 (sqrt (- a (/ 1.0 3.0)))) rand))))
14.0ms	(* (/ 1.0 (sqrt (- a (/ 1.0 3.0)))) rand)
9.0ms	(/ 1.0 (sqrt (- a (/ 1.0 3.0))))
21.0ms	(* (/ 1 (sqrt 9.0)) (* (/ 1.0 (sqrt (- a (/ 1.0 3.0)))) rand))

series601.0ms

Counts

4 → 12

Calls

4 calls:

154.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1 (sqrt 9.0)) (* (/ 1.0 (sqrt (- a (/ 1.0 3.0)))) rand))))
153.0ms	(* (/ 1.0 (sqrt (- a (/ 1.0 3.0)))) rand)
78.0ms	(/ 1.0 (sqrt (- a (/ 1.0 3.0))))
216.0ms	(* (/ 1 (sqrt 9.0)) (* (/ 1.0 (sqrt (- a (/ 1.0 3.0)))) rand))

simplify51.0ms

Algorithm

egg-herbie

Counts

211 → 211

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1127	2217
1	5001	1992

prune524.0ms

Filtered

211 candidates to 152 candidates (72.0%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	209	2	211
Fresh	3	4	7
Picked	1	0	1
Done	0	0	0
Total	213	6	219

Merged error: 0.0b

Counts

219 → 6

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ 1.0 (sqrt (- a (/ 1.0 3.0)))) rand)
0.2b	(/ (* (- a (/ 1.0 3.0)) (* (/ 1.0 (sqrt (- a (/ 1.0 3.0)))) rand)) (sqrt 9.0))
0.3b	(/ 1.0 (sqrt (- a (/ 1.0 3.0))))
8.9b	(* (- a (/ 1.0 3.0)) (* (/ 1.0 (sqrt (- a (/ 1.0 3.0)))) rand))

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

92×	`add-sqr-sqrt`
70×	`times-frac`
60×	`*-un-lft-identity`
49×	`sqrt-prod`
44×	`add-cube-cbrt`
39×	`associate-l`
34×	`add-exp-log` `add-cbrt-cube`
16×	`difference-of-squares`
15×	`associate-/r*`
12×	`prod-exp` `cbrt-unprod`
11×	`pow1` `associate-*l/`
8×	`cbrt-undiv` `div-exp` `distribute-lft-out--`
6×	`flip3--` `flip--`
5×	`associate-/l/`
4×	`expm1-log1p-u` `frac-times` `sqrt-div` `associate-r` `pow-prod-down` `associate-/r/` `log1p-expm1-u` `associate-/l*` `add-log-exp`
3×	`div-inv` `unswap-sqr`
2×	`frac-2neg` `associate-r/` `clear-num` `-commutative`

Counts

4 → 178

Calls

4 calls:

16.0ms	(* (/ 1.0 (sqrt (- a (/ 1.0 3.0)))) rand)
20.0ms	(/ (* (- a (/ 1.0 3.0)) (* (/ 1.0 (sqrt (- a (/ 1.0 3.0)))) rand)) (sqrt 9.0))
9.0ms	(/ 1.0 (sqrt (- a (/ 1.0 3.0))))
18.0ms	(* (- a (/ 1.0 3.0)) (* (/ 1.0 (sqrt (- a (/ 1.0 3.0)))) rand))

series560.0ms

Counts

4 → 12

Calls

4 calls:

154.0ms	(* (/ 1.0 (sqrt (- a (/ 1.0 3.0)))) rand)
196.0ms	(/ (* (- a (/ 1.0 3.0)) (* (/ 1.0 (sqrt (- a (/ 1.0 3.0)))) rand)) (sqrt 9.0))
78.0ms	(/ 1.0 (sqrt (- a (/ 1.0 3.0))))
132.0ms	(* (- a (/ 1.0 3.0)) (* (/ 1.0 (sqrt (- a (/ 1.0 3.0)))) rand))

simplify102.0ms

Algorithm

egg-herbie

Counts

190 → 190

Iterations

Useful iterations: 2 (82.0ms)

Iter	Nodes	Cost
0	939	1895
1	3969	1664
2	5003	1637

prune443.0ms

Filtered

190 candidates to 136 candidates (71.6%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	189	1	190
Fresh	1	4	5
Picked	1	0	1
Done	0	0	0
Total	191	5	196

Merged error: 0.0b

Counts

196 → 5

regimes73.0ms

Accuracy

0% (0.2b 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	19	14
1	19	14

end0.0ms

sample1.8s

Algorithm

intervals

Results

863.0ms	27038×	body	80	nan
313.0ms	9182×	body	80	valid