Details

sample97.0ms

Algorithm

intervals

Results

50.0ms	818×	body	80	nan
16.0ms	293×	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)))
0.3b	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
0.3b	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
0.8b	(sqrt (* 9.0 (- a (/ 1.0 3.0))))

rewrite47.0ms

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:

13.0ms	(* (- 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))))

series553.0ms

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)))
192.0ms	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
150.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
88.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))

simplify91.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 1 (20.0ms)

Iter	Nodes	Cost
0	823	1338
1	3607	1238
2	5002	1238

prune346.0ms

Filtered

126 candidates to 105 candidates (83.3%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	117	9	126
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	118	9	127

Merged error: 0b

Counts

127 → 9

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)))))
0.8b	(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)))
14.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))))
15.0ms	(/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
7.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))

series458.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(* 9.0 (- a (/ 1.0 3.0)))
132.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))))
210.0ms	(/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
76.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))

simplify83.0ms

Algorithm

egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 1 (18.0ms)

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

prune244.0ms

Filtered

109 candidates to 83 candidates (76.1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	108	1	109
Fresh	3	5	8
Picked	0	1	1
Done	0	0	0
Total	111	7	118

Merged error: 0b

Counts

118 → 7

localize11.0ms

Local error

Found 4 expressions with local error:

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)))))
0.8b	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
7.9b	(* (- a (/ 1.0 3.0)) (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
26×	`times-frac`
25×	`*-un-lft-identity`
24×	`associate-l`
23×	`add-cube-cbrt`
20×	`add-exp-log` `add-cbrt-cube`
14×	`pow1`
8×	`sqrt-prod`
7×	`associate-*r/` `prod-exp` `cbrt-unprod`
6×	`sqrt-div` `associate-*l/`
5×	`flip3--` `pow-prod-down` `flip--`
4×	`associate-r` `associate-/r*` `associate-/r/` `add-log-exp`
3×	`cbrt-undiv` `div-exp` `associate-/l*`
2×	`frac-times` `sqrt-pow1` `*-commutative` `div-inv` `difference-of-squares` `unswap-sqr`
1×	`frac-2neg` `pow1/2` `clear-num` `distribute-lft-out--`

Counts

4 → 111

Calls

4 calls:

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

series578.0ms

Counts

4 → 12

Calls

4 calls:

189.0ms	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
148.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
75.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
164.0ms	(* (- a (/ 1.0 3.0)) (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand))

simplify77.0ms

Algorithm

egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 1 (18.0ms)

Iter	Nodes	Cost
0	754	1232
1	3048	1085
2	5001	1085

prune305.0ms

Filtered

123 candidates to 99 candidates (80.5%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	123	0	123
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	123	7	130

Merged error: 0b

Counts

130 → 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))))

rewrite69.0ms

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:

6.0ms	(sqrt (- a (/ 1.0 3.0)))
39.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (/ (/ (* 1.0 rand) (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0))))))
15.0ms	(/ (/ (* 1.0 rand) (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0))))

series438.0ms

Counts

3 → 9

Calls

3 calls:

44.0ms	(sqrt (- a (/ 1.0 3.0)))
151.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (/ (/ (* 1.0 rand) (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0))))))
242.0ms	(/ (/ (* 1.0 rand) (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0))))

simplify111.0ms

Algorithm

egg-herbie

Counts

187 → 187

Iterations

Useful iterations: 1 (21.0ms)

Iter	Nodes	Cost
0	988	2523
1	4418	2362
2	5001	2362

prune390.0ms

Filtered

187 candidates to 118 candidates (63.1%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	186	1	187
Fresh	1	3	4
Picked	0	1	1
Done	1	1	2
Total	188	6	194

Merged error: 0b

Counts

194 → 6

regimes114.0ms

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	19	13
1	19	13

end0.0ms

sample2.4s

Algorithm

intervals

Results

1.4s	27539×	body	80	nan
419.0ms	9150×	body	80	valid