Details

sample288.0ms

Algorithm

intervals

Results

13.0ms	312×	body	80	nan
13.0ms	256×	body	80	valid

simplify13.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	16	6
1	19	6
2	21	6
3	21	6

prune4.0ms

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: 0.0b

Counts

2 → 1

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- 1.0 x) (+ 1.0 x))
0.0b	(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))
0.0b	(sqrt (/ (- 1.0 x) (+ 1.0 x)))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

64×	`*-un-lft-identity`
45×	`add-sqr-sqrt`
41×	`times-frac`
26×	`sqrt-prod`
24×	`add-cube-cbrt`
11×	`distribute-lft-out`
9×	`distribute-lft-out--` `difference-of-squares`
5×	`add-exp-log` `add-cbrt-cube` `associate-/l*`
4×	`pow1` `associate-/r*` `associate-/r/`
3×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square` `flip3-+` `flip-+` `div-inv` `associate-/l/`
1×	`cbrt-undiv` `flip3--` `frac-2neg` `sqrt-pow1` `pow1/2` `sqrt-div` `div-sub` `div-exp` `clear-num` `flip--`

Counts

3 → 97

Calls

3 calls:

8.0ms	(/ (- 1.0 x) (+ 1.0 x))
1.0ms	(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))
10.0ms	(sqrt (/ (- 1.0 x) (+ 1.0 x)))

series150.0ms

Counts

3 → 9

Calls

3 calls:

32.0ms	(/ (- 1.0 x) (+ 1.0 x))
7.0ms	(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))
111.0ms	(sqrt (/ (- 1.0 x) (+ 1.0 x)))

simplify44.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	370	779
1	1128	734
2	5001	719

prune203.0ms

Filtered

106 candidates to 76 candidates (71.7%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	104	2	106
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	105	2	107

Merged error: 0b

Counts

107 → 2

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ 1.0 x))
0.0b	(sqrt (- 1.0 x))
0.0b	(/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x)))
0.0b	(atan (/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x))))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

85×	`sqrt-prod`
78×	`*-un-lft-identity`
62×	`add-sqr-sqrt`
56×	`times-frac`
40×	`add-cube-cbrt`
10×	`distribute-lft-out`
9×	`distribute-lft-out--` `difference-of-squares`
8×	`sqrt-div` `associate-/l*`
7×	`associate-/r*`
6×	`pow1` `add-exp-log` `add-cbrt-cube`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square` `flip3--` `sqrt-pow1` `flip3-+` `pow1/2` `associate-/r/` `flip--` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `sqrt-undiv` `frac-2neg` `div-exp` `clear-num` `hypot-def` `div-inv`

Counts

4 → 137

Calls

4 calls:

3.0ms	(sqrt (+ 1.0 x))
4.0ms	(sqrt (- 1.0 x))
10.0ms	(/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x)))
3.0ms	(atan (/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x))))

series155.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(sqrt (+ 1.0 x))
31.0ms	(sqrt (- 1.0 x))
91.0ms	(/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x)))
2.0ms	(atan (/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x))))

simplify53.0ms

Algorithm

egg-herbie

Counts

149 → 149

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	372	1291
1	1144	1218
2	5002	1156

prune243.0ms

Filtered

149 candidates to 89 candidates (59.7%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	149	0	149
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	149	2	151

Merged error: 0b

Counts

151 → 2

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (* (- 1.0 x) (/ 1 (+ 1.0 x))))
0.0b	(atan (sqrt (* (- 1.0 x) (/ 1 (+ 1.0 x)))))
0.0b	(/ 1 (+ 1.0 x))
0.0b	(* (- 1.0 x) (/ 1 (+ 1.0 x)))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

39×	`*-un-lft-identity`
31×	`add-sqr-sqrt`
26×	`times-frac`
22×	`add-cube-cbrt`
18×	`associate-r`
17×	`add-exp-log`
11×	`add-cbrt-cube`
10×	`pow1`
7×	`distribute-lft-out`
6×	`sqrt-div`
5×	`associate-l`
4×	`expm1-log1p-u` `frac-times` `flip3--` `div-exp` `associate-l/` `prod-exp` `associate-/r` `associate-/r/` `flip--` `log1p-expm1-u` `add-log-exp`
3×	`associate-/l*` `unswap-sqr`
2×	`cbrt-undiv` `rec-exp` `sqrt-pow1` `flip3-+` `1-exp` `associate-*r/` `pow-prod-down` `un-div-inv` `cbrt-unprod` `flip-+` `div-inv`
1×	`pow-flip` `frac-2neg` `pow1/2` `clear-num` `sqrt-prod` `*-commutative` `distribute-lft-out--` `inv-pow` `difference-of-squares`

Counts

4 → 116

Calls

4 calls:

12.0ms	(sqrt (* (- 1.0 x) (/ 1 (+ 1.0 x))))
1.0ms	(atan (sqrt (* (- 1.0 x) (/ 1 (+ 1.0 x)))))
5.0ms	(/ 1 (+ 1.0 x))
13.0ms	(* (- 1.0 x) (/ 1 (+ 1.0 x)))

series149.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(sqrt (* (- 1.0 x) (/ 1 (+ 1.0 x))))
2.0ms	(atan (sqrt (* (- 1.0 x) (/ 1 (+ 1.0 x)))))
23.0ms	(/ 1 (+ 1.0 x))
32.0ms	(* (- 1.0 x) (/ 1 (+ 1.0 x)))

simplify63.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	447	756
1	1955	670
2	5003	615

prune191.0ms

Filtered

128 candidates to 81 candidates (63.3%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	128	0	128
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	128	2	130

Merged error: 0b

Counts

130 → 2

regimes18.0ms

Accuracy

0% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 0.0b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	7
1	12	7

end0.0ms

sample888.0ms

Algorithm

intervals

Results

398.0ms	8000×	body	80	valid
287.0ms	8149×	body	80	nan