Details

sample284.0ms

Algorithm

intervals

Results

10.0ms	256×	body	80	valid
7.0ms	227×	body	80	nan

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

localize10.0ms

Local error

Found 3 expressions with local error:

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

rewrite25.0ms

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:

1.0ms	(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))
8.0ms	(sqrt (/ (- 1.0 x) (+ 1.0 x)))
11.0ms	(/ (- 1.0 x) (+ 1.0 x))

series155.0ms

Counts

3 → 9

Calls

3 calls:

3.0ms	(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))
95.0ms	(sqrt (/ (- 1.0 x) (+ 1.0 x)))
57.0ms	(/ (- 1.0 x) (+ 1.0 x))

simplify42.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 2 (31.0ms)

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

prune207.0ms

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

localize11.0ms

Local error

Found 3 expressions with local error:

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

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

81×	`sqrt-prod`
74×	`*-un-lft-identity`
57×	`add-sqr-sqrt`
56×	`times-frac`
38×	`add-cube-cbrt`
9×	`distribute-lft-out` `distribute-lft-out--` `difference-of-squares`
8×	`associate-/l*`
7×	`associate-/r*`
6×	`sqrt-div`
5×	`add-exp-log` `add-cbrt-cube`
4×	`pow1`
3×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`flip3--` `associate-/r/` `flip--` `associate-/l/`
1×	`cbrt-undiv` `rem-sqrt-square` `sqrt-undiv` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `div-exp` `clear-num` `flip-+` `div-inv`

Counts

3 → 118

Calls

3 calls:

4.0ms	(sqrt (- 1.0 x))
3.0ms	(atan (/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x))))
11.0ms	(/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x)))

series127.0ms

Counts

3 → 9

Calls

3 calls:

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

simplify44.0ms

Algorithm

egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	351	1194
1	1086	1129
2	5002	1072

prune197.0ms

Filtered

127 candidates to 72 candidates (56.7%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	127	0	127
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	127	2	129

Merged error: 0b

Counts

129 → 2

localize14.0ms

Local error

Found 4 expressions with local error:

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

rewrite85.0ms

Algorithm

rewrite-expression-head

Rules

148×	`add-sqr-sqrt`
144×	`*-un-lft-identity`
134×	`times-frac`
84×	`sqrt-prod`
72×	`add-cube-cbrt`
41×	`associate-r`
32×	`add-exp-log`
27×	`associate-l`
20×	`add-cbrt-cube`
18×	`distribute-lft-out`
15×	`distribute-lft-out--` `difference-of-squares` `unswap-sqr`
14×	`associate-/r*`
11×	`pow1` `sqrt-div` `div-exp`
8×	`prod-exp` `associate-/r/` `associate-/l*`
6×	`cbrt-undiv`
4×	`expm1-log1p-u` `flip3-+` `cbrt-unprod` `flip-+` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`rec-exp` `pow-flip` `sqrt-pow1` `1-exp`
2×	`frac-times` `frac-2neg` `pow1/2` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `associate-/l/`
1×	`flip3--` `div-sub` `*-commutative` `flip--` `inv-pow`

Counts

4 → 244

Calls

4 calls:

16.0ms	(sqrt (* (/ 1 (sqrt (+ 1.0 x))) (/ (- 1.0 x) (sqrt (+ 1.0 x)))))
36.0ms	(* (/ 1 (sqrt (+ 1.0 x))) (/ (- 1.0 x) (sqrt (+ 1.0 x))))
10.0ms	(/ (- 1.0 x) (sqrt (+ 1.0 x)))
7.0ms	(/ 1 (sqrt (+ 1.0 x)))

series279.0ms

Counts

4 → 12

Calls

4 calls:

94.0ms	(sqrt (* (/ 1 (sqrt (+ 1.0 x))) (/ (- 1.0 x) (sqrt (+ 1.0 x)))))
39.0ms	(* (/ 1 (sqrt (+ 1.0 x))) (/ (- 1.0 x) (sqrt (+ 1.0 x))))
93.0ms	(/ (- 1.0 x) (sqrt (+ 1.0 x)))
53.0ms	(/ 1 (sqrt (+ 1.0 x)))

simplify99.0ms

Algorithm

egg-herbie

Counts

256 → 256

Iterations

Useful iterations: 2 (76.0ms)

Iter	Nodes	Cost
0	832	2377
1	3895	2084
2	5001	1955

prune403.0ms

Filtered

256 candidates to 137 candidates (53.5%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	256	0	256
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	256	2	258

Merged error: 0b

Counts

258 → 2

regimes14.0ms

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

sample670.0ms

Algorithm

intervals

Results

297.0ms	8000×	body	80	valid
184.0ms	7846×	body	80	nan