Details

sample285.0ms

Algorithm

intervals

Results

12.0ms	256×	body	80	valid
9.0ms	222×	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	(/ (- 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)))

series157.0ms

Counts

3 → 9

Calls

3 calls:

33.0ms	(/ (- 1.0 x) (+ 1.0 x))
8.0ms	(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))
115.0ms	(sqrt (/ (- 1.0 x) (+ 1.0 x)))

simplify42.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 2 (32.0ms)

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

prune206.0ms

Filtered

106 candidates to 76 candidates (71.7%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	102	4	106
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	103	4	107

Merged error: 0b

Counts

107 → 4

localize9.0ms

Local error

Found 4 expressions with local error:

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

rewrite30.0ms

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

series157.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(atan (/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x))))
31.0ms	(sqrt (+ 1.0 x))
32.0ms	(sqrt (- 1.0 x))
92.0ms	(/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x)))

simplify50.0ms

Algorithm

egg-herbie

Counts

149 → 149

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	372	1291
1	1144	1218
2	5001	1156

prune251.0ms

Filtered

149 candidates to 89 candidates (59.7%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	149	0	149
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	149	4	153

Merged error: 0b

Counts

153 → 4

localize12.0ms

Local error

Found 4 expressions with local error:

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

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

121×	`*-un-lft-identity`
106×	`sqrt-prod`
97×	`add-sqr-sqrt`
93×	`times-frac`
59×	`add-cube-cbrt`
16×	`distribute-lft-out`
15×	`distribute-lft-out--` `difference-of-squares`
14×	`associate-/r*`
10×	`add-exp-log`
9×	`sqrt-div`
8×	`pow1` `add-cbrt-cube` `associate-/l*`
6×	`associate-/r/`
4×	`expm1-log1p-u` `rem-sqrt-square` `flip3-+` `flip-+` `log1p-expm1-u` `add-log-exp`
3×	`pow-flip` `sqrt-pow1` `pow1/2` `div-exp` `div-inv`
2×	`cbrt-undiv` `frac-2neg` `clear-num` `associate-/l/`
1×	`rec-exp` `flip3--` `1-exp` `div-sub` `flip--` `hypot-def` `inv-pow`

Counts

4 → 194

Calls

4 calls:

4.0ms	(sqrt (+ 1.0 x))
10.0ms	(sqrt (/ (- 1.0 x) (sqrt (+ 1.0 x))))
10.0ms	(/ 1 (sqrt (+ 1.0 x)))
10.0ms	(/ (- 1.0 x) (sqrt (+ 1.0 x)))

series451.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(sqrt (+ 1.0 x))
267.0ms	(sqrt (/ (- 1.0 x) (sqrt (+ 1.0 x))))
57.0ms	(/ 1 (sqrt (+ 1.0 x)))
95.0ms	(/ (- 1.0 x) (sqrt (+ 1.0 x)))

simplify70.0ms

Algorithm

egg-herbie

Counts

206 → 206

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	681	1734
1	2357	1567
2	5001	1519

prune416.0ms

Filtered

206 candidates to 117 candidates (56.8%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	206	0	206
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	206	4	210

Merged error: 0b

Counts

210 → 4

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(atan (cbrt (pow (sqrt (/ (- 1.0 x) (+ x 1.0))) 3)))
0.0b	(sqrt (/ (- 1.0 x) (+ x 1.0)))
0.0b	(cbrt (pow (sqrt (/ (- 1.0 x) (+ x 1.0))) 3))
0.0b	(pow (sqrt (/ (- 1.0 x) (+ x 1.0))) 3)

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

150×	`*-un-lft-identity`
130×	`sqrt-prod`
103×	`add-sqr-sqrt`
101×	`times-frac`
64×	`cbrt-prod`
60×	`add-cube-cbrt`
58×	`unpow-prod-down` `cube-prod`
25×	`distribute-lft-out`
20×	`distribute-lft-out--` `difference-of-squares`
10×	`associate-/r/`
7×	`pow1`
5×	`add-exp-log` `flip3-+` `add-cbrt-cube` `flip-+` `div-inv`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow` `pow-pow` `sqrt-div`
2×	`cube-div` `cube-mult` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `unpow3` `sqr-pow`
1×	`pow-to-exp` `cbrt-div` `pow1/3` `pow-exp` `sqrt-pow2` `rem-cbrt-cube` `rem-cube-cbrt`

Counts

4 → 206

Calls

4 calls:

1.0ms	(atan (cbrt (pow (sqrt (/ (- 1.0 x) (+ x 1.0))) 3)))
8.0ms	(sqrt (/ (- 1.0 x) (+ x 1.0)))
13.0ms	(cbrt (pow (sqrt (/ (- 1.0 x) (+ x 1.0))) 3))
16.0ms	(pow (sqrt (/ (- 1.0 x) (+ x 1.0))) 3)

series387.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(atan (cbrt (pow (sqrt (/ (- 1.0 x) (+ x 1.0))) 3)))
95.0ms	(sqrt (/ (- 1.0 x) (+ x 1.0)))
94.0ms	(cbrt (pow (sqrt (/ (- 1.0 x) (+ x 1.0))) 3))
195.0ms	(pow (sqrt (/ (- 1.0 x) (+ x 1.0))) 3)

simplify72.0ms

Algorithm

egg-herbie

Counts

218 → 218

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	628	2063
1	1957	1918
2	5001	1875

prune319.0ms

Filtered

218 candidates to 103 candidates (47.2%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	218	0	218
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	218	4	222

Merged error: 0b

Counts

222 → 4

regimes57.0ms

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

sample847.0ms

Algorithm

intervals

Results

372.0ms	8000×	body	80	valid
276.0ms	8036×	body	80	nan