Details

sample281.0ms

Algorithm

intervals

Results

10.0ms	256×	body	80	valid
8.0ms	259×	body	80	nan

simplify16.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	9	11
1	16	11
2	19	11
3	21	11
done	21	11

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

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))

rewrite30.0ms

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:

0.0ms	(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))
11.0ms	(sqrt (/ (- 1.0 x) (+ 1.0 x)))
14.0ms	(/ (- 1.0 x) (+ 1.0 x))

series146.0ms

Counts

3 → 9

Calls

3 calls:

3.0ms	(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))
93.0ms	(sqrt (/ (- 1.0 x) (+ 1.0 x)))
50.0ms	(/ (- 1.0 x) (+ 1.0 x))

simplify1.2s

Counts

106 → 106

Iterations

Useful iterations: 3 (551.0ms)

Iter	Nodes	Cost
0	173	1505
1	368	1422
2	901	1373
3	2446	1320
done	5000	1320

prune240.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize9.0ms

Local error

Found 4 expressions with local error:

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

rewrite35.0ms

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:

13.0ms	(/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x)))
4.0ms	(atan (/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x))))
4.0ms	(sqrt (+ 1.0 x))
6.0ms	(sqrt (- 1.0 x))

series158.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x)))
2.0ms	(atan (/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x))))
30.0ms	(sqrt (+ 1.0 x))
33.0ms	(sqrt (- 1.0 x))

simplify1.1s

Counts

149 → 149

Iterations

Useful iterations: 3 (472.0ms)

Iter	Nodes	Cost
0	195	2255
1	370	2017
2	888	1941
3	2426	1925
done	5000	1925

prune315.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize12.0ms

Local error

Found 4 expressions with local error:

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

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

111×	`sqrt-prod`
58×	`add-sqr-sqrt`
41×	`*-un-lft-identity` `sqrt-pow1`
34×	`sqrt-div`
32×	`pow1`
21×	`add-cube-cbrt` `pow1/2`
18×	`swap-sqr`
10×	`associate-r` `associate-l`
9×	`pow-prod-up` `unswap-sqr`
8×	`flip3-+` `flip-+` `distribute-lft-out`
6×	`add-exp-log` `add-cbrt-cube`
5×	`rem-sqrt-square` `pow-prod-down` `pow-sqr`
4×	`expm1-log1p-u` `frac-times` `log1p-expm1-u` `add-log-exp`
2×	`associate-r/` `associate-l/`
1×	`pow2` `flip3--` `pow-plus` `sqrt-unprod` `prod-exp` `rem-square-sqrt` `*-commutative` `flip--` `cbrt-unprod` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 157

Calls

4 calls:

5.0ms	(sqrt (sqrt (+ 1.0 x)))
5.0ms	(sqrt (sqrt (+ 1.0 x)))
5.0ms	(sqrt (- 1.0 x))
30.0ms	(* (sqrt (sqrt (+ 1.0 x))) (sqrt (sqrt (+ 1.0 x))))

series246.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(sqrt (sqrt (+ 1.0 x)))
90.0ms	(sqrt (sqrt (+ 1.0 x)))
35.0ms	(sqrt (- 1.0 x))
31.0ms	(* (sqrt (sqrt (+ 1.0 x))) (sqrt (sqrt (+ 1.0 x))))

simplify1.4s

Counts

169 → 169

Iterations

Useful iterations: 3 (748.0ms)

Iter	Nodes	Cost
0	196	2326
1	391	1490
2	1042	1414
3	3307	1348
done	5000	1348

prune359.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	12
1	12	12
done	12	12

end0.0ms

sample724.0ms

Algorithm

intervals

Results

320.0ms	8000×	body	80	valid
213.0ms	8082×	body	80	nan