Details

sample32.0ms

Algorithm

intervals

Results

7.0ms	312×	body	80	nan
5.0ms	49×	body	1280	valid
4.0ms	48×	body	640	valid
3.0ms	123×	body	80	valid
2.0ms	28×	body	320	valid
0.0ms	8×	body	160	valid

simplify4.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	10
2	10
1	9
0	6

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.6b

localize17.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt (+ x 1.0))
2.4b	(- (sqrt (+ x 1.0)) (sqrt x))

rewrite91.0ms

Algorithm

rewrite-expression-head

Rules

61×	`sqrt-prod`
54×	`*-un-lft-identity`
42×	`add-sqr-sqrt` `prod-diff`
31×	`add-cube-cbrt`
9×	`distribute-lft-out`
7×	`fma-neg`
4×	`add-log-exp` `difference-of-squares`
3×	`pow1` `distribute-lft-out--`
2×	`expm1-log1p-u` `add-cbrt-cube` `sqrt-div` `add-exp-log` `log1p-expm1-u`
1×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `flip3-+` `flip3--` `pow1/2` `diff-log` `flip-+` `hypot-def` `flip--`

Counts

2 → 89

Calls

2 calls:

6.0ms	(sqrt (+ x 1.0))
82.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

series132.0ms

Counts

2 → 6

Calls

2 calls:

41.0ms	(sqrt (+ x 1.0))
91.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

simplify2.2s

Counts

95 → 95

Iterations

Iter	Nodes
done	5003
3	2271
2	785
1	322
0	139

prune307.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 30.3b

localize20.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (+ 1.0 x))
0.0b	(/ (- (+ 1.0 x) x) (+ (sqrt (+ 1.0 x)) (sqrt x)))
1.7b	(- (+ 1.0 x) x)

rewrite182.0ms

Algorithm

rewrite-expression-head

Rules

125×	`*-un-lft-identity`
45×	`add-sqr-sqrt`
41×	`distribute-lft-out`
36×	`times-frac`
32×	`sqrt-prod`
26×	`add-cube-cbrt`
16×	`distribute-lft-out--`
12×	`prod-diff`
8×	`add-log-exp` `difference-of-squares`
6×	`associate-/r` `associate-/l`
5×	`add-cbrt-cube` `add-exp-log`
4×	`pow1` `fma-neg`
3×	`expm1-log1p-u` `log1p-expm1-u`
2×	`flip3-+` `flip3--` `sqrt-div` `diff-log` `associate-/r/` `flip-+` `flip--` `associate-/l/`
1×	`cbrt-undiv` `rem-sqrt-square` `clear-num` `sum-log` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `div-exp` `associate--l+` `hypot-def` `div-inv`

Counts

3 → 121

Calls

3 calls:

6.0ms	(sqrt (+ 1.0 x))
133.0ms	(/ (- (+ 1.0 x) x) (+ (sqrt (+ 1.0 x)) (sqrt x)))
38.0ms	(- (+ 1.0 x) x)

series245.0ms

Counts

3 → 9

Calls

3 calls:

40.0ms	(sqrt (+ 1.0 x))
203.0ms	(/ (- (+ 1.0 x) x) (+ (sqrt (+ 1.0 x)) (sqrt x)))
1.0ms	(- (+ 1.0 x) x)

simplify1.8s

Counts

130 → 130

Iterations

Iter	Nodes
done	5001
2	1605
1	515
0	202

prune574.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize24.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt (+ 1.0 x))
0.2b	(/ 1.0 (+ (sqrt (+ 1.0 x)) (sqrt x)))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

44×	`*-un-lft-identity`
20×	`sqrt-prod`
18×	`times-frac`
17×	`add-sqr-sqrt` `distribute-lft-out`
14×	`add-cube-cbrt`
6×	`associate-/r*`
4×	`add-cbrt-cube` `add-exp-log`
3×	`pow1` `associate-/l*`
2×	`expm1-log1p-u` `flip3-+` `sqrt-div` `associate-/r/` `flip-+` `log1p-expm1-u` `add-log-exp`
1×	`cbrt-undiv` `rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `hypot-def` `div-inv`

Counts

2 → 62

Calls

2 calls:

12.0ms	(sqrt (+ 1.0 x))
46.0ms	(/ 1.0 (+ (sqrt (+ 1.0 x)) (sqrt x)))

series270.0ms

Counts

2 → 6

Calls

2 calls:

54.0ms	(sqrt (+ 1.0 x))
216.0ms	(/ 1.0 (+ (sqrt (+ 1.0 x)) (sqrt x)))

simplify2.3s

Counts

68 → 68

Iterations

Iter	Nodes
done	5000
3	3699
2	1057
1	349
0	146

prune350.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ 1.0 x))
0.0b	(log1p (/ 1.0 (+ (sqrt (+ 1.0 x)) (sqrt x))))
0.0b	(expm1 (log1p (/ 1.0 (+ (sqrt (+ 1.0 x)) (sqrt x)))))
0.2b	(/ 1.0 (+ (sqrt (+ 1.0 x)) (sqrt x)))

rewrite85.0ms

Algorithm

rewrite-expression-head

Rules

46×	`*-un-lft-identity`
20×	`sqrt-prod`
19×	`add-sqr-sqrt`
18×	`times-frac`
17×	`distribute-lft-out`
16×	`add-cube-cbrt`
6×	`associate-/r*` `add-cbrt-cube` `add-exp-log`
5×	`expm1-log1p-u` `pow1`
4×	`log1p-expm1-u` `add-log-exp`
3×	`associate-/l*`
2×	`flip3-+` `sqrt-div` `associate-/r/` `flip-+`
1×	`cbrt-undiv` `rem-sqrt-square` `log1p-udef` `expm1-log1p` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `log1p-expm1` `hypot-def` `div-inv` `expm1-udef`

Counts

4 → 84

Calls

4 calls:

12.0ms	(sqrt (+ 1.0 x))
1.0ms	(log1p (/ 1.0 (+ (sqrt (+ 1.0 x)) (sqrt x))))
0.0ms	(expm1 (log1p (/ 1.0 (+ (sqrt (+ 1.0 x)) (sqrt x)))))
68.0ms	(/ 1.0 (+ (sqrt (+ 1.0 x)) (sqrt x)))

series2.1s

Counts

4 → 12

Calls

4 calls:

57.0ms	(sqrt (+ 1.0 x))
719.0ms	(log1p (/ 1.0 (+ (sqrt (+ 1.0 x)) (sqrt x))))
1.1s	(expm1 (log1p (/ 1.0 (+ (sqrt (+ 1.0 x)) (sqrt x)))))
196.0ms	(/ 1.0 (+ (sqrt (+ 1.0 x)) (sqrt x)))

simplify3.1s

Counts

96 → 96

Iterations

Iter	Nodes
done	5000
2	2165
1	623
0	239

prune553.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

regimes72.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify1.0ms

Iterations

Iter	Nodes
done	11
1	11
0	9

end0.0ms

sample1.5s

Algorithm

intervals

Results

365.0ms	7998×	body	80	nan
294.0ms	1648×	body	1280	valid
281.0ms	1266×	body	640	valid
138.0ms	4138×	body	80	valid
112.0ms	668×	body	320	valid
17.0ms	280×	body	160	valid