Details

sample51.0ms

Algorithm

intervals

Results

14.0ms	66×	body	1280	valid
11.0ms	258×	body	80	nan
8.0ms	47×	body	640	valid
5.0ms	117×	body	80	valid
1.0ms	13×	body	320	valid
1.0ms	13×	body	160	valid

simplify8.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	12
2	12
1	11
0	6

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.1b

localize18.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt (+ x 1))
3.2b	(- (sqrt (+ x 1)) (sqrt x))

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

61×	`sqrt-prod`
55×	`*-un-lft-identity`
43×	`add-sqr-sqrt`
42×	`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` `hypot-def` `insert-posit16` `log1p-expm1-u`
1×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `flip3-+` `flip3--` `pow1/2` `diff-log` `flip-+` `flip--`

Counts

2 → 92

Calls

2 calls:

6.0ms	(sqrt (+ x 1))
65.0ms	(- (sqrt (+ x 1)) (sqrt x))

series88.0ms

Counts

2 → 6

Calls

2 calls:

28.0ms	(sqrt (+ x 1))
60.0ms	(- (sqrt (+ x 1)) (sqrt x))

simplify1.1s

Counts

98 → 98

Iterations

Iter	Nodes
done	2000
4	2000
3	1554
2	618
1	294
0	134

prune350.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 31.5b

localize31.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ x 1))
0.0b	(+ (sqrt (+ x 1)) (sqrt x))
0.1b	(/ (- (+ x 1) x) (+ (sqrt (+ x 1)) (sqrt x)))
2.2b	(- (+ x 1) x)

rewrite186.0ms

Algorithm

rewrite-expression-head

Rules

138×	`*-un-lft-identity`
49×	`add-sqr-sqrt`
46×	`distribute-lft-out`
40×	`sqrt-prod`
36×	`times-frac`
29×	`add-cube-cbrt`
16×	`distribute-lft-out--`
12×	`prod-diff`
11×	`add-log-exp`
8×	`difference-of-squares`
7×	`fma-def`
6×	`associate-/r` `add-cbrt-cube` `add-exp-log` `associate-/l`
5×	`pow1`
4×	`expm1-log1p-u` `fma-neg` `insert-posit16` `log1p-expm1-u`
3×	`flip3-+` `flip-+`
2×	`sum-log` `flip3--` `sqrt-div` `diff-log` `associate-/r/` `hypot-def` `flip--` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `clear-num` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `div-exp` `associate--l+` `div-inv`

Counts

4 → 149

Calls

4 calls:

5.0ms	(sqrt (+ x 1))
28.0ms	(+ (sqrt (+ x 1)) (sqrt x))
117.0ms	(/ (- (+ x 1) x) (+ (sqrt (+ x 1)) (sqrt x)))
33.0ms	(- (+ x 1) x)

series175.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(sqrt (+ x 1))
66.0ms	(+ (sqrt (+ x 1)) (sqrt x))
84.0ms	(/ (- (+ x 1) x) (+ (sqrt (+ x 1)) (sqrt x)))
1.0ms	(- (+ x 1) x)

simplify1.2s

Counts

161 → 161

Iterations

Iter	Nodes
done	2003
3	2003
2	1308
1	446
0	183

prune602.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize23.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (+ x 1))
0.0b	(+ (sqrt (+ x 1)) (sqrt x))
0.1b	(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))

rewrite107.0ms

Algorithm

rewrite-expression-head

Rules

57×	`*-un-lft-identity`
28×	`sqrt-prod`
22×	`distribute-lft-out`
21×	`add-sqr-sqrt`
18×	`times-frac`
17×	`add-cube-cbrt`
7×	`fma-def` `add-exp-log`
6×	`associate-/r*`
5×	`pow1` `add-cbrt-cube` `add-log-exp`
3×	`expm1-log1p-u` `flip3-+` `flip-+` `insert-posit16` `log1p-expm1-u` `associate-/l*`
2×	`sqrt-div` `div-exp` `associate-/r/` `hypot-def`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `rec-exp` `clear-num` `sum-log` `frac-2neg` `sqrt-pow1` `pow1/2` `1-exp` `div-inv` `pow-flip` `inv-pow`

Counts

3 → 93

Calls

3 calls:

8.0ms	(sqrt (+ x 1))
45.0ms	(+ (sqrt (+ x 1)) (sqrt x))
53.0ms	(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))

series230.0ms

Counts

3 → 9

Calls

3 calls:

44.0ms	(sqrt (+ x 1))
88.0ms	(+ (sqrt (+ x 1)) (sqrt x))
97.0ms	(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))

simplify1.5s

Counts

102 → 102

Iterations

Iter	Nodes
done	2011
4	2011
3	1839
2	719
1	264
0	126

prune376.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 3 expressions with local error:

0.0b	(hypot (sqrt x) 1)
0.0b	(+ (hypot (sqrt x) 1) (sqrt x))
0.1b	(/ 1 (+ (hypot (sqrt x) 1) (sqrt x)))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

23×	`*-un-lft-identity`
13×	`add-sqr-sqrt` `add-cube-cbrt`
12×	`times-frac`
7×	`add-exp-log`
5×	`add-cbrt-cube` `distribute-lft-out` `add-log-exp`
4×	`pow1` `associate-/r*`
3×	`expm1-log1p-u` `fma-def` `insert-posit16` `log1p-expm1-u` `associate-/l*`
2×	`flip3-+` `div-exp` `associate-/r/` `flip-+`
1×	`cbrt-undiv` `+-commutative` `rec-exp` `hypot-udef` `clear-num` `sum-log` `frac-2neg` `1-exp` `div-inv` `pow-flip` `inv-pow`

Counts

3 → 69

Calls

3 calls:

0.0ms	(hypot (sqrt x) 1)
5.0ms	(+ (hypot (sqrt x) 1) (sqrt x))
15.0ms	(/ 1 (+ (hypot (sqrt x) 1) (sqrt x)))

series1.2s

Counts

3 → 9

Calls

3 calls:

235.0ms	(hypot (sqrt x) 1)
315.0ms	(+ (hypot (sqrt x) 1) (sqrt x))
658.0ms	(/ 1 (+ (hypot (sqrt x) 1) (sqrt x)))

simplify1.5s

Counts

78 → 78

Iterations

Iter	Nodes
done	2035
3	2035
2	1281
1	445
0	173

prune330.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

regimes43.0ms

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	9
1	9
0	6

end0.0ms

sample2.3s

Algorithm

intervals

Results

692.0ms	1254×	body	640	valid
565.0ms	1686×	body	1280	valid
418.0ms	8102×	body	80	nan
281.0ms	4159×	body	80	valid
130.0ms	612×	body	320	valid
29.0ms	289×	body	160	valid