Details

sample37.0ms

Algorithm

intervals

Results

11.0ms	46×	body	640	valid
7.0ms	55×	body	1280	valid
5.0ms	211×	body	80	nan
3.0ms	132×	body	80	valid
1.0ms	16×	body	320	valid
0.0ms	7×	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: 29.9b

localize12.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt (+ x 1))
2.1b	(- (sqrt (+ x 1)) (sqrt x))

rewrite64.0ms

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:

8.0ms	(sqrt (+ x 1))
53.0ms	(- (sqrt (+ x 1)) (sqrt x))

series130.0ms

Counts

2 → 6

Calls

2 calls:

45.0ms	(sqrt (+ x 1))
85.0ms	(- (sqrt (+ x 1)) (sqrt x))

simplify2.9s

Counts

98 → 98

Iterations

Iter	Nodes
done	5000
4	4262
3	1554
2	618
1	294
0	134

prune268.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 28.9b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ 1 x))
0.0b	(+ (sqrt x) (sqrt (+ 1 x)))
0.1b	(/ (- (+ 1 x) x) (+ (sqrt x) (sqrt (+ 1 x))))
1.7b	(- (+ 1 x) x)

rewrite256.0ms

Algorithm

rewrite-expression-head

Rules

136×	`*-un-lft-identity`
50×	`add-sqr-sqrt`
45×	`distribute-lft-out`
39×	`sqrt-prod`
36×	`times-frac`
29×	`add-cube-cbrt`
16×	`distribute-lft-out--`
12×	`prod-diff`
11×	`add-log-exp`
8×	`difference-of-squares`
6×	`associate-/r` `fma-def` `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+` `hypot-1-def` `div-inv`

Counts

4 → 149

Calls

4 calls:

15.0ms	(sqrt (+ 1 x))
34.0ms	(+ (sqrt x) (sqrt (+ 1 x)))
145.0ms	(/ (- (+ 1 x) x) (+ (sqrt x) (sqrt (+ 1 x))))
54.0ms	(- (+ 1 x) x)

series226.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(sqrt (+ 1 x))
66.0ms	(+ (sqrt x) (sqrt (+ 1 x)))
118.0ms	(/ (- (+ 1 x) x) (+ (sqrt x) (sqrt (+ 1 x))))
2.0ms	(- (+ 1 x) x)

simplify3.4s

Counts

161 → 161

Iterations

Iter	Nodes
done	5011
3	3180
2	1272
1	455
0	186

prune509.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

localize43.0ms

Local error

Found 4 expressions with local error:

0.0b	(log1p (/ 1 (+ (sqrt (+ 1 x)) (sqrt x))))
0.0b	(+ (sqrt (+ 1 x)) (sqrt x))
0.0b	(expm1 (log1p (/ 1 (+ (sqrt (+ 1 x)) (sqrt x)))))
0.2b	(/ 1 (+ (sqrt (+ 1 x)) (sqrt x)))

rewrite122.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 96

Calls

4 calls:

0.0ms	(log1p (/ 1 (+ (sqrt (+ 1 x)) (sqrt x))))
43.0ms	(+ (sqrt (+ 1 x)) (sqrt x))
0.0ms	(expm1 (log1p (/ 1 (+ (sqrt (+ 1 x)) (sqrt x)))))
76.0ms	(/ 1 (+ (sqrt (+ 1 x)) (sqrt x)))

series580.0ms

Counts

4 → 12

Calls

4 calls:

186.0ms	(log1p (/ 1 (+ (sqrt (+ 1 x)) (sqrt x))))
61.0ms	(+ (sqrt (+ 1 x)) (sqrt x))
242.0ms	(expm1 (log1p (/ 1 (+ (sqrt (+ 1 x)) (sqrt x)))))
92.0ms	(/ 1 (+ (sqrt (+ 1 x)) (sqrt x)))

simplify3.1s

Counts

108 → 108

Iterations

Iter	Nodes
done	5020
4	2906
3	1201
2	563
1	249
0	121

prune459.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize51.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (+ 1 x))
0.3b	(cbrt (+ 1 x))
0.3b	(cbrt (+ 1 x))
0.3b	(* (cbrt (+ 1 x)) (cbrt (+ 1 x)))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

36×	`cbrt-prod`
35×	`*-un-lft-identity`
23×	`add-sqr-sqrt`
18×	`cbrt-div`
15×	`add-cube-cbrt`
11×	`pow1`
9×	`flip3-+` `pow1/3` `swap-sqr` `flip-+` `distribute-lft-out`
7×	`associate-r` `associate-l`
6×	`add-exp-log`
4×	`expm1-log1p-u` `frac-times` `add-cbrt-cube` `insert-posit16` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `associate-l/` `associate-r/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 107

Calls

4 calls:

4.0ms	(cbrt (+ 1 x))
4.0ms	(cbrt (+ 1 x))
4.0ms	(cbrt (+ 1 x))
40.0ms	(* (cbrt (+ 1 x)) (cbrt (+ 1 x)))

series207.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(cbrt (+ 1 x))
41.0ms	(cbrt (+ 1 x))
49.0ms	(cbrt (+ 1 x))
64.0ms	(* (cbrt (+ 1 x)) (cbrt (+ 1 x)))

simplify2.1s

Counts

119 → 119

Iterations

Iter	Nodes
done	5000
3	2025
2	869
1	297
0	127

prune694.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

regimes108.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify5.0ms

Iterations

Iter	Nodes
done	13
1	13
0	9

end0.0ms

sample2.1s

Algorithm

intervals

Results

866.0ms	7974×	body	80	nan
411.0ms	1720×	body	1280	valid
230.0ms	4071×	body	80	valid
192.0ms	1264×	body	640	valid
73.0ms	613×	body	320	valid
73.0ms	332×	body	160	valid