Details

sample56.0ms

Algorithm

intervals

Results

16.0ms	66×	body	1280	valid
12.0ms	245×	body	80	nan
7.0ms	138×	body	80	valid
4.0ms	21×	body	640	valid
3.0ms	22×	body	320	valid
1.0ms	9×	body	160	valid

simplify5.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	12
2	12
1	11
0	6

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.5b

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt (+ x 1))
2.9b	(- (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:

9.0ms	(sqrt (+ x 1))
51.0ms	(- (sqrt (+ x 1)) (sqrt x))

series106.0ms

Counts

2 → 6

Calls

2 calls:

30.0ms	(sqrt (+ x 1))
77.0ms	(- (sqrt (+ x 1)) (sqrt x))

simplify2.8s

Counts

98 → 98

Iterations

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

prune304.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 27.4b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ 1 x))
0.0b	(+ (sqrt x) (sqrt (+ 1 x)))
0.0b	(/ (- (+ 1 x) x) (+ (sqrt x) (sqrt (+ 1 x))))
2.4b	(- (+ 1 x) x)

rewrite171.0ms

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:

5.0ms	(sqrt (+ 1 x))
16.0ms	(+ (sqrt x) (sqrt (+ 1 x)))
98.0ms	(/ (- (+ 1 x) x) (+ (sqrt x) (sqrt (+ 1 x))))
49.0ms	(- (+ 1 x) x)

series189.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(sqrt (+ 1 x))
64.0ms	(+ (sqrt x) (sqrt (+ 1 x)))
84.0ms	(/ (- (+ 1 x) x) (+ (sqrt x) (sqrt (+ 1 x))))
1.0ms	(- (+ 1 x) x)

simplify3.0s

Counts

161 → 161

Iterations

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

prune502.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize15.0ms

Local error

Found 3 expressions with local error:

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

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

57×	`*-un-lft-identity`
28×	`sqrt-prod`
22×	`add-sqr-sqrt` `distribute-lft-out`
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` `hypot-1-def` `div-inv` `pow-flip` `inv-pow`

Counts

3 → 94

Calls

3 calls:

6.0ms	(sqrt (+ 1 x))
20.0ms	(+ (sqrt (+ 1 x)) (sqrt x))
34.0ms	(/ 1 (+ (sqrt (+ 1 x)) (sqrt x)))

series162.0ms

Counts

3 → 9

Calls

3 calls:

33.0ms	(sqrt (+ 1 x))
56.0ms	(+ (sqrt (+ 1 x)) (sqrt x))
73.0ms	(/ 1 (+ (sqrt (+ 1 x)) (sqrt x)))

simplify3.2s

Counts

103 → 103

Iterations

Iter	Nodes
done	5000
4	4459
3	1879
2	725
1	266
0	126

prune308.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (+ (sqrt (+ 1 x)) (sqrt x)))
0.1b	(sqrt (+ (sqrt (+ 1 x)) (sqrt x)))
0.2b	(/ 1 (sqrt (+ (sqrt (+ 1 x)) (sqrt x))))
0.2b	(/ (/ 1 (sqrt (+ (sqrt (+ 1 x)) (sqrt x)))) (sqrt (+ (sqrt (+ 1 x)) (sqrt x))))

rewrite213.0ms

Algorithm

rewrite-expression-head

Rules

742×	`*-un-lft-identity`
708×	`sqrt-prod`
594×	`times-frac`
280×	`distribute-lft-out`
270×	`add-sqr-sqrt`
252×	`add-cube-cbrt`
36×	`associate-/l*`
28×	`sqrt-div`
24×	`associate-/r/`
18×	`associate-/r*`
17×	`add-exp-log`
15×	`pow1`
14×	`flip3-+` `flip-+`
12×	`div-inv`
11×	`add-cbrt-cube`
8×	`div-exp` `hypot-def` `pow-flip`
7×	`sqrt-pow1` `pow1/2`
6×	`pow-div`
4×	`expm1-log1p-u` `cbrt-undiv` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square` `rec-exp` `clear-num` `frac-2neg` `1-exp` `inv-pow`
1×	`associate-/l/`

Counts

4 → 479

Calls

4 calls:

24.0ms	(sqrt (+ (sqrt (+ 1 x)) (sqrt x)))
43.0ms	(sqrt (+ (sqrt (+ 1 x)) (sqrt x)))
45.0ms	(/ 1 (sqrt (+ (sqrt (+ 1 x)) (sqrt x))))
79.0ms	(/ (/ 1 (sqrt (+ (sqrt (+ 1 x)) (sqrt x)))) (sqrt (+ (sqrt (+ 1 x)) (sqrt x))))

series538.0ms

Counts

4 → 12

Calls

4 calls:

120.0ms	(sqrt (+ (sqrt (+ 1 x)) (sqrt x)))
133.0ms	(sqrt (+ (sqrt (+ 1 x)) (sqrt x)))
191.0ms	(/ 1 (sqrt (+ (sqrt (+ 1 x)) (sqrt x))))
94.0ms	(/ (/ 1 (sqrt (+ (sqrt (+ 1 x)) (sqrt x)))) (sqrt (+ (sqrt (+ 1 x)) (sqrt x))))

simplify2.1s

Counts

491 → 491

Iterations

Iter	Nodes
done	5000
2	1785
1	881
0	370

prune1.4s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

regimes37.0ms

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	7

end0.0ms

sample2.1s

Algorithm

intervals

Results

637.0ms	1233×	body	640	valid
511.0ms	1731×	body	1280	valid
391.0ms	7851×	body	80	nan
213.0ms	4077×	body	80	valid
102.0ms	636×	body	320	valid
26.0ms	323×	body	160	valid