Details

sample60.0ms

Algorithm

intervals

Results

17.0ms	278×	body	80	nan
12.0ms	55×	body	1280	valid
8.0ms	39×	body	640	valid
7.0ms	134×	body	80	valid
2.0ms	18×	body	320	valid
1.0ms	10×	body	160	valid

simplify6.0ms

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: 29.3b

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt (+ x 1))
2.8b	(- (sqrt (+ x 1)) (sqrt x))

rewrite52.0ms

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:

5.0ms	(sqrt (+ x 1))
45.0ms	(- (sqrt (+ x 1)) (sqrt x))

series106.0ms

Counts

2 → 6

Calls

2 calls:

31.0ms	(sqrt (+ x 1))
75.0ms	(- (sqrt (+ x 1)) (sqrt x))

simplify1.0s

Counts

98 → 98

Iterations

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

prune827.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 28.2b

localize32.0ms

Local error

Found 4 expressions with local error:

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

rewrite156.0ms

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:

22.0ms	(+ (sqrt (+ x 1)) (sqrt x))
5.0ms	(sqrt (+ x 1))
86.0ms	(/ (- (+ x 1) x) (+ (sqrt (+ x 1)) (sqrt x)))
40.0ms	(- (+ x 1) x)

series198.0ms

Counts

4 → 12

Calls

4 calls:

87.0ms	(+ (sqrt (+ x 1)) (sqrt x))
26.0ms	(sqrt (+ x 1))
84.0ms	(/ (- (+ x 1) x) (+ (sqrt (+ x 1)) (sqrt x)))
1.0ms	(- (+ x 1) x)

simplify1.1s

Counts

161 → 161

Iterations

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

prune1.4s

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)))

rewrite74.0ms

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:

5.0ms	(sqrt (+ x 1))
21.0ms	(+ (sqrt (+ x 1)) (sqrt x))
47.0ms	(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))

series191.0ms

Counts

3 → 9

Calls

3 calls:

33.0ms	(sqrt (+ x 1))
62.0ms	(+ (sqrt (+ x 1)) (sqrt x))
96.0ms	(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))

simplify1.4s

Counts

102 → 102

Iterations

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

prune816.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 4 expressions with local error:

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

rewrite206.0ms

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:

40.0ms	(sqrt (+ (sqrt (+ x 1)) (sqrt x)))
44.0ms	(sqrt (+ (sqrt (+ x 1)) (sqrt x)))
74.0ms	(/ (/ 1 (sqrt (+ (sqrt (+ x 1)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1)) (sqrt x))))
29.0ms	(/ 1 (sqrt (+ (sqrt (+ x 1)) (sqrt x))))

series559.0ms

Counts

4 → 12

Calls

4 calls:

146.0ms	(sqrt (+ (sqrt (+ x 1)) (sqrt x)))
127.0ms	(sqrt (+ (sqrt (+ x 1)) (sqrt x)))
95.0ms	(/ (/ 1 (sqrt (+ (sqrt (+ x 1)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1)) (sqrt x))))
191.0ms	(/ 1 (sqrt (+ (sqrt (+ x 1)) (sqrt x))))

simplify1.4s

Counts

491 → 491

Iterations

Iter	Nodes
done	2014
3	2014
2	1770
1	872
0	370

prune4.7s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

regimes77.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	13
1	13
0	9

end0.0ms

sample2.4s

Algorithm

intervals

Results

782.0ms	1698×	body	1280	valid
576.0ms	8086×	body	80	nan
410.0ms	1266×	body	640	valid
250.0ms	4089×	body	80	valid
105.0ms	650×	body	320	valid
31.0ms	297×	body	160	valid