Details

sample46.0ms

Algorithm

intervals

Results

13.0ms	62×	body	1280	valid
8.0ms	213×	body	80	nan
6.0ms	134×	body	80	valid
5.0ms	30×	body	640	valid
3.0ms	26×	body	320	valid
1.0ms	4×	body	160	valid

simplify10.0ms

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

localize21.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt (+ x 1))
2.0b	(- (sqrt (+ x 1)) (sqrt x))

rewrite69.0ms

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))
63.0ms	(- (sqrt (+ x 1)) (sqrt x))

series103.0ms

Counts

2 → 6

Calls

2 calls:

27.0ms	(sqrt (+ x 1))
76.0ms	(- (sqrt (+ x 1)) (sqrt x))

simplify867.0ms

Counts

98 → 98

Iterations

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

prune281.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 28.2b

localize29.0ms

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)))
1.7b	(- (+ x 1) x)

rewrite197.0ms

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:

31.0ms	(+ (sqrt (+ x 1)) (sqrt x))
10.0ms	(sqrt (+ x 1))
124.0ms	(/ (- (+ x 1) x) (+ (sqrt (+ x 1)) (sqrt x)))
29.0ms	(- (+ x 1) x)

series209.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(+ (sqrt (+ x 1)) (sqrt x))
38.0ms	(sqrt (+ x 1))
87.0ms	(/ (- (+ x 1) x) (+ (sqrt (+ x 1)) (sqrt x)))
1.0ms	(- (+ x 1) x)

simplify744.0ms

Counts

161 → 161

Iterations

Iter	Nodes
done	2003
2	1308
1	446
0	183

prune442.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize16.0ms

Local error

Found 3 expressions with local error:

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

rewrite69.0ms

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:

9.0ms	(sqrt (+ x 1))
21.0ms	(+ (sqrt (+ x 1)) (sqrt x))
36.0ms	(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))

series189.0ms

Counts

3 → 9

Calls

3 calls:

25.0ms	(sqrt (+ x 1))
71.0ms	(+ (sqrt (+ x 1)) (sqrt x))
93.0ms	(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))

simplify1.2s

Counts

102 → 102

Iterations

Iter	Nodes
done	2000
3	1839
2	719
1	264
0	126

prune408.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize41.0ms

Local error

Found 4 expressions with local error:

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

rewrite101.0ms

Algorithm

rewrite-expression-head

Rules

106×	`sqrt-prod`
62×	`add-sqr-sqrt`
46×	`*-un-lft-identity`
40×	`sqrt-pow1`
32×	`pow1` `sqrt-div`
28×	`add-cube-cbrt`
20×	`pow1/2`
18×	`swap-sqr`
10×	`associate-r` `associate-l` `add-exp-log`
9×	`flip3-+` `times-frac` `pow-prod-up` `flip-+` `unswap-sqr`
8×	`add-cbrt-cube` `distribute-lft-out`
5×	`pow-prod-down` `pow-sqr`
4×	`expm1-log1p-u` `frac-times` `rem-sqrt-square` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r` `associate-/l`
2×	`div-exp` `associate-l/` `associate-r/` `associate-/r/`
1×	`pow2` `cbrt-undiv` `rec-exp` `clear-num` `rem-square-sqrt` `frac-2neg` `pow-plus` `sqrt-unprod` `1-exp` `prod-exp` `*-commutative` `cbrt-unprod` `div-inv` `pow-flip` `inv-pow`

Counts

4 → 177

Calls

4 calls:

5.0ms	(sqrt (sqrt (+ x 1)))
5.0ms	(sqrt (sqrt (+ x 1)))
52.0ms	(/ 1 (+ (* (sqrt (sqrt (+ x 1))) (sqrt (sqrt (+ x 1)))) (sqrt x)))
35.0ms	(* (sqrt (sqrt (+ x 1))) (sqrt (sqrt (+ x 1))))

series212.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(sqrt (sqrt (+ x 1)))
42.0ms	(sqrt (sqrt (+ x 1)))
96.0ms	(/ 1 (+ (* (sqrt (sqrt (+ x 1))) (sqrt (sqrt (+ x 1)))) (sqrt x)))
29.0ms	(* (sqrt (sqrt (+ x 1))) (sqrt (sqrt (+ x 1))))

simplify863.0ms

Counts

189 → 189

Iterations

Iter	Nodes
done	2001
2	1049
1	458
0	217

prune597.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

regimes70.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify6.0ms

Iterations

Iter	Nodes
done	22
1	22
0	16

end0.0ms

sample2.3s

Algorithm

intervals

Results

841.0ms	1749×	body	1280	valid
423.0ms	7964×	body	80	nan
388.0ms	4127×	body	80	valid
276.0ms	1191×	body	640	valid
151.0ms	624×	body	320	valid
34.0ms	309×	body	160	valid