Details

sample51.0ms

Algorithm

intervals

Results

10.0ms	54×	body	1280	valid
10.0ms	270×	body	80	nan
5.0ms	135×	body	80	valid
5.0ms	31×	body	640	valid
2.0ms	21×	body	320	valid
1.0ms	15×	body	160	valid

simplify4.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	10
2	10
1	9
0	6

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.1b

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt (+ x 1.0))
4.0b	(- (sqrt (+ x 1.0)) (sqrt x))

rewrite102.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 89

Calls

2 calls:

12.0ms	(sqrt (+ x 1.0))
83.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

series172.0ms

Counts

2 → 6

Calls

2 calls:

48.0ms	(sqrt (+ x 1.0))
124.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

simplify2.2s

Counts

95 → 95

Iterations

Iter	Nodes
done	5003
3	2271
2	785
1	322
0	139

prune300.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 27.6b

localize36.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ 1.0 x))
0.0b	(+ (sqrt (+ 1.0 x)) (sqrt x))
0.0b	(/ (- (+ 1.0 x) x) (+ (sqrt (+ 1.0 x)) (sqrt x)))
3.2b	(- (+ 1.0 x) x)

rewrite297.0ms

Algorithm

rewrite-expression-head

Rules

137×	`*-un-lft-identity`
48×	`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` `log1p-expm1-u`
3×	`flip3-+` `flip-+`
2×	`sum-log` `flip3--` `sqrt-div` `diff-log` `associate-/r/` `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-def` `div-inv`

Counts

4 → 144

Calls

4 calls:

12.0ms	(sqrt (+ 1.0 x))
55.0ms	(+ (sqrt (+ 1.0 x)) (sqrt x))
150.0ms	(/ (- (+ 1.0 x) x) (+ (sqrt (+ 1.0 x)) (sqrt x)))
69.0ms	(- (+ 1.0 x) x)

series287.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(sqrt (+ 1.0 x))
73.0ms	(+ (sqrt (+ 1.0 x)) (sqrt x))
180.0ms	(/ (- (+ 1.0 x) x) (+ (sqrt (+ 1.0 x)) (sqrt x)))
2.0ms	(- (+ 1.0 x) x)

simplify1.8s

Counts

156 → 156

Iterations

Iter	Nodes
done	5000
2	1716
1	558
0	217

prune644.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize24.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (+ 1.0 x))
0.0b	(+ (sqrt (+ 1.0 x)) (sqrt x))
0.1b	(/ 1.0 (+ (sqrt (+ 1.0 x)) (sqrt x)))

rewrite143.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 85

Calls

3 calls:

12.0ms	(sqrt (+ 1.0 x))
55.0ms	(+ (sqrt (+ 1.0 x)) (sqrt x))
73.0ms	(/ 1.0 (+ (sqrt (+ 1.0 x)) (sqrt x)))

series326.0ms

Counts

3 → 9

Calls

3 calls:

32.0ms	(sqrt (+ 1.0 x))
113.0ms	(+ (sqrt (+ 1.0 x)) (sqrt x))
180.0ms	(/ 1.0 (+ (sqrt (+ 1.0 x)) (sqrt x)))

simplify2.7s

Counts

94 → 94

Iterations

Iter	Nodes
done	5000
3	4094
2	1182
1	394
0	162

prune470.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize38.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (/ 1.0 (+ (sqrt (+ 1.0 x)) (sqrt x))))
0.1b	(/ 1.0 (+ (sqrt (+ 1.0 x)) (sqrt x)))
0.1b	(/ 1.0 (+ (sqrt (+ 1.0 x)) (sqrt x)))
0.3b	(* (sqrt (/ 1.0 (+ (sqrt (+ 1.0 x)) (sqrt x)))) (sqrt (/ 1.0 (+ (sqrt (+ 1.0 x)) (sqrt x)))))

rewrite426.0ms

Algorithm

rewrite-expression-head

Rules

297×	`*-un-lft-identity`
274×	`sqrt-prod`
157×	`times-frac`
119×	`add-sqr-sqrt`
116×	`distribute-lft-out`
88×	`add-cube-cbrt`
41×	`swap-sqr`
27×	`associate-r` `associate-l`
20×	`pow1`
14×	`associate-/r/`
12×	`associate-/r*`
10×	`add-cbrt-cube` `add-exp-log`
9×	`sqrt-pow1` `pow1/2` `unswap-sqr`
7×	`flip3-+` `flip-+` `div-inv`
6×	`associate-/l*`
5×	`sqrt-div` `pow-prod-up`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-prod-down` `pow-sqr`
2×	`cbrt-undiv` `rem-sqrt-square` `clear-num` `frac-2neg` `div-exp`
1×	`pow2` `frac-times` `rem-square-sqrt` `pow-plus` `sqrt-unprod` `associate-l/` `prod-exp` `associate-r/` `*-commutative` `cbrt-unprod`

Counts

4 → 258

Calls

4 calls:

55.0ms	(sqrt (/ 1.0 (+ (sqrt (+ 1.0 x)) (sqrt x))))
67.0ms	(/ 1.0 (+ (sqrt (+ 1.0 x)) (sqrt x)))
68.0ms	(/ 1.0 (+ (sqrt (+ 1.0 x)) (sqrt x)))
218.0ms	(* (sqrt (/ 1.0 (+ (sqrt (+ 1.0 x)) (sqrt x)))) (sqrt (/ 1.0 (+ (sqrt (+ 1.0 x)) (sqrt x)))))

series1.2s

Counts

4 → 12

Calls

4 calls:

516.0ms	(sqrt (/ 1.0 (+ (sqrt (+ 1.0 x)) (sqrt x))))
188.0ms	(/ 1.0 (+ (sqrt (+ 1.0 x)) (sqrt x)))
211.0ms	(/ 1.0 (+ (sqrt (+ 1.0 x)) (sqrt x)))
244.0ms	(* (sqrt (/ 1.0 (+ (sqrt (+ 1.0 x)) (sqrt x)))) (sqrt (/ 1.0 (+ (sqrt (+ 1.0 x)) (sqrt x)))))

simplify2.2s

Counts

270 → 270

Iterations

Iter	Nodes
done	5006
2	2003
1	720
0	316

prune1.0s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

regimes85.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	9
1	9
0	7

end0.0ms

sample1.9s

Algorithm

intervals

Results

776.0ms	1729×	body	1280	valid
323.0ms	7925×	body	80	nan
289.0ms	1249×	body	640	valid
135.0ms	4039×	body	80	valid
63.0ms	659×	body	320	valid
28.0ms	324×	body	160	valid