Details

sample43.0ms

Algorithm

intervals

Results

9.0ms	271×	body	80	nan
9.0ms	50×	body	1280	valid
7.0ms	49×	body	640	valid
5.0ms	133×	body	80	valid
1.0ms	14×	body	320	valid
1.0ms	10×	body	160	valid

simplify9.0ms

Counts

1 → 1

Iterations

Iter	Nodes
3	10
2	10
1	9
0	6

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.6b

localize19.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt (+ x 1))
2.5b	(- (sqrt (+ x 1)) (sqrt x))

rewrite75.0ms

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:

10.0ms	(sqrt (+ x 1))
63.0ms	(- (sqrt (+ x 1)) (sqrt x))

series136.0ms

Counts

2 → 6

Calls

2 calls:

39.0ms	(sqrt (+ x 1))
97.0ms	(- (sqrt (+ x 1)) (sqrt x))

simplify3.5s

Counts

98 → 98

Iterations

Iter	Nodes
4	3956
3	1441
2	597
1	283
0	134

prune872.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize16.0ms

Local error

Found 3 expressions with local error:

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

rewrite79.0ms

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:

31.0ms	(+ (sqrt (+ x 1)) (sqrt x))
5.0ms	(sqrt (+ x 1))
41.0ms	(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))

series208.0ms

Counts

3 → 9

Calls

3 calls:

79.0ms	(+ (sqrt (+ x 1)) (sqrt x))
40.0ms	(sqrt (+ x 1))
89.0ms	(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))

simplify2.1s

Counts

102 → 102

Iterations

Iter	Nodes
4	2635
3	1164
2	569
1	256
0	126

prune711.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize31.0ms

Local error

Found 3 expressions with local error:

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

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

55×	`*-un-lft-identity`
27×	`sqrt-prod`
21×	`add-sqr-sqrt` `distribute-lft-out`
18×	`times-frac`
17×	`add-cube-cbrt`
7×	`add-exp-log`
6×	`associate-/r*` `fma-def`
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 → 92

Calls

3 calls:

12.0ms	(+ (sqrt x) (sqrt (+ x 1)))
5.0ms	(sqrt (+ x 1))
24.0ms	(/ 1 (+ (sqrt x) (sqrt (+ x 1))))

series226.0ms

Counts

3 → 9

Calls

3 calls:

76.0ms	(+ (sqrt x) (sqrt (+ x 1)))
26.0ms	(sqrt (+ x 1))
124.0ms	(/ 1 (+ (sqrt x) (sqrt (+ x 1))))

simplify2.3s

Counts

101 → 101

Iterations

Iter	Nodes
4	2529
3	1171
2	573
1	257
0	126

prune895.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize24.0ms

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

rewrite255.0ms

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:

51.0ms	(sqrt (+ (sqrt (+ x 1)) (sqrt x)))
29.0ms	(sqrt (+ (sqrt (+ x 1)) (sqrt x)))
47.0ms	(/ 1 (sqrt (+ (sqrt (+ x 1)) (sqrt x))))
103.0ms	(/ (/ 1 (sqrt (+ (sqrt (+ x 1)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1)) (sqrt x))))

series502.0ms

Counts

4 → 12

Calls

4 calls:

123.0ms	(sqrt (+ (sqrt (+ x 1)) (sqrt x)))
120.0ms	(sqrt (+ (sqrt (+ x 1)) (sqrt x)))
172.0ms	(/ 1 (sqrt (+ (sqrt (+ x 1)) (sqrt x))))
87.0ms	(/ (/ 1 (sqrt (+ (sqrt (+ x 1)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1)) (sqrt x))))

simplify1.2m

Counts

491 → 491

Iterations

Iter	Nodes
3	4201
2	1636
1	855
0	370

prune2.9s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

regimes38.0ms

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
2	9
1	9
0	7

end0.0ms

sample1.6s

Algorithm

intervals

Results

503.0ms	1286×	body	640	valid
385.0ms	1718×	body	1280	valid
312.0ms	8041×	body	80	nan
189.0ms	4111×	body	80	valid
61.0ms	595×	body	320	valid
20.0ms	290×	body	160	valid