Details

sample67.0ms

Algorithm

intervals

Results

22.0ms	55×	body	1280	valid
14.0ms	278×	body	80	nan
8.0ms	39×	body	640	valid
7.0ms	134×	body	80	valid
3.0ms	18×	body	320	valid
1.0ms	10×	body	160	valid

simplify7.0ms

Counts

1 → 1

Iterations

Iter	Nodes
3	10
2	10
1	9
0	6

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.3b

localize20.0ms

Local error

Found 2 expressions with local error:

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

rewrite45.0ms

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:

11.0ms	(sqrt (+ x 1))
31.0ms	(- (sqrt (+ x 1)) (sqrt x))

series134.0ms

Counts

2 → 6

Calls

2 calls:

40.0ms	(sqrt (+ x 1))
94.0ms	(- (sqrt (+ x 1)) (sqrt x))

simplify3.5s

Counts

98 → 98

Iterations

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

prune799.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize26.0ms

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)))

rewrite77.0ms

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:

6.0ms	(sqrt (+ x 1))
21.0ms	(+ (sqrt (+ x 1)) (sqrt x))
47.0ms	(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))

series173.0ms

Counts

3 → 9

Calls

3 calls:

31.0ms	(sqrt (+ x 1))
66.0ms	(+ (sqrt (+ x 1)) (sqrt x))
77.0ms	(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))

simplify2.3s

Counts

102 → 102

Iterations

Iter	Nodes
4	2673
3	1160
2	569
1	256
0	126

prune876.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize28.0ms

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))))

rewrite227.0ms

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:

29.0ms	(sqrt (+ (sqrt (+ x 1)) (sqrt x)))
39.0ms	(sqrt (+ (sqrt (+ x 1)) (sqrt x)))
98.0ms	(/ (/ 1 (sqrt (+ (sqrt (+ x 1)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1)) (sqrt x))))
36.0ms	(/ 1 (sqrt (+ (sqrt (+ x 1)) (sqrt x))))

series538.0ms

Counts

4 → 12

Calls

4 calls:

143.0ms	(sqrt (+ (sqrt (+ x 1)) (sqrt x)))
138.0ms	(sqrt (+ (sqrt (+ x 1)) (sqrt x)))
102.0ms	(/ (/ 1 (sqrt (+ (sqrt (+ x 1)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1)) (sqrt x))))
154.0ms	(/ 1 (sqrt (+ (sqrt (+ x 1)) (sqrt x))))

simplify1.2m

Counts

491 → 491

Iterations

Iter	Nodes
3	4440
2	1672
1	848
0	370

prune3.1s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ x 1))
0.0b	(log1p (expm1 (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))))
0.1b	(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
0.5b	(expm1 (/ 1 (+ (sqrt (+ x 1)) (sqrt x))))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

47×	`*-un-lft-identity`
20×	`add-sqr-sqrt` `sqrt-prod`
18×	`times-frac`
17×	`distribute-lft-out`
16×	`add-cube-cbrt`
8×	`add-exp-log`
6×	`pow1` `associate-/r*` `add-cbrt-cube`
5×	`log1p-expm1-u`
4×	`expm1-log1p-u` `insert-posit16` `add-log-exp`
3×	`associate-/l*`
2×	`flip3-+` `sqrt-div` `div-exp` `associate-/r/` `flip-+` `hypot-def`
1×	`cbrt-undiv` `rem-sqrt-square` `rec-exp` `log1p-udef` `expm1-log1p` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `1-exp` `log1p-expm1` `div-inv` `pow-flip` `inv-pow` `expm1-udef`

Counts

4 → 93

Calls

4 calls:

5.0ms	(sqrt (+ x 1))
0.0ms	(log1p (expm1 (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))))
26.0ms	(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
0.0ms	(expm1 (/ 1 (+ (sqrt (+ x 1)) (sqrt x))))

series390.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(sqrt (+ x 1))
180.0ms	(log1p (expm1 (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))))
69.0ms	(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
118.0ms	(expm1 (/ 1 (+ (sqrt (+ x 1)) (sqrt x))))

simplify2.1s

Counts

105 → 105

Iterations

Iter	Nodes
4	3731
3	1485
2	679
1	313
0	153

prune669.0ms

Pruning

7 alts after pruning (6 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	11
1	11
0	9

end0.0ms

sample1.7s

Algorithm

intervals

Results

441.0ms	1698×	body	1280	valid
323.0ms	297×	body	160	valid
316.0ms	8086×	body	80	nan
278.0ms	1266×	body	640	valid
157.0ms	4089×	body	80	valid
70.0ms	650×	body	320	valid