Details

sample43.0ms

Algorithm

intervals

Results

9.0ms	54×	body	1280	valid
9.0ms	249×	body	80	nan
6.0ms	44×	body	640	valid
5.0ms	20×	body	320	valid
4.0ms	121×	body	80	valid
1.0ms	17×	body	160	valid

simplify5.0ms

Counts

1 → 1

Iterations

Iter	Nodes
3	12
2	12
1	11
0	6

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.2b

localize11.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt (+ x 1))
4.4b	(- (sqrt (+ x 1)) (sqrt x))

rewrite62.0ms

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))
50.0ms	(- (sqrt (+ x 1)) (sqrt x))

series98.0ms

Counts

2 → 6

Calls

2 calls:

27.0ms	(sqrt (+ x 1))
71.0ms	(- (sqrt (+ x 1)) (sqrt x))

simplify2.5s

Counts

98 → 98

Iterations

Iter	Nodes
4	4001
3	1450
2	620
1	285
0	134

prune790.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.2b

localize13.0ms

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)))

rewrite67.0ms

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))
32.0ms	(+ (sqrt (+ x 1)) (sqrt x))
28.0ms	(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))

series156.0ms

Counts

3 → 9

Calls

3 calls:

28.0ms	(sqrt (+ x 1))
50.0ms	(+ (sqrt (+ x 1)) (sqrt x))
78.0ms	(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))

simplify1.4s

Counts

102 → 102

Iterations

Iter	Nodes
4	2651
3	1150
2	574
1	257
0	126

prune944.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize26.0ms

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))))

rewrite249.0ms

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:

38.0ms	(sqrt (+ (sqrt (+ x 1)) (sqrt x)))
50.0ms	(sqrt (+ (sqrt (+ x 1)) (sqrt x)))
113.0ms	(/ (/ 1 (sqrt (+ (sqrt (+ x 1)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1)) (sqrt x))))
35.0ms	(/ 1 (sqrt (+ (sqrt (+ x 1)) (sqrt x))))

series531.0ms

Counts

4 → 12

Calls

4 calls:

170.0ms	(sqrt (+ (sqrt (+ x 1)) (sqrt x)))
117.0ms	(sqrt (+ (sqrt (+ x 1)) (sqrt x)))
77.0ms	(/ (/ 1 (sqrt (+ (sqrt (+ x 1)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1)) (sqrt x))))
166.0ms	(/ 1 (sqrt (+ (sqrt (+ x 1)) (sqrt x))))

simplify2.6s

Counts

491 → 491

Iterations

Iter	Nodes
3	4633
2	1670
1	848
0	370

prune5.0s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

localize27.0ms

Local error

Found 4 expressions with local error:

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

rewrite93.0ms

Algorithm

rewrite-expression-head

Rules

234×	`*-un-lft-identity` `times-frac`
170×	`sqrt-prod`
124×	`add-sqr-sqrt`
122×	`add-cube-cbrt`
64×	`distribute-lft-out`
36×	`associate-/l*`
17×	`add-exp-log`
12×	`associate-/r*`
11×	`add-cbrt-cube`
10×	`sqrt-div` `associate-/r/`
8×	`pow1` `div-exp`
6×	`div-inv`
5×	`sqrt-pow1` `flip3-+` `flip-+`
4×	`expm1-log1p-u` `cbrt-undiv` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow1/2` `pow-flip`
2×	`rem-sqrt-square` `rec-exp` `clear-num` `frac-2neg` `1-exp`
1×	`hypot-udef` `inv-pow` `associate-/l/`

Counts

4 → 250

Calls

4 calls:

2.0ms	(sqrt (sqrt x))
0.0ms	(hypot (sqrt (sqrt (+ x 1))) (sqrt (sqrt x)))
58.0ms	(/ (/ 1 (sqrt (+ (sqrt (+ x 1)) (sqrt x)))) (hypot (sqrt (sqrt (+ x 1))) (sqrt (sqrt x))))
28.0ms	(/ 1 (sqrt (+ (sqrt (+ x 1)) (sqrt x))))

series1.3s

Counts

4 → 12

Calls

4 calls:

227.0ms	(sqrt (sqrt x))
312.0ms	(hypot (sqrt (sqrt (+ x 1))) (sqrt (sqrt x)))
601.0ms	(/ (/ 1 (sqrt (+ (sqrt (+ x 1)) (sqrt x)))) (hypot (sqrt (sqrt (+ x 1))) (sqrt (sqrt x))))
180.0ms	(/ 1 (sqrt (+ (sqrt (+ x 1)) (sqrt x))))

simplify3.6s

Counts

262 → 262

Iterations

Iter	Nodes
2	4053
1	1328
0	519

prune3.7s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

regimes63.0ms

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
2	11
1	11
0	7

end0.0ms

sample2.0s

Algorithm

intervals

Results

551.0ms	7978×	body	80	nan
529.0ms	1712×	body	1280	valid
288.0ms	1260×	body	640	valid
246.0ms	4111×	body	80	valid
132.0ms	605×	body	320	valid
60.0ms	312×	body	160	valid