Details

sample72.0ms

Algorithm

intervals

Results

19.0ms	40×	body	640	valid
15.0ms	55×	body	1280	valid
13.0ms	246×	body	80	nan
7.0ms	128×	body	80	valid
3.0ms	20×	body	320	valid
2.0ms	13×	body	160	valid

simplify10.0ms

Counts

1 → 1

Iterations

Iter	Nodes
3	12
2	12
1	11
0	6

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.7b

localize17.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt (+ x 1))
4.0b	(- (sqrt (+ x 1)) (sqrt x))

rewrite36.0ms

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))
30.0ms	(- (sqrt (+ x 1)) (sqrt x))

series100.0ms

Counts

2 → 6

Calls

2 calls:

28.0ms	(sqrt (+ x 1))
72.0ms	(- (sqrt (+ x 1)) (sqrt x))

simplify2.8s

Counts

98 → 98

Iterations

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

prune753.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize25.0ms

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)))

rewrite84.0ms

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))
40.0ms	(+ (sqrt (+ x 1)) (sqrt x))
32.0ms	(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))

series198.0ms

Counts

3 → 9

Calls

3 calls:

32.0ms	(sqrt (+ x 1))
72.0ms	(+ (sqrt (+ x 1)) (sqrt x))
94.0ms	(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))

simplify1.2s

Counts

102 → 102

Iterations

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

prune905.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (hypot (sqrt x) 1) (sqrt x))
0.0b	(hypot (sqrt x) 1)
0.1b	(/ 1 (+ (hypot (sqrt x) 1) (sqrt x)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

23×	`*-un-lft-identity`
13×	`add-sqr-sqrt` `add-cube-cbrt`
12×	`times-frac`
7×	`add-exp-log`
5×	`add-cbrt-cube` `distribute-lft-out` `add-log-exp`
4×	`pow1` `associate-/r*`
3×	`expm1-log1p-u` `fma-def` `insert-posit16` `log1p-expm1-u` `associate-/l*`
2×	`flip3-+` `div-exp` `associate-/r/` `flip-+`
1×	`cbrt-undiv` `+-commutative` `rec-exp` `hypot-udef` `clear-num` `sum-log` `frac-2neg` `1-exp` `div-inv` `pow-flip` `inv-pow`

Counts

3 → 69

Calls

3 calls:

5.0ms	(+ (hypot (sqrt x) 1) (sqrt x))
0.0ms	(hypot (sqrt x) 1)
16.0ms	(/ 1 (+ (hypot (sqrt x) 1) (sqrt x)))

series1.2s

Counts

3 → 9

Calls

3 calls:

289.0ms	(+ (hypot (sqrt x) 1) (sqrt x))
221.0ms	(hypot (sqrt x) 1)
706.0ms	(/ 1 (+ (hypot (sqrt x) 1) (sqrt x)))

simplify2.8s

Counts

78 → 78

Iterations

Iter	Nodes
3	4800
2	1255
1	437
0	173

prune712.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 4 expressions with local error:

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

rewrite107.0ms

Algorithm

rewrite-expression-head

Rules

145×	`*-un-lft-identity`
132×	`sqrt-prod`
118×	`add-sqr-sqrt`
114×	`times-frac`
70×	`add-cube-cbrt`
31×	`pow1` `swap-sqr`
29×	`distribute-lft-out`
27×	`sqrt-pow1`
21×	`associate-r` `associate-l`
16×	`unswap-sqr`
14×	`add-exp-log` `associate-/r/`
11×	`pow-flip` `inv-pow`
10×	`add-cbrt-cube`
9×	`pow1/2` `pow-prod-up` `div-inv`
8×	`associate-/r*`
7×	`flip3-+` `flip-+`
6×	`associate-/l*`
5×	`sqrt-div` `pow-prod-down` `pow-sqr`
4×	`expm1-log1p-u` `div-exp` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`rem-sqrt-square`
2×	`cbrt-undiv` `rec-exp` `clear-num` `frac-2neg` `1-exp`
1×	`pow2` `frac-times` `rem-square-sqrt` `pow-plus` `sqrt-unprod` `associate-l/` `prod-exp` `associate-r/` `*-commutative` `cbrt-unprod`

Counts

4 → 244

Calls

4 calls:

16.0ms	(sqrt (/ 1 (+ (hypot (sqrt x) 1) (sqrt x))))
18.0ms	(/ 1 (+ (hypot (sqrt x) 1) (sqrt x)))
24.0ms	(/ 1 (+ (hypot (sqrt x) 1) (sqrt x)))
41.0ms	(* (sqrt (/ 1 (+ (hypot (sqrt x) 1) (sqrt x)))) (sqrt (/ 1 (+ (hypot (sqrt x) 1) (sqrt x)))))

series3.1s

Counts

4 → 12

Calls

4 calls:

1.1s	(sqrt (/ 1 (+ (hypot (sqrt x) 1) (sqrt x))))
733.0ms	(/ 1 (+ (hypot (sqrt x) 1) (sqrt x)))
633.0ms	(/ 1 (+ (hypot (sqrt x) 1) (sqrt x)))
639.0ms	(* (sqrt (/ 1 (+ (hypot (sqrt x) 1) (sqrt x)))) (sqrt (/ 1 (+ (hypot (sqrt x) 1) (sqrt x)))))

simplify6.0s

Counts

256 → 256

Iterations

Iter	Nodes
3	7090
2	1933
1	659
0	295

prune2.4s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

regimes80.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
2	14
1	14
0	10

end0.0ms

sample1.8s

Algorithm

intervals

Results

482.0ms	8213×	body	80	nan
406.0ms	1658×	body	1280	valid
331.0ms	4164×	body	80	valid
263.0ms	1218×	body	640	valid
115.0ms	621×	body	320	valid
32.0ms	339×	body	160	valid