Details

sample50.0ms

Algorithm

intervals

Results

19.0ms	60×	body	1280	valid
9.0ms	262×	body	80	nan
6.0ms	42×	body	640	valid
5.0ms	125×	body	80	valid
2.0ms	19×	body	320	valid
1.0ms	10×	body	160	valid

simplify4.0ms

Counts

1 → 1

Iterations

Iter	Nodes
3	10
2	10
1	9
0	6

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.6b

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt (+ x 1))
2.9b	(- (sqrt (+ x 1)) (sqrt x))

rewrite31.0ms

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` `log1p-expm1-u`
1×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `flip3-+` `flip3--` `pow1/2` `diff-log` `flip-+` `flip--`

Counts

2 → 90

Calls

2 calls:

4.0ms	(sqrt (+ x 1))
25.0ms	(- (sqrt (+ x 1)) (sqrt x))

series88.0ms

Counts

2 → 6

Calls

2 calls:

25.0ms	(sqrt (+ x 1))
62.0ms	(- (sqrt (+ x 1)) (sqrt x))

simplify3.2s

Counts

96 → 96

Iterations

Iter	Nodes
4	3872
3	1431
2	593
1	281
0	132

prune798.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize12.0ms

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)))

rewrite80.0ms

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-+` `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 → 90

Calls

3 calls:

4.0ms	(sqrt (+ x 1))
32.0ms	(+ (sqrt (+ x 1)) (sqrt x))
42.0ms	(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))

series190.0ms

Counts

3 → 9

Calls

3 calls:

42.0ms	(sqrt (+ x 1))
68.0ms	(+ (sqrt (+ x 1)) (sqrt x))
81.0ms	(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))

simplify2.5s

Counts

99 → 99

Iterations

Iter	Nodes
4	2647
3	1157
2	566
1	253
0	123

prune777.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1 (+ (* (fabs (cbrt (+ x 1))) (sqrt (cbrt (+ x 1)))) (sqrt x)))
0.2b	(* (fabs (cbrt (+ x 1))) (sqrt (cbrt (+ x 1))))
0.3b	(cbrt (+ x 1))
0.3b	(cbrt (+ x 1))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt` `*-un-lft-identity`
18×	`add-cube-cbrt`
13×	`cbrt-prod`
10×	`associate-r` `add-exp-log`
9×	`times-frac` `sqrt-prod`
8×	`add-cbrt-cube`
7×	`pow1`
6×	`cbrt-div`
4×	`expm1-log1p-u` `flip3-+` `flip-+` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r` `associate-l` `distribute-lft-out` `associate-/l` `unswap-sqr`
2×	`pow1/3` `sqrt-div` `div-exp` `associate-*r/` `associate-/r/`
1×	`cbrt-undiv` `rec-exp` `clear-num` `frac-2neg` `1-exp` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `div-inv` `pow-flip` `inv-pow`

Counts

4 → 98

Calls

4 calls:

35.0ms	(/ 1 (+ (* (fabs (cbrt (+ x 1))) (sqrt (cbrt (+ x 1)))) (sqrt x)))
20.0ms	(* (fabs (cbrt (+ x 1))) (sqrt (cbrt (+ x 1))))
2.0ms	(cbrt (+ x 1))
2.0ms	(cbrt (+ x 1))

series284.0ms

Counts

4 → 12

Calls

4 calls:

124.0ms	(/ 1 (+ (* (fabs (cbrt (+ x 1))) (sqrt (cbrt (+ x 1)))) (sqrt x)))
73.0ms	(* (fabs (cbrt (+ x 1))) (sqrt (cbrt (+ x 1))))
51.0ms	(cbrt (+ x 1))
36.0ms	(cbrt (+ x 1))

simplify2.2s

Counts

110 → 110

Iterations

Iter	Nodes
2	2620
1	727
0	283

prune1.2s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.0b

localize34.0ms

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))))

rewrite215.0ms

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` `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 → 475

Calls

4 calls:

22.0ms	(sqrt (+ (sqrt (+ x 1)) (sqrt x)))
33.0ms	(sqrt (+ (sqrt (+ x 1)) (sqrt x)))
31.0ms	(/ 1 (sqrt (+ (sqrt (+ x 1)) (sqrt x))))
109.0ms	(/ (/ 1 (sqrt (+ (sqrt (+ x 1)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1)) (sqrt x))))

series466.0ms

Counts

4 → 12

Calls

4 calls:

100.0ms	(sqrt (+ (sqrt (+ x 1)) (sqrt x)))
113.0ms	(sqrt (+ (sqrt (+ x 1)) (sqrt x)))
147.0ms	(/ 1 (sqrt (+ (sqrt (+ x 1)) (sqrt x))))
105.0ms	(/ (/ 1 (sqrt (+ (sqrt (+ x 1)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1)) (sqrt x))))

simplify1.2m

Counts

487 → 487

Iterations

Iter	Nodes
3	4168
2	1636
1	852
0	367

prune2.7s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

regimes32.0ms

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

sample1.5s

Algorithm

intervals

Results

584.0ms	8145×	body	80	nan
305.0ms	1735×	body	1280	valid
200.0ms	1251×	body	640	valid
181.0ms	4107×	body	80	valid
79.0ms	596×	body	320	valid
20.0ms	311×	body	160	valid