Details

sample51.0ms

Algorithm

intervals

Results

9.0ms	253×	body	80	nan
9.0ms	54×	body	1280	valid
6.0ms	143×	body	80	valid
5.0ms	34×	body	640	valid
1.0ms	14×	body	320	valid
1.0ms	11×	body	160	valid

simplify6.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	10
2	10
1	9
0	6

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.1b

localize16.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt (+ x 1.0))
2.5b	(- (sqrt (+ x 1.0)) (sqrt x))

rewrite90.0ms

Algorithm

rewrite-expression-head

Rules

61×	`sqrt-prod`
54×	`*-un-lft-identity`
42×	`add-sqr-sqrt` `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` `log1p-expm1-u`
1×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `flip3-+` `flip3--` `pow1/2` `diff-log` `flip-+` `hypot-def` `flip--`

Counts

2 → 89

Calls

2 calls:

12.0ms	(sqrt (+ x 1.0))
74.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

series136.0ms

Counts

2 → 6

Calls

2 calls:

42.0ms	(sqrt (+ x 1.0))
95.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

simplify996.0ms

Counts

95 → 95

Iterations

Iter	Nodes
done	5001
2	1076
1	322
0	139

prune328.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize14.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (+ x 1.0))
0.0b	(+ (sqrt (+ x 1.0)) (sqrt x))
0.1b	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))

rewrite121.0ms

Algorithm

rewrite-expression-head

Rules

78×	`*-un-lft-identity`
33×	`distribute-lft-out`
32×	`sqrt-prod`
24×	`times-frac`
21×	`add-sqr-sqrt`
18×	`add-cube-cbrt`
7×	`fma-def`
6×	`associate-/r*`
5×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
4×	`pow1` `flip3-+` `flip-+` `associate-/l*`
3×	`expm1-log1p-u` `log1p-expm1-u`
2×	`sqrt-div` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `clear-num` `sum-log` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `hypot-def` `div-inv`

Counts

3 → 94

Calls

3 calls:

7.0ms	(sqrt (+ x 1.0))
46.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
65.0ms	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))

series359.0ms

Counts

3 → 9

Calls

3 calls:

39.0ms	(sqrt (+ x 1.0))
99.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
221.0ms	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify1.8s

Counts

103 → 103

Iterations

Iter	Nodes
done	5000
2	2060
1	439
0	173

prune469.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (+ x 1.0))
0.0b	(+ (sqrt (+ x 1.0)) (sqrt x))
0.1b	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

rewrite131.0ms

Algorithm

rewrite-expression-head

Rules

56×	`*-un-lft-identity`
28×	`sqrt-prod`
22×	`distribute-lft-out`
20×	`add-sqr-sqrt`
18×	`times-frac`
17×	`add-cube-cbrt`
7×	`fma-def`
6×	`associate-/r*`
5×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
4×	`pow1`
3×	`expm1-log1p-u` `flip3-+` `flip-+` `log1p-expm1-u` `associate-/l*`
2×	`sqrt-div` `associate-/r/`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `clear-num` `sum-log` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `hypot-def` `div-inv`

Counts

3 → 85

Calls

3 calls:

6.0ms	(sqrt (+ x 1.0))
55.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
68.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

series334.0ms

Counts

3 → 9

Calls

3 calls:

40.0ms	(sqrt (+ x 1.0))
94.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
199.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify1.4s

Counts

94 → 94

Iterations

Iter	Nodes
done	5001
2	1632
1	393
0	162

prune400.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize39.0ms

Local error

Found 4 expressions with local error:

0.2b	(cbrt (+ x 1.0))
0.2b	(cbrt (+ x 1.0))
0.2b	(cbrt (+ x 1.0))
0.3b	(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

36×	`cbrt-prod`
35×	`*-un-lft-identity`
23×	`add-sqr-sqrt`
18×	`cbrt-div`
15×	`add-cube-cbrt`
11×	`pow1`
9×	`flip3-+` `pow1/3` `swap-sqr` `flip-+` `distribute-lft-out`
7×	`associate-r` `associate-l`
6×	`add-exp-log`
4×	`expm1-log1p-u` `frac-times` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `associate-l/` `associate-r/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 103

Calls

4 calls:

6.0ms	(cbrt (+ x 1.0))
6.0ms	(cbrt (+ x 1.0))
6.0ms	(cbrt (+ x 1.0))
51.0ms	(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))

series539.0ms

Counts

4 → 12

Calls

4 calls:

121.0ms	(cbrt (+ x 1.0))
125.0ms	(cbrt (+ x 1.0))
118.0ms	(cbrt (+ x 1.0))
174.0ms	(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))

simplify1.4s

Counts

115 → 115

Iterations

Iter	Nodes
done	5000
2	1235
1	346
0	143

prune770.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

regimes58.0ms

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
done	9
1	9
0	7

end0.0ms

sample2.0s

Algorithm

intervals

Results

755.0ms	1750×	body	1280	valid
332.0ms	7946×	body	80	nan
247.0ms	1314×	body	640	valid
196.0ms	4066×	body	80	valid
50.0ms	560×	body	320	valid
19.0ms	310×	body	160	valid