Details

sample55.0ms

Algorithm

intervals

Results

11.0ms	54×	body	1280	valid
10.0ms	253×	body	80	nan
6.0ms	143×	body	80	valid
6.0ms	34×	body	640	valid
2.0ms	14×	body	320	valid
1.0ms	11×	body	160	valid

simplify7.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	10
2	10
1	9
0	6

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.1b

localize9.0ms

Local error

Found 2 expressions with local error:

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

rewrite64.0ms

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:

6.0ms	(sqrt (+ 1.0 x))
54.0ms	(- (sqrt (+ 1.0 x)) (sqrt x))

series119.0ms

Counts

2 → 6

Calls

2 calls:

34.0ms	(sqrt (+ 1.0 x))
85.0ms	(- (sqrt (+ 1.0 x)) (sqrt x))

simplify877.0ms

Counts

95 → 95

Iterations

Iter	Nodes
done	5000
2	1090
1	323
0	139

prune245.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize13.0ms

Local error

Found 3 expressions with local error:

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

rewrite122.0ms

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:

11.0ms	(sqrt (+ 1.0 x))
28.0ms	(+ (sqrt (+ 1.0 x)) (sqrt x))
77.0ms	(/ (+ 1.0 0) (+ (sqrt (+ 1.0 x)) (sqrt x)))

series379.0ms

Counts

3 → 9

Calls

3 calls:

54.0ms	(sqrt (+ 1.0 x))
118.0ms	(+ (sqrt (+ 1.0 x)) (sqrt x))
206.0ms	(/ (+ 1.0 0) (+ (sqrt (+ 1.0 x)) (sqrt x)))

simplify1.5s

Counts

103 → 103

Iterations

Iter	Nodes
done	5000
2	2042
1	439
0	173

prune449.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 3 expressions with local error:

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

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

39×	`*-un-lft-identity`
18×	`add-sqr-sqrt`
16×	`times-frac`
15×	`add-cube-cbrt`
12×	`distribute-lft-out`
5×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
4×	`pow1` `associate-/r` `flip3-+` `sqrt-prod` `flip-+` `associate-/l`
3×	`expm1-log1p-u` `fma-def` `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 → 78

Calls

3 calls:

12.0ms	(sqrt (+ 1.0 x))
9.0ms	(+ (fabs (sqrt (+ 1.0 x))) (sqrt x))
26.0ms	(/ (+ 1.0 0) (+ (fabs (sqrt (+ 1.0 x))) (sqrt x)))

series149.0ms

Counts

3 → 9

Calls

3 calls:

54.0ms	(sqrt (+ 1.0 x))
51.0ms	(+ (fabs (sqrt (+ 1.0 x))) (sqrt x))
44.0ms	(/ (+ 1.0 0) (+ (fabs (sqrt (+ 1.0 x))) (sqrt x)))

simplify1.4s

Counts

87 → 87

Iterations

Iter	Nodes
done	5004
2	2197
1	453
0	178

prune376.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize49.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (+ (sqrt (+ 1.0 x)) (sqrt x)))
0.1b	(sqrt (+ (sqrt (+ 1.0 x)) (sqrt x)))
0.2b	(/ 1.0 (sqrt (+ (sqrt (+ 1.0 x)) (sqrt x))))
0.2b	(/ (/ 1.0 (sqrt (+ (sqrt (+ 1.0 x)) (sqrt x)))) (sqrt (+ (sqrt (+ 1.0 x)) (sqrt x))))

rewrite390.0ms

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*`
14×	`flip3-+` `flip-+`
12×	`div-inv`
11×	`add-cbrt-cube` `add-exp-log`
8×	`hypot-def`
6×	`pow1`
4×	`expm1-log1p-u` `cbrt-undiv` `div-exp` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2`
1×	`associate-/l/`

Counts

4 → 461

Calls

4 calls:

62.0ms	(sqrt (+ (sqrt (+ 1.0 x)) (sqrt x)))
46.0ms	(sqrt (+ (sqrt (+ 1.0 x)) (sqrt x)))
68.0ms	(/ 1.0 (sqrt (+ (sqrt (+ 1.0 x)) (sqrt x))))
163.0ms	(/ (/ 1.0 (sqrt (+ (sqrt (+ 1.0 x)) (sqrt x)))) (sqrt (+ (sqrt (+ 1.0 x)) (sqrt x))))

series1.1s

Counts

4 → 12

Calls

4 calls:

215.0ms	(sqrt (+ (sqrt (+ 1.0 x)) (sqrt x)))
256.0ms	(sqrt (+ (sqrt (+ 1.0 x)) (sqrt x)))
424.0ms	(/ 1.0 (sqrt (+ (sqrt (+ 1.0 x)) (sqrt x))))
173.0ms	(/ (/ 1.0 (sqrt (+ (sqrt (+ 1.0 x)) (sqrt x)))) (sqrt (+ (sqrt (+ 1.0 x)) (sqrt x))))

simplify1.6s

Counts

473 → 473

Iterations

Iter	Nodes
done	5000
2	4313
1	1103
0	448

prune1.3s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

regimes75.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
done	14
2	14
1	13
0	10

end0.0ms

sample1.7s

Algorithm

intervals

Results

673.0ms	1750×	body	1280	valid
301.0ms	7946×	body	80	nan
190.0ms	1314×	body	640	valid
167.0ms	4066×	body	80	valid
79.0ms	560×	body	320	valid
19.0ms	310×	body	160	valid