Details

sample56.0ms

Algorithm

intervals

Results

11.0ms	288×	body	80	nan
11.0ms	55×	body	1280	valid
6.0ms	142×	body	80	valid
5.0ms	31×	body	640	valid
3.0ms	22×	body	320	valid
0.0ms	6×	body	160	valid

simplify6.0ms

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: 27.6b

localize16.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt (+ 1.0 x))
3.0b	(- (sqrt (+ 1.0 x)) (sqrt x))

rewrite79.0ms

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))
69.0ms	(- (sqrt (+ 1.0 x)) (sqrt x))

series107.0ms

Counts

2 → 6

Calls

2 calls:

32.0ms	(sqrt (+ 1.0 x))
75.0ms	(- (sqrt (+ 1.0 x)) (sqrt x))

simplify1.0s

Counts

95 → 95

Iterations

Iter	Nodes
done	5000
2	1090
1	323
0	139

prune276.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (+ 1.0 x))
0.0b	(+ (sqrt (+ 1.0 x)) (sqrt x))
0.2b	(/ (+ 1.0 0) (+ (sqrt (+ 1.0 x)) (sqrt x)))

rewrite129.0ms

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))
48.0ms	(+ (sqrt (+ 1.0 x)) (sqrt x))
65.0ms	(/ (+ 1.0 0) (+ (sqrt (+ 1.0 x)) (sqrt x)))

series378.0ms

Counts

3 → 9

Calls

3 calls:

54.0ms	(sqrt (+ 1.0 x))
104.0ms	(+ (sqrt (+ 1.0 x)) (sqrt x))
220.0ms	(/ (+ 1.0 0) (+ (sqrt (+ 1.0 x)) (sqrt x)))

simplify1.4s

Counts

103 → 103

Iterations

Iter	Nodes
done	5000
2	2042
1	439
0	173

prune503.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (sqrt (+ 1.0 x)) (sqrt x))
0.0b	(log1p (expm1 (/ 1.0 (+ (sqrt (+ 1.0 x)) (sqrt x)))))
0.2b	(/ 1.0 (+ (sqrt (+ 1.0 x)) (sqrt x)))
0.5b	(expm1 (/ 1.0 (+ (sqrt (+ 1.0 x)) (sqrt x))))

rewrite98.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 88

Calls

4 calls:

57.0ms	(+ (sqrt (+ 1.0 x)) (sqrt x))
0.0ms	(log1p (expm1 (/ 1.0 (+ (sqrt (+ 1.0 x)) (sqrt x)))))
35.0ms	(/ 1.0 (+ (sqrt (+ 1.0 x)) (sqrt x)))
0.0ms	(expm1 (/ 1.0 (+ (sqrt (+ 1.0 x)) (sqrt x))))

series1.3s

Counts

4 → 12

Calls

4 calls:

100.0ms	(+ (sqrt (+ 1.0 x)) (sqrt x))
632.0ms	(log1p (expm1 (/ 1.0 (+ (sqrt (+ 1.0 x)) (sqrt x)))))
177.0ms	(/ 1.0 (+ (sqrt (+ 1.0 x)) (sqrt x)))
421.0ms	(expm1 (/ 1.0 (+ (sqrt (+ 1.0 x)) (sqrt x))))

simplify1.0s

Counts

100 → 100

Iterations

Iter	Nodes
done	5002
2	2321
1	543
0	208

prune485.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize38.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (sqrt (+ 1.0 x)))
0.1b	(fma (sqrt (sqrt (+ 1.0 x))) (sqrt (sqrt (+ 1.0 x))) (sqrt x))
0.2b	(/ 1.0 (fma (sqrt (sqrt (+ 1.0 x))) (sqrt (sqrt (+ 1.0 x))) (sqrt x)))
0.5b	(expm1 (/ 1.0 (fma (sqrt (sqrt (+ 1.0 x))) (sqrt (sqrt (+ 1.0 x))) (sqrt x))))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt` `*-un-lft-identity`
14×	`add-cube-cbrt`
12×	`sqrt-prod`
9×	`times-frac`
6×	`pow1` `add-cbrt-cube` `add-exp-log`
5×	`log1p-expm1-u`
4×	`expm1-log1p-u` `sqrt-pow1` `sqrt-div` `add-log-exp`
3×	`associate-/r` `associate-/l`
2×	`rem-sqrt-square` `pow1/2`
1×	`cbrt-undiv` `expm1-log1p` `clear-num` `frac-2neg` `flip3-+` `div-exp` `flip-+` `fma-udef` `div-inv` `distribute-lft-out` `expm1-udef`

Counts

4 → 74

Calls

4 calls:

13.0ms	(sqrt (sqrt (+ 1.0 x)))
0.0ms	(fma (sqrt (sqrt (+ 1.0 x))) (sqrt (sqrt (+ 1.0 x))) (sqrt x))
7.0ms	(/ 1.0 (fma (sqrt (sqrt (+ 1.0 x))) (sqrt (sqrt (+ 1.0 x))) (sqrt x)))
1.0ms	(expm1 (/ 1.0 (fma (sqrt (sqrt (+ 1.0 x))) (sqrt (sqrt (+ 1.0 x))) (sqrt x))))

series1.5s

Counts

4 → 12

Calls

4 calls:

108.0ms	(sqrt (sqrt (+ 1.0 x)))
279.0ms	(fma (sqrt (sqrt (+ 1.0 x))) (sqrt (sqrt (+ 1.0 x))) (sqrt x))
450.0ms	(/ 1.0 (fma (sqrt (sqrt (+ 1.0 x))) (sqrt (sqrt (+ 1.0 x))) (sqrt x)))
646.0ms	(expm1 (/ 1.0 (fma (sqrt (sqrt (+ 1.0 x))) (sqrt (sqrt (+ 1.0 x))) (sqrt x))))

simplify764.0ms

Counts

86 → 86

Iterations

Iter	Nodes
done	5000
1	1170
0	409

prune545.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

regimes51.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
done	15
2	15
1	14
0	11

end0.0ms

sample2.0s

Algorithm

intervals

Results

768.0ms	7906×	body	80	nan
350.0ms	1654×	body	1280	valid
251.0ms	1305×	body	640	valid
202.0ms	4072×	body	80	valid
66.0ms	670×	body	320	valid
20.0ms	299×	body	160	valid