Details

sample45.0ms

Algorithm

intervals

Results

6.0ms	55×	body	1280	valid
5.0ms	211×	body	80	nan
4.0ms	46×	body	640	valid
3.0ms	132×	body	80	valid
1.0ms	16×	body	320	valid
0.0ms	7×	body	160	valid

simplify26.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	10
2	10
1	9
0	6

prune17.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.9b

localize31.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt (+ x 1.0))
2.1b	(- (sqrt (+ x 1.0)) (sqrt x))

rewrite216.0ms

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` `insert-posit16` `log1p-expm1-u`
1×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `flip3-+` `flip3--` `pow1/2` `diff-log` `flip-+` `hypot-def` `flip--`

Counts

2 → 91

Calls

2 calls:

25.0ms	(sqrt (+ x 1.0))
171.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

series178.0ms

Counts

2 → 6

Calls

2 calls:

58.0ms	(sqrt (+ x 1.0))
120.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

simplify4.4s

Counts

97 → 97

Iterations

Iter	Nodes
done	5001
3	2215
2	778
1	322
0	141

prune710.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 28.9b

localize35.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ x 1.0))
0.0b	(+ (sqrt (+ x 1.0)) (sqrt x))
0.1b	(/ (- (+ x 1.0) x) (+ (sqrt (+ x 1.0)) (sqrt x)))
1.7b	(- (+ x 1.0) x)

rewrite447.0ms

Algorithm

rewrite-expression-head

Rules

137×	`*-un-lft-identity`
48×	`add-sqr-sqrt`
46×	`distribute-lft-out`
40×	`sqrt-prod`
36×	`times-frac`
29×	`add-cube-cbrt`
16×	`distribute-lft-out--`
12×	`prod-diff`
11×	`add-log-exp`
8×	`difference-of-squares`
7×	`fma-def`
6×	`associate-/r` `add-cbrt-cube` `add-exp-log` `associate-/l`
5×	`pow1`
4×	`expm1-log1p-u` `fma-neg` `insert-posit16` `log1p-expm1-u`
3×	`flip3-+` `flip-+`
2×	`sum-log` `flip3--` `sqrt-div` `diff-log` `associate-/r/` `flip--` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `clear-num` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `div-exp` `associate--l+` `hypot-def` `div-inv`

Counts

4 → 148

Calls

4 calls:

24.0ms	(sqrt (+ x 1.0))
70.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
239.0ms	(/ (- (+ x 1.0) x) (+ (sqrt (+ x 1.0)) (sqrt x)))
89.0ms	(- (+ x 1.0) x)

series415.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(sqrt (+ x 1.0))
109.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
242.0ms	(/ (- (+ x 1.0) x) (+ (sqrt (+ x 1.0)) (sqrt x)))
3.0ms	(- (+ x 1.0) x)

simplify3.7s

Counts

160 → 160

Iterations

Iter	Nodes
done	5000
2	1755
1	562
0	221

prune1.3s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.2b

localize25.0ms

Local error

Found 3 expressions with local error:

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

rewrite164.0ms

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-+` `insert-posit16` `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 → 88

Calls

3 calls:

12.0ms	(sqrt (+ x 1.0))
56.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
90.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

series330.0ms

Counts

3 → 9

Calls

3 calls:

36.0ms	(sqrt (+ x 1.0))
78.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
216.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify6.0s

Counts

97 → 97

Iterations

Iter	Nodes
done	5000
3	4083
2	1220
1	396
0	165

prune1000.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize51.0ms

Local error

Found 4 expressions with local error:

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

rewrite187.0ms

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×	`expm1-log1p-u`
4×	`pow1` `insert-posit16` `log1p-expm1-u`
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 → 92

Calls

4 calls:

1.0ms	(log1p (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))
96.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
2.0ms	(expm1 (log1p (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))))
82.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

series2.5s

Counts

4 → 12

Calls

4 calls:

775.0ms	(log1p (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))
113.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
1.3s	(expm1 (log1p (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))))
248.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify4.5s

Counts

104 → 104

Iterations

Iter	Nodes
done	5003
2	1972
1	614
0	233

prune1.1s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

regimes222.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify6.0ms

Iterations

Iter	Nodes
done	11
1	11
0	9

end0.0ms

sample2.0s

Algorithm

intervals

Results

699.0ms	7974×	body	80	nan
409.0ms	1720×	body	1280	valid
222.0ms	1264×	body	640	valid
177.0ms	4071×	body	80	valid
64.0ms	613×	body	320	valid
22.0ms	332×	body	160	valid