Details

sample46.0ms

Algorithm

intervals

Results

7.0ms	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
1.0ms	7×	body	160	valid

simplify24.0ms

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: 29.9b

localize15.0ms

Local error

Found 2 expressions with local error:

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

rewrite117.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `*-un-lft-identity` `sqrt-prod`
4×	`add-log-exp` `difference-of-squares`
3×	`pow1` `add-cube-cbrt` `distribute-lft-out--`
2×	`add-cbrt-cube` `sqrt-div` `add-exp-log` `insert-posit16` `distribute-lft-out`
1×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `flip3-+` `flip3--` `pow1/2` `diff-log` `flip-+` `flip--`

Counts

2 → 37

Calls

2 calls:

10.0ms	(sqrt (+ x 1.0))
105.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

series160.0ms

Counts

2 → 6

Calls

2 calls:

45.0ms	(sqrt (+ x 1.0))
115.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

simplify3.4s

Counts

43 → 43

Iterations

Iter	Nodes
done	5001
3	1606
2	534
1	195
0	88

prune492.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 29.0b

localize31.0ms

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)

rewrite374.0ms

Algorithm

rewrite-expression-head

Rules

117×	`*-un-lft-identity`
41×	`distribute-lft-out`
36×	`add-sqr-sqrt` `times-frac` `sqrt-prod`
19×	`add-cube-cbrt`
16×	`distribute-lft-out--`
11×	`add-log-exp`
8×	`difference-of-squares`
6×	`associate-/r` `add-cbrt-cube` `add-exp-log` `associate-/l`
5×	`pow1`
4×	`insert-posit16`
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+` `div-inv`

Counts

4 → 116

Calls

4 calls:

21.0ms	(sqrt (+ x 1.0))
60.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
203.0ms	(/ (- (+ x 1.0) x) (+ (sqrt (+ x 1.0)) (sqrt x)))
70.0ms	(- (+ x 1.0) x)

series397.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(sqrt (+ x 1.0))
97.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
237.0ms	(/ (- (+ x 1.0) x) (+ (sqrt (+ x 1.0)) (sqrt x)))
3.0ms	(- (+ x 1.0) x)

simplify2.9s

Counts

128 → 128

Iterations

Iter	Nodes
done	5000
2	1593
1	492
0	192

prune1.1s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.2b

localize42.0ms

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)))

rewrite183.0ms

Algorithm

rewrite-expression-head

Rules

52×	`*-un-lft-identity`
24×	`sqrt-prod`
21×	`distribute-lft-out`
18×	`times-frac`
16×	`add-sqr-sqrt`
15×	`add-cube-cbrt`
6×	`associate-/r*`
5×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
4×	`pow1`
3×	`flip3-+` `flip-+` `insert-posit16` `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` `div-inv`

Counts

3 → 74

Calls

3 calls:

13.0ms	(sqrt (+ x 1.0))
51.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
108.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

series372.0ms

Counts

3 → 9

Calls

3 calls:

61.0ms	(sqrt (+ x 1.0))
93.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
216.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify5.4s

Counts

83 → 83

Iterations

Iter	Nodes
done	5000
3	3643
2	1107
1	374
0	159

prune730.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize93.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))
0.2b	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
0.2b	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
0.3b	(* (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))))

rewrite748.0ms

Algorithm

rewrite-expression-head

Rules

297×	`*-un-lft-identity`
274×	`sqrt-prod`
157×	`times-frac`
119×	`add-sqr-sqrt`
116×	`distribute-lft-out`
88×	`add-cube-cbrt`
41×	`swap-sqr`
27×	`associate-r` `associate-l`
20×	`pow1`
14×	`associate-/r/`
12×	`associate-/r*`
10×	`add-cbrt-cube` `add-exp-log`
9×	`sqrt-pow1` `pow1/2` `unswap-sqr`
7×	`flip3-+` `flip-+` `div-inv`
6×	`associate-/l*`
5×	`sqrt-div` `pow-prod-up`
4×	`insert-posit16` `add-log-exp`
3×	`pow-prod-down` `pow-sqr`
2×	`cbrt-undiv` `rem-sqrt-square` `clear-num` `frac-2neg` `div-exp`
1×	`pow2` `frac-times` `rem-square-sqrt` `pow-plus` `sqrt-unprod` `associate-l/` `prod-exp` `associate-r/` `*-commutative` `cbrt-unprod`

Counts

4 → 254

Calls

4 calls:

98.0ms	(sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))
89.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
83.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
436.0ms	(* (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))))

series1.3s

Counts

4 → 12

Calls

4 calls:

524.0ms	(sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))
238.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
222.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
297.0ms	(* (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))))

simplify3.5s

Counts

266 → 266

Iterations

Iter	Nodes
done	5000
2	1891
1	693
0	313

prune1.6s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

regimes176.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	9
1	9
0	7

end0.0ms

sample1.8s

Algorithm

intervals

Results

705.0ms	7974×	body	80	nan
385.0ms	1720×	body	1280	valid
181.0ms	1264×	body	640	valid
129.0ms	4071×	body	80	valid
55.0ms	613×	body	320	valid
20.0ms	332×	body	160	valid