Details

sample71.0ms

Algorithm

intervals

Results

25.0ms	288×	body	80	nan
8.0ms	52×	body	640	valid
6.0ms	34×	body	1280	valid
6.0ms	142×	body	80	valid
3.0ms	22×	body	320	valid
0.0ms	6×	body	160	valid

simplify10.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	14
2	14
1	11
0	8

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ x 1.0))
0.1b	(/ 1.0 (sqrt (+ x 1.0)))
0.2b	(/ 1.0 (sqrt x))
3.0b	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

rewrite148.0ms

Algorithm

rewrite-expression-head

Rules

75×	`*-un-lft-identity`
73×	`add-sqr-sqrt`
69×	`times-frac`
50×	`sqrt-prod`
42×	`add-cube-cbrt`
13×	`associate-/r*`
11×	`distribute-lft-out--`
9×	`difference-of-squares`
8×	`add-cbrt-cube` `add-exp-log` `distribute-lft-out`
6×	`associate-/l*` `add-log-exp`
5×	`pow1`
4×	`sqrt-div` `div-inv`
2×	`cbrt-undiv` `clear-num` `frac-2neg` `flip3-+` `div-exp` `associate-/r/` `flip-+`
1×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `flip3--` `pow1/2` `diff-log` `frac-sub` `flip--`

Counts

4 → 133

Calls

4 calls:

7.0ms	(sqrt (+ x 1.0))
20.0ms	(/ 1.0 (sqrt (+ x 1.0)))
9.0ms	(/ 1.0 (sqrt x))
106.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

series430.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(sqrt (+ x 1.0))
135.0ms	(/ 1.0 (sqrt (+ x 1.0)))
66.0ms	(/ 1.0 (sqrt x))
172.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

simplify888.0ms

Counts

145 → 145

Iterations

Iter	Nodes
done	5001
2	1655
1	462
0	216

prune560.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 16.4b

localize32.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ x 1.0))
0.1b	(/ (* 1.0 (- (sqrt (+ x 1.0)) (sqrt x))) (* (sqrt (+ x 1.0)) (sqrt x)))
0.2b	(* (sqrt (+ x 1.0)) (sqrt x))
3.0b	(- (sqrt (+ x 1.0)) (sqrt x))

rewrite177.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt`
23×	`sqrt-prod`
20×	`*-un-lft-identity`
18×	`add-cbrt-cube` `add-exp-log`
9×	`pow1` `add-cube-cbrt`
7×	`associate-l`
6×	`sqrt-div` `associate-r` `add-log-exp`
5×	`prod-exp` `cbrt-unprod`
4×	`cbrt-undiv` `div-exp` `associate-*l/` `difference-of-squares` `unswap-sqr`
3×	`sqrt-pow1` `flip3-+` `pow1/2` `pow-prod-down` `flip-+` `distribute-lft-out` `distribute-lft-out--`
2×	`flip3--` `associate-*r/` `associate-/r/` `flip--` `associate-/l/`
1×	`rem-sqrt-square` `clear-num` `associate-/r` `sub-neg` `frac-2neg` `times-frac` `sqrt-unprod` `diff-log` `-commutative` `div-inv` `associate-/l*`

Counts

4 → 93

Calls

4 calls:

12.0ms	(sqrt (+ x 1.0))
66.0ms	(/ (* 1.0 (- (sqrt (+ x 1.0)) (sqrt x))) (* (sqrt (+ x 1.0)) (sqrt x)))
28.0ms	(* (sqrt (+ x 1.0)) (sqrt x))
65.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

series625.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(sqrt (+ x 1.0))
369.0ms	(/ (* 1.0 (- (sqrt (+ x 1.0)) (sqrt x))) (* (sqrt (+ x 1.0)) (sqrt x)))
100.0ms	(* (sqrt (+ x 1.0)) (sqrt x))
101.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

simplify1.3s

Counts

105 → 105

Iterations

Iter	Nodes
done	5000
2	3032
1	531
0	192

prune469.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.2b

localize36.0ms

Local error

Found 4 expressions with local error:

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

rewrite265.0ms

Algorithm

rewrite-expression-head

Rules

107×	`*-un-lft-identity`
43×	`distribute-lft-out`
39×	`sqrt-prod`
31×	`times-frac`
29×	`add-sqr-sqrt` `add-cbrt-cube` `add-exp-log`
21×	`add-cube-cbrt`
9×	`cbrt-undiv` `div-exp`
8×	`pow1` `prod-exp` `cbrt-unprod`
7×	`associate-/r` `associate-l*` `distribute-lft-out--`
6×	`associate-r` `associate-/l*` `add-log-exp`
5×	`flip3-+` `flip-+`
4×	`sqrt-div` `associate-*l/` `associate-/r/` `unswap-sqr`
3×	`pow-prod-down` `associate-/l/`
2×	`clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `div-inv`
1×	`+-commutative` `associate-+r-` `sum-log` `sqrt-unprod` `div-sub` `associate-r/` `-commutative`

Counts

4 → 133

Calls

4 calls:

49.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
94.0ms	(/ (+ 1.0 (- x x)) (+ (sqrt (+ x 1.0)) (sqrt x)))
75.0ms	(/ (* 1.0 (/ (+ 1.0 (- x x)) (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt (+ x 1.0)) (sqrt x)))
39.0ms	(* (sqrt (+ x 1.0)) (sqrt x))

series1.1s

Counts

4 → 12

Calls

4 calls:

113.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
181.0ms	(/ (+ 1.0 (- x x)) (+ (sqrt (+ x 1.0)) (sqrt x)))
743.0ms	(/ (* 1.0 (/ (+ 1.0 (- x x)) (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt (+ x 1.0)) (sqrt x)))
79.0ms	(* (sqrt (+ x 1.0)) (sqrt x))

simplify2.2s

Counts

145 → 145

Iterations

Iter	Nodes
done	5002
2	4982
1	760
0	269

prune551.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite186.0ms

Algorithm

rewrite-expression-head

Rules

89×	`add-sqr-sqrt`
73×	`times-frac`
71×	`*-un-lft-identity`
55×	`add-cube-cbrt`
41×	`sqrt-prod`
34×	`associate-l`
24×	`associate-r`
22×	`add-cbrt-cube` `add-exp-log`
11×	`associate-/r*`
10×	`pow1` `unswap-sqr`
8×	`associate-/r/` `distribute-lft-out`
7×	`distribute-rgt-out`
6×	`cbrt-undiv` `sqrt-div` `div-exp` `associate-/l*`
5×	`flip3-+` `prod-exp` `cbrt-unprod` `flip-+`
4×	`pow-prod-down` `div-inv` `add-log-exp`
3×	`associate-*l/`
2×	`clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `*-commutative`
1×	`frac-times` `sqrt-unprod` `associate-*r/`

Counts

4 → 182

Calls

4 calls:

99.0ms	(* (/ 1.0 (sqrt (+ 1.0 x))) (/ 1.0 (+ (* (sqrt (+ 1.0 x)) (sqrt x)) x)))
25.0ms	(/ 1.0 (+ (* (sqrt (+ 1.0 x)) (sqrt x)) x))
14.0ms	(/ 1.0 (sqrt (+ 1.0 x)))
34.0ms	(* (sqrt (+ 1.0 x)) (sqrt x))

series546.0ms

Counts

4 → 12

Calls

4 calls:

297.0ms	(* (/ 1.0 (sqrt (+ 1.0 x))) (/ 1.0 (+ (* (sqrt (+ 1.0 x)) (sqrt x)) x)))
92.0ms	(/ 1.0 (+ (* (sqrt (+ 1.0 x)) (sqrt x)) x))
88.0ms	(/ 1.0 (sqrt (+ 1.0 x)))
68.0ms	(* (sqrt (+ 1.0 x)) (sqrt x))

simplify472.0ms

Counts

194 → 194

Iterations

Iter	Nodes
done	5000
1	862
0	304

prune731.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

regimes52.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	17
1	17
0	12

end0.0ms

sample1.8s

Algorithm

intervals

Results

518.0ms	4066×	body	80	valid
346.0ms	1849×	body	640	valid
302.0ms	7906×	body	80	nan
256.0ms	1118×	body	1280	valid
83.0ms	668×	body	320	valid
21.0ms	299×	body	160	valid