Details

sample82.0ms

Algorithm

intervals

Results

15.0ms	61×	body	640	valid
15.0ms	291×	body	80	nan
12.0ms	39×	body	1280	valid
8.0ms	129×	body	80	valid
4.0ms	21×	body	320	valid
1.0ms	6×	body	160	valid

simplify28.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	14
2	14
1	11
0	8

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 20.3b

localize34.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ x 1.0))
0.2b	(/ 1.0 (sqrt (+ x 1.0)))
0.3b	(/ 1.0 (sqrt x))
2.4b	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

rewrite144.0ms

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:

6.0ms	(sqrt (+ x 1.0))
10.0ms	(/ 1.0 (sqrt (+ x 1.0)))
7.0ms	(/ 1.0 (sqrt x))
111.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

series388.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(sqrt (+ x 1.0))
100.0ms	(/ 1.0 (sqrt (+ x 1.0)))
43.0ms	(/ 1.0 (sqrt x))
204.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

simplify780.0ms

Counts

145 → 145

Iterations

Iter	Nodes
done	5001
2	1655
1	462
0	216

prune699.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 19.8b

localize34.0ms

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)))
0.3b	(* (sqrt (+ x 1.0)) (sqrt x))
2.4b	(- (sqrt (+ x 1.0)) (sqrt x))

rewrite165.0ms

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:

6.0ms	(sqrt (+ x 1.0))
77.0ms	(/ (* 1.0 (- (sqrt (+ x 1.0)) (sqrt x))) (* (sqrt (+ x 1.0)) (sqrt x)))
29.0ms	(* (sqrt (+ x 1.0)) (sqrt x))
49.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

series1.1s

Counts

4 → 12

Calls

4 calls:

52.0ms	(sqrt (+ x 1.0))
798.0ms	(/ (* 1.0 (- (sqrt (+ x 1.0)) (sqrt x))) (* (sqrt (+ x 1.0)) (sqrt x)))
109.0ms	(* (sqrt (+ x 1.0)) (sqrt x))
128.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

simplify1.3s

Counts

105 → 105

Iterations

Iter	Nodes
done	5000
2	3032
1	531
0	192

prune565.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.3b

localize51.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (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	(/ (+ 1.0 (- x x)) (+ (sqrt (+ x 1.0)) (sqrt x)))
0.3b	(* (sqrt (+ x 1.0)) (sqrt x))

rewrite250.0ms

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:

28.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
76.0ms	(/ (* 1.0 (/ (+ 1.0 (- x x)) (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt (+ x 1.0)) (sqrt x)))
89.0ms	(/ (+ 1.0 (- x x)) (+ (sqrt (+ x 1.0)) (sqrt x)))
48.0ms	(* (sqrt (+ x 1.0)) (sqrt x))

series1.1s

Counts

4 → 12

Calls

4 calls:

78.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
741.0ms	(/ (* 1.0 (/ (+ 1.0 (- x x)) (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt (+ x 1.0)) (sqrt x)))
201.0ms	(/ (+ 1.0 (- x x)) (+ (sqrt (+ x 1.0)) (sqrt x)))
64.0ms	(* (sqrt (+ x 1.0)) (sqrt x))

simplify1.9s

Counts

145 → 145

Iterations

Iter	Nodes
done	5002
2	4957
1	759
0	269

prune645.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* (sqrt (+ 1.0 x)) x) (* (+ 1.0 x) (sqrt x)))
0.1b	(* (sqrt (+ 1.0 x)) x)
0.1b	(* (+ 1.0 x) (sqrt x))
0.6b	(/ (* 1.0 (+ 1.0 (- x x))) (+ (* (sqrt (+ 1.0 x)) x) (* (+ 1.0 x) (sqrt x))))

rewrite123.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt` `associate-*l/`
16×	`*-un-lft-identity`
13×	`flip3-+` `add-cbrt-cube` `add-exp-log` `flip-+`
12×	`add-cube-cbrt`
11×	`associate-l`
10×	`sqrt-div`
9×	`associate-r` `sqrt-prod`
8×	`pow1` `frac-add`
6×	`associate-/r/` `add-log-exp`
4×	`unswap-sqr`
3×	`associate-/r*` `times-frac` `prod-exp` `cbrt-unprod`
2×	`cbrt-undiv` `div-exp` `pow-prod-down` `associate-r/` `-commutative` `distribute-lft-out` `associate-/l/`
1×	`+-commutative` `clear-num` `sum-log` `frac-2neg` `div-inv` `associate-/l*`

Counts

4 → 94

Calls

4 calls:

13.0ms	(+ (* (sqrt (+ 1.0 x)) x) (* (+ 1.0 x) (sqrt x)))
35.0ms	(* (sqrt (+ 1.0 x)) x)
33.0ms	(* (+ 1.0 x) (sqrt x))
39.0ms	(/ (* 1.0 (+ 1.0 (- x x))) (+ (* (sqrt (+ 1.0 x)) x) (* (+ 1.0 x) (sqrt x))))

series713.0ms

Counts

4 → 12

Calls

4 calls:

173.0ms	(+ (* (sqrt (+ 1.0 x)) x) (* (+ 1.0 x) (sqrt x)))
108.0ms	(* (sqrt (+ 1.0 x)) x)
76.0ms	(* (+ 1.0 x) (sqrt x))
356.0ms	(/ (* 1.0 (+ 1.0 (- x x))) (+ (* (sqrt (+ 1.0 x)) x) (* (+ 1.0 x) (sqrt x))))

simplify1.9s

Counts

106 → 106

Iterations

Iter	Nodes
done	5000
2	4520
1	741
0	248

prune432.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.0b

regimes79.0ms

Accuracy

0% (0.6b remaining)

Error of 0.6b against oracle of 0.0b and baseline of 0.6b

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	18
1	18
0	12

end0.0ms

sample1.8s

Algorithm

intervals

Results

594.0ms	1868×	body	640	valid
361.0ms	8152×	body	80	nan
242.0ms	4034×	body	80	valid
199.0ms	1163×	body	1280	valid
105.0ms	637×	body	320	valid
21.0ms	298×	body	160	valid