Details

sample70.0ms

Algorithm

intervals

Results

13.0ms	51×	body	640	valid
12.0ms	225×	body	80	nan
11.0ms	36×	body	1280	valid
8.0ms	133×	body	80	valid
5.0ms	26×	body	320	valid
1.0ms	10×	body	160	valid

simplify6.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	14
2	14
1	11
0	8

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 19.1b

localize38.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ x 1.0))
0.1b	(/ 1.0 (sqrt (+ x 1.0)))
0.3b	(/ 1.0 (sqrt x))
3.4b	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

rewrite150.0ms

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:

11.0ms	(sqrt (+ x 1.0))
19.0ms	(/ 1.0 (sqrt (+ x 1.0)))
12.0ms	(/ 1.0 (sqrt x))
98.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

series384.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(sqrt (+ x 1.0))
106.0ms	(/ 1.0 (sqrt (+ x 1.0)))
52.0ms	(/ 1.0 (sqrt x))
186.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

simplify2.2s

Counts

145 → 145

Iterations

Iter	Nodes
done	5002
3	3464
2	1158
1	462
0	216

prune638.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 18.5b

localize37.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ x 1.0))
0.2b	(/ (- (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0)) (* (sqrt x) (sqrt (+ x 1.0))))
0.2b	(* (sqrt x) (sqrt (+ x 1.0)))
3.4b	(- (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0))

rewrite139.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 87

Calls

4 calls:

11.0ms	(sqrt (+ x 1.0))
61.0ms	(/ (- (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0)) (* (sqrt x) (sqrt (+ x 1.0))))
34.0ms	(* (sqrt x) (sqrt (+ x 1.0)))
29.0ms	(- (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0))

series642.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(sqrt (+ x 1.0))
364.0ms	(/ (- (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0)) (* (sqrt x) (sqrt (+ x 1.0))))
96.0ms	(* (sqrt x) (sqrt (+ x 1.0)))
138.0ms	(- (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0))

simplify2.0s

Counts

99 → 99

Iterations

Iter	Nodes
done	5001
2	1997
1	545
0	193

prune594.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 18.2b

localize65.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sqrt x) (sqrt (+ x 1.0)))
0.2b	(* (* 1.0 (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
0.5b	(* (* (sqrt x) 1.0) (* (sqrt x) 1.0))
2.7b	(- (* (* 1.0 (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0)))) (* (* (sqrt x) 1.0) (* (sqrt x) 1.0)))

rewrite218.0ms

Algorithm

rewrite-expression-head

Rules

86×	`pow1`
37×	`pow-prod-down`
30×	`add-cbrt-cube` `add-exp-log`
17×	`prod-exp` `cbrt-unprod`
16×	`add-sqr-sqrt` `associate-*r/`
14×	`sqrt-div`
11×	`sqrt-prod`
10×	`*-un-lft-identity`
9×	`associate-r`
8×	`associate-l` `pow-sqr` `pow-prod-up` `add-cube-cbrt`
7×	`flip3-+` `flip-+`
6×	`add-log-exp`
4×	`frac-times` `pow-plus` `unswap-sqr`
3×	`*-commutative`
2×	`pow2` `sqrt-pow1` `pow1/2` `swap-sqr` `associate-*l/`
1×	`sub-neg` `flip3--` `sqrt-unprod` `diff-log` `flip--` `distribute-lft-out` `difference-of-squares`

Counts

4 → 122

Calls

4 calls:

38.0ms	(* (sqrt x) (sqrt (+ x 1.0)))
71.0ms	(* (* 1.0 (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
31.0ms	(* (* (sqrt x) 1.0) (* (sqrt x) 1.0))
70.0ms	(- (* (* 1.0 (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0)))) (* (* (sqrt x) 1.0) (* (sqrt x) 1.0)))

series199.0ms

Counts

4 → 12

Calls

4 calls:

84.0ms	(* (sqrt x) (sqrt (+ x 1.0)))
52.0ms	(* (* 1.0 (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
36.0ms	(* (* (sqrt x) 1.0) (* (sqrt x) 1.0))
27.0ms	(- (* (* 1.0 (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0)))) (* (* (sqrt x) 1.0) (* (sqrt x) 1.0)))

simplify1.3s

Counts

134 → 134

Iterations

Iter	Nodes
done	5002
2	1432
1	463
0	172

prune557.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.3b

localize47.0ms

Local error

Found 4 expressions with local error:

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

rewrite224.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 103

Calls

4 calls:

12.0ms	(+ (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0))
103.0ms	(* (* (sqrt x) (sqrt (+ x 1.0))) (+ (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0)))
41.0ms	(* (sqrt x) (sqrt (+ x 1.0)))
66.0ms	(/ 1.0 (* (* (sqrt x) (sqrt (+ x 1.0))) (+ (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0))))

series1.3s

Counts

4 → 12

Calls

4 calls:

119.0ms	(+ (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0))
363.0ms	(* (* (sqrt x) (sqrt (+ x 1.0))) (+ (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0)))
63.0ms	(* (sqrt x) (sqrt (+ x 1.0)))
750.0ms	(/ 1.0 (* (* (sqrt x) (sqrt (+ x 1.0))) (+ (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0))))

simplify2.6s

Counts

115 → 115

Iterations

Iter	Nodes
done	5029
2	3204
1	808
0	264

prune585.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 0.0b

regimes126.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	16
1	16
0	11

end0.0ms

sample2.0s

Algorithm

intervals

Results

702.0ms	7962×	body	80	nan
410.0ms	1862×	body	640	valid
259.0ms	1143×	body	1280	valid
239.0ms	4043×	body	80	valid
72.0ms	630×	body	320	valid
50.0ms	322×	body	160	valid