Details

sample28.0ms

Algorithm

intervals

Results

11.0ms	256×	body	80	valid
3.0ms	89×	body	80	nan

simplify3.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	8
1	8
0	6

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize13.0ms

Local error

Found 2 expressions with local error:

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

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

22×	`*-un-lft-identity`
13×	`add-sqr-sqrt`
12×	`times-frac` `add-cube-cbrt`
5×	`distribute-lft-out`
4×	`associate-/r*` `add-cbrt-cube` `add-exp-log` `sqrt-prod`
3×	`pow1` `associate-/l*`
2×	`flip3-+` `sqrt-div` `associate-/r/` `flip-+` `add-log-exp`
1×	`cbrt-undiv` `rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `div-inv`

Counts

2 → 49

Calls

2 calls:

6.0ms	(sqrt (+ x 1.0))
39.0ms	(/ x (+ 1.0 (sqrt (+ x 1.0))))

series210.0ms

Counts

2 → 6

Calls

2 calls:

36.0ms	(sqrt (+ x 1.0))
174.0ms	(/ x (+ 1.0 (sqrt (+ x 1.0))))

simplify847.0ms

Counts

55 → 55

Iterations

Iter	Nodes
done	5001
2	1373
1	291
0	127

prune264.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize18.0ms

Local error

Found 4 expressions with local error:

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

rewrite91.0ms

Algorithm

rewrite-expression-head

Rules

106×	`sqrt-prod`
62×	`add-sqr-sqrt`
46×	`*-un-lft-identity`
40×	`sqrt-pow1`
32×	`sqrt-div`
31×	`pow1`
28×	`add-cube-cbrt`
20×	`pow1/2`
18×	`swap-sqr`
10×	`associate-r` `associate-l`
9×	`flip3-+` `times-frac` `pow-prod-up` `flip-+` `unswap-sqr`
8×	`add-cbrt-cube` `add-exp-log` `distribute-lft-out`
5×	`pow-prod-down` `pow-sqr`
4×	`frac-times` `rem-sqrt-square` `add-log-exp`
3×	`associate-/r` `associate-/l`
2×	`associate-l/` `associate-r/` `associate-/r/`
1×	`pow2` `cbrt-undiv` `clear-num` `rem-square-sqrt` `frac-2neg` `pow-plus` `sqrt-unprod` `div-exp` `prod-exp` `*-commutative` `cbrt-unprod` `div-inv`

Counts

4 → 161

Calls

4 calls:

6.0ms	(sqrt (sqrt (+ x 1.0)))
7.0ms	(sqrt (sqrt (+ x 1.0)))
8.0ms	(/ x (+ 1.0 (* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0))))))
64.0ms	(* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0))))

series465.0ms

Counts

4 → 12

Calls

4 calls:

118.0ms	(sqrt (sqrt (+ x 1.0)))
105.0ms	(sqrt (sqrt (+ x 1.0)))
193.0ms	(/ x (+ 1.0 (* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0))))))
49.0ms	(* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0))))

simplify1.8s

Counts

173 → 173

Iterations

Iter	Nodes
done	5000
2	2841
1	551
0	239

prune455.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ 1.0 x))
0.1b	(* (sqrt (+ 1.0 x)) (+ 1.0 x))
0.2b	(/ x (+ 1.0 (cbrt (* (sqrt (+ 1.0 x)) (+ 1.0 x)))))
6.6b	(cbrt (* (sqrt (+ 1.0 x)) (+ 1.0 x)))

rewrite87.0ms

Algorithm

rewrite-expression-head

Rules

31×	`*-un-lft-identity`
24×	`add-sqr-sqrt`
17×	`add-cube-cbrt`
14×	`flip3-+` `sqrt-div` `flip-+`
12×	`times-frac`
11×	`pow1`
9×	`sqrt-prod`
8×	`frac-times` `cbrt-div` `add-cbrt-cube` `add-exp-log`
7×	`associate-l` `distribute-lft-out`
4×	`associate-/r` `associate-r` `associate-l/` `associate-*r/` `add-log-exp`
3×	`sqrt-pow1` `pow1/2` `associate-/l*`
2×	`pow-plus` `cube-unmult` `associate-/r/` `pow-prod-up` `unswap-sqr`
1×	`cbrt-prod` `distribute-rgt-in` `cbrt-undiv` `rem-sqrt-square` `clear-num` `frac-2neg` `distribute-lft-in` `pow1/3` `div-exp` `pow-prod-down` `prod-exp` `*-commutative` `rem-cbrt-cube` `cbrt-unprod` `div-inv`

Counts

4 → 106

Calls

4 calls:

9.0ms	(sqrt (+ 1.0 x))
45.0ms	(* (sqrt (+ 1.0 x)) (+ 1.0 x))
9.0ms	(/ x (+ 1.0 (cbrt (* (sqrt (+ 1.0 x)) (+ 1.0 x)))))
18.0ms	(cbrt (* (sqrt (+ 1.0 x)) (+ 1.0 x)))

series325.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(sqrt (+ 1.0 x))
72.0ms	(* (sqrt (+ 1.0 x)) (+ 1.0 x))
163.0ms	(/ x (+ 1.0 (cbrt (* (sqrt (+ 1.0 x)) (+ 1.0 x)))))
49.0ms	(cbrt (* (sqrt (+ 1.0 x)) (+ 1.0 x)))

simplify1.8s

Counts

118 → 118

Iterations

Iter	Nodes
done	5001
2	2843
1	511
0	195

prune494.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize18.0ms

Local error

Found 3 expressions with local error:

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

rewrite108.0ms

Algorithm

rewrite-expression-head

Rules

66×	`*-un-lft-identity`
55×	`add-sqr-sqrt`
52×	`times-frac`
39×	`sqrt-prod`
38×	`add-cube-cbrt`
30×	`associate-r`
14×	`distribute-lft-out`
10×	`add-cbrt-cube` `add-exp-log`
6×	`pow1` `associate-l` `associate-/l*` `unswap-sqr`
4×	`associate-/r*` `associate-/r/`
3×	`flip3-+` `flip-+` `add-log-exp`
2×	`cbrt-undiv` `sqrt-div` `div-exp` `prod-exp` `cbrt-unprod` `div-inv`
1×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `pow-prod-down` `associate-r/` `-commutative`

Counts

3 → 120

Calls

3 calls:

5.0ms	(sqrt (+ x 1.0))
25.0ms	(/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0))))
73.0ms	(* (sqrt x) (/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0)))))

series565.0ms

Counts

3 → 9

Calls

3 calls:

36.0ms	(sqrt (+ x 1.0))
344.0ms	(/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0))))
184.0ms	(* (sqrt x) (/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0)))))

simplify2.9s

Counts

129 → 129

Iterations

Iter	Nodes
done	5001
2	3844
1	522
0	203

prune549.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes39.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	10
1	10
0	8

end0.0ms

sample652.0ms

Algorithm

intervals

Results

379.0ms	7998×	body	80	valid
72.0ms	2570×	body	80	nan
0.0ms	2×	body	1280	valid