Details

sample16.0ms

Algorithm

intervals

Results

6.0ms	256×	body	80	valid
2.0ms	89×	body	80	nan

simplify2.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	8
1	8
0	6

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize9.0ms

Local error

Found 2 expressions with local error:

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

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

22×	`*-un-lft-identity`
15×	`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×	`expm1-log1p-u` `flip3-+` `sqrt-div` `associate-/r/` `flip-+` `log1p-expm1-u` `add-log-exp`
1×	`cbrt-undiv` `rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `hypot-def` `div-inv`

Counts

2 → 54

Calls

2 calls:

7.0ms	(sqrt (+ x 1.0))
28.0ms	(/ x (+ 1.0 (sqrt (+ x 1.0))))

series251.0ms

Counts

2 → 6

Calls

2 calls:

55.0ms	(sqrt (+ x 1.0))
196.0ms	(/ x (+ 1.0 (sqrt (+ x 1.0))))

simplify1.3s

Counts

60 → 60

Iterations

Iter	Nodes
done	5001
2	1445
1	303
0	131

prune323.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize17.0ms

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))))

rewrite118.0ms

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×	`expm1-log1p-u` `frac-times` `rem-sqrt-square` `log1p-expm1-u` `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 → 169

Calls

4 calls:

8.0ms	(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))))))
83.0ms	(* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0))))

series481.0ms

Counts

4 → 12

Calls

4 calls:

107.0ms	(sqrt (sqrt (+ x 1.0)))
125.0ms	(sqrt (sqrt (+ x 1.0)))
188.0ms	(/ x (+ 1.0 (* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0))))))
61.0ms	(* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0))))

simplify2.2s

Counts

181 → 181

Iterations

Iter	Nodes
done	5002
2	2741
1	566
0	245

prune624.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize23.0ms

Local error

Found 4 expressions with local error:

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

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

31×	`*-un-lft-identity`
26×	`add-sqr-sqrt`
17×	`add-cube-cbrt`
14×	`flip3-+` `sqrt-div` `flip-+`
12×	`times-frac`
10×	`pow1`
9×	`sqrt-prod`
8×	`frac-times` `cbrt-div` `add-cbrt-cube` `add-exp-log`
7×	`associate-r` `distribute-lft-out`
4×	`expm1-log1p-u` `associate-/r` `associate-l` `associate-l/` `associate-*r/` `log1p-expm1-u` `add-log-exp`
3×	`associate-/l*`
2×	`sqrt-pow1` `pow1/2` `pow3` `associate-/r/` `pow-prod-up` `unswap-sqr`
1×	`cbrt-prod` `cbrt-undiv` `rem-sqrt-square` `clear-num` `frac-2neg` `pow1/3` `div-exp` `pow-prod-down` `prod-exp` `*-commutative` `rem-cbrt-cube` `cbrt-unprod` `hypot-def` `div-inv`

Counts

4 → 111

Calls

4 calls:

6.0ms	(sqrt (+ x 1.0))
46.0ms	(* (+ x 1.0) (sqrt (+ x 1.0)))
9.0ms	(/ x (+ 1.0 (cbrt (* (+ x 1.0) (sqrt (+ x 1.0))))))
11.0ms	(cbrt (* (+ x 1.0) (sqrt (+ x 1.0))))

series368.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(sqrt (+ x 1.0))
70.0ms	(* (+ x 1.0) (sqrt (+ x 1.0)))
233.0ms	(/ x (+ 1.0 (cbrt (* (+ x 1.0) (sqrt (+ x 1.0))))))
33.0ms	(cbrt (* (+ x 1.0) (sqrt (+ x 1.0))))

simplify1.4s

Counts

123 → 123

Iterations

Iter	Nodes
done	5001
2	2430
1	452
0	200

prune613.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize25.0ms

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)))))

rewrite163.0ms

Algorithm

rewrite-expression-head

Rules

66×	`*-un-lft-identity`
57×	`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×	`expm1-log1p-u` `flip3-+` `flip-+` `log1p-expm1-u` `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` `hypot-def`

Counts

3 → 127

Calls

3 calls:

6.0ms	(sqrt (+ x 1.0))
36.0ms	(/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0))))
116.0ms	(* (sqrt x) (/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0)))))

series526.0ms

Counts

3 → 9

Calls

3 calls:

33.0ms	(sqrt (+ x 1.0))
340.0ms	(/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0))))
153.0ms	(* (sqrt x) (/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0)))))

simplify2.9s

Counts

136 → 136

Iterations

Iter	Nodes
done	5001
2	3865
1	542
0	209

prune589.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes44.0ms

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

sample555.0ms

Algorithm

intervals

Results

300.0ms	7998×	body	80	valid
91.0ms	2570×	body	80	nan
0.0ms	2×	body	1280	valid