Details

sample30.0ms

Algorithm

intervals

Results

11.0ms	256×	body	80	valid
3.0ms	100×	body	80	nan

simplify3.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	8
1	8
0	6

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

localize9.0ms

Local error

Found 3 expressions with local error:

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

rewrite77.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 61

Calls

3 calls:

23.0ms	(+ 1.0 (sqrt (+ 1.0 x)))
11.0ms	(sqrt (+ 1.0 x))
40.0ms	(/ x (+ 1.0 (sqrt (+ 1.0 x))))

series323.0ms

Counts

3 → 9

Calls

3 calls:

76.0ms	(+ 1.0 (sqrt (+ 1.0 x)))
51.0ms	(sqrt (+ 1.0 x))
196.0ms	(/ x (+ 1.0 (sqrt (+ 1.0 x))))

simplify695.0ms

Counts

70 → 70

Iterations

Iter	Nodes
done	5000
2	1500
1	317
0	137

prune287.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize26.0ms

Local error

Found 4 expressions with local error:

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

rewrite126.0ms

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:

11.0ms	(sqrt (sqrt (+ 1.0 x)))
11.0ms	(sqrt (sqrt (+ 1.0 x)))
12.0ms	(/ x (+ 1.0 (* (sqrt (sqrt (+ 1.0 x))) (sqrt (sqrt (+ 1.0 x))))))
78.0ms	(* (sqrt (sqrt (+ 1.0 x))) (sqrt (sqrt (+ 1.0 x))))

series524.0ms

Counts

4 → 12

Calls

4 calls:

129.0ms	(sqrt (sqrt (+ 1.0 x)))
132.0ms	(sqrt (sqrt (+ 1.0 x)))
214.0ms	(/ x (+ 1.0 (* (sqrt (sqrt (+ 1.0 x))) (sqrt (sqrt (+ 1.0 x))))))
49.0ms	(* (sqrt (sqrt (+ 1.0 x))) (sqrt (sqrt (+ 1.0 x))))

simplify2.0s

Counts

173 → 173

Iterations

Iter	Nodes
done	5001
2	2845
1	552
0	239

prune518.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize17.0ms

Local error

Found 4 expressions with local error:

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

rewrite182.0ms

Algorithm

rewrite-expression-head

Rules

360×	`times-frac`
287×	`*-un-lft-identity`
190×	`sqrt-prod`
186×	`add-sqr-sqrt`
185×	`add-cube-cbrt`
51×	`distribute-lft-out`
34×	`associate-/r*`
11×	`add-cbrt-cube` `add-exp-log`
10×	`associate-/l*`
9×	`div-inv`
6×	`add-log-exp`
5×	`pow1`
4×	`cbrt-undiv` `div-exp`
3×	`flip3-+` `flip-+`
2×	`clear-num` `frac-2neg` `sqrt-div` `associate-/l/`
1×	`+-commutative` `rem-sqrt-square` `sum-log` `sqrt-pow1` `pow1/2` `associate-/r/`

Counts

4 → 293

Calls

4 calls:

24.0ms	(+ 1.0 (sqrt (+ 1.0 x)))
11.0ms	(sqrt (+ 1.0 x))
81.0ms	(/ (+ 1.0 (sqrt (+ 1.0 x))) (sqrt x))
45.0ms	(/ (sqrt x) (/ (+ 1.0 (sqrt (+ 1.0 x))) (sqrt x)))

series473.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(+ 1.0 (sqrt (+ 1.0 x)))
47.0ms	(sqrt (+ 1.0 x))
165.0ms	(/ (+ 1.0 (sqrt (+ 1.0 x))) (sqrt x))
185.0ms	(/ (sqrt x) (/ (+ 1.0 (sqrt (+ 1.0 x))) (sqrt x)))

simplify712.0ms

Counts

305 → 305

Iterations

Iter	Nodes
done	5000
1	979
0	372

prune932.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sqrt x) (cbrt (+ (sqrt (+ 1.0 x)) 1.0)))
0.9b	(cbrt (+ (sqrt (+ 1.0 x)) 1.0))
0.9b	(cbrt (+ (sqrt (+ 1.0 x)) 1.0))
0.9b	(cbrt (+ (sqrt (+ 1.0 x)) 1.0))

rewrite139.0ms

Algorithm

rewrite-expression-head

Rules

57×	`*-un-lft-identity`
42×	`times-frac`
40×	`cbrt-prod`
37×	`add-sqr-sqrt` `add-cube-cbrt`
24×	`sqrt-prod`
10×	`distribute-lft-out`
8×	`cbrt-div`
7×	`associate-/r*`
6×	`add-exp-log` `associate-/l*`
5×	`add-cbrt-cube`
4×	`pow1` `flip3-+` `flip-+` `add-log-exp`
3×	`pow1/3`
2×	`associate-/r/`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `div-inv`

Counts

4 → 111

Calls

4 calls:

54.0ms	(/ (sqrt x) (cbrt (+ (sqrt (+ 1.0 x)) 1.0)))
15.0ms	(cbrt (+ (sqrt (+ 1.0 x)) 1.0))
28.0ms	(cbrt (+ (sqrt (+ 1.0 x)) 1.0))
34.0ms	(cbrt (+ (sqrt (+ 1.0 x)) 1.0))

series2.6s

Counts

4 → 12

Calls

4 calls:

1.6s	(/ (sqrt x) (cbrt (+ (sqrt (+ 1.0 x)) 1.0)))
321.0ms	(cbrt (+ (sqrt (+ 1.0 x)) 1.0))
361.0ms	(cbrt (+ (sqrt (+ 1.0 x)) 1.0))
360.0ms	(cbrt (+ (sqrt (+ 1.0 x)) 1.0))

simplify892.0ms

Counts

123 → 123

Iterations

Iter	Nodes
done	5001
2	1882
1	493
0	214

prune639.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes60.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	10
1	10
0	8

end0.0ms

sample712.0ms

Algorithm

intervals

Results

398.0ms	7998×	body	80	valid
78.0ms	2622×	body	80	nan
0.0ms	2×	body	1280	valid