Details

sample19.0ms

Algorithm

intervals

Results

7.0ms	256×	body	80	valid
2.0ms	100×	body	80	nan

simplify2.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	8
1	8
0	6

prune365.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

localize18.0ms

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))))

rewrite60.0ms

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:

14.0ms	(+ 1.0 (sqrt (+ 1.0 x)))
6.0ms	(sqrt (+ 1.0 x))
38.0ms	(/ x (+ 1.0 (sqrt (+ 1.0 x))))

series329.0ms

Counts

3 → 9

Calls

3 calls:

63.0ms	(+ 1.0 (sqrt (+ 1.0 x)))
48.0ms	(sqrt (+ 1.0 x))
218.0ms	(/ x (+ 1.0 (sqrt (+ 1.0 x))))

simplify657.0ms

Counts

70 → 70

Iterations

Iter	Nodes
done	5000
2	1500
1	317
0	137

prune260.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize14.0ms

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))))

rewrite117.0ms

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:

14.0ms	(sqrt (sqrt (+ 1.0 x)))
14.0ms	(sqrt (sqrt (+ 1.0 x)))
14.0ms	(/ x (+ 1.0 (* (sqrt (sqrt (+ 1.0 x))) (sqrt (sqrt (+ 1.0 x))))))
63.0ms	(* (sqrt (sqrt (+ 1.0 x))) (sqrt (sqrt (+ 1.0 x))))

series523.0ms

Counts

4 → 12

Calls

4 calls:

127.0ms	(sqrt (sqrt (+ 1.0 x)))
108.0ms	(sqrt (sqrt (+ 1.0 x)))
236.0ms	(/ x (+ 1.0 (* (sqrt (sqrt (+ 1.0 x))) (sqrt (sqrt (+ 1.0 x))))))
51.0ms	(* (sqrt (sqrt (+ 1.0 x))) (sqrt (sqrt (+ 1.0 x))))

simplify1.6s

Counts

173 → 173

Iterations

Iter	Nodes
done	5001
2	2845
1	552
0	239

prune662.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize25.0ms

Local error

Found 4 expressions with local error:

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

rewrite250.0ms

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:

11.0ms	(sqrt (+ 1.0 x))
33.0ms	(+ (sqrt (+ 1.0 x)) 1.0)
103.0ms	(/ (+ (sqrt (+ 1.0 x)) 1.0) (sqrt x))
74.0ms	(/ (sqrt x) (/ (+ (sqrt (+ 1.0 x)) 1.0) (sqrt x)))

series482.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(sqrt (+ 1.0 x))
59.0ms	(+ (sqrt (+ 1.0 x)) 1.0)
189.0ms	(/ (+ (sqrt (+ 1.0 x)) 1.0) (sqrt x))
198.0ms	(/ (sqrt x) (/ (+ (sqrt (+ 1.0 x)) 1.0) (sqrt x)))

simplify637.0ms

Counts

305 → 305

Iterations

Iter	Nodes
done	5000
1	979
0	372

prune948.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize37.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cbrt (+ (sqrt (+ x 1.0)) 1.0)) (cbrt (+ (sqrt (+ x 1.0)) 1.0)))
0.9b	(cbrt (+ (sqrt (+ x 1.0)) 1.0))
0.9b	(cbrt (+ (sqrt (+ x 1.0)) 1.0))
0.9b	(cbrt (+ (sqrt (+ x 1.0)) 1.0))

rewrite258.0ms

Algorithm

rewrite-expression-head

Rules

36×	`cbrt-prod`
35×	`*-un-lft-identity`
23×	`add-sqr-sqrt`
18×	`cbrt-div`
15×	`add-cube-cbrt`
11×	`pow1`
9×	`flip3-+` `pow1/3` `swap-sqr` `flip-+` `distribute-lft-out`
7×	`associate-r` `associate-l`
6×	`add-exp-log`
4×	`frac-times` `add-cbrt-cube` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `associate-l/` `associate-r/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 95

Calls

4 calls:

189.0ms	(* (cbrt (+ (sqrt (+ x 1.0)) 1.0)) (cbrt (+ (sqrt (+ x 1.0)) 1.0)))
23.0ms	(cbrt (+ (sqrt (+ x 1.0)) 1.0))
27.0ms	(cbrt (+ (sqrt (+ x 1.0)) 1.0))
15.0ms	(cbrt (+ (sqrt (+ x 1.0)) 1.0))

series1.5s

Counts

4 → 12

Calls

4 calls:

514.0ms	(* (cbrt (+ (sqrt (+ x 1.0)) 1.0)) (cbrt (+ (sqrt (+ x 1.0)) 1.0)))
312.0ms	(cbrt (+ (sqrt (+ x 1.0)) 1.0))
335.0ms	(cbrt (+ (sqrt (+ x 1.0)) 1.0))
357.0ms	(cbrt (+ (sqrt (+ x 1.0)) 1.0))

simplify868.0ms

Counts

107 → 107

Iterations

Iter	Nodes
done	5000
2	1565
1	382
0	150

prune672.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes34.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Iter	Nodes
done	10
1	10
0	8

end0.0ms

sample793.0ms

Algorithm

intervals

Results

405.0ms	7998×	body	80	valid
112.0ms	2622×	body	80	nan
0.0ms	2×	body	1280	valid