Details

sample24.0ms

Algorithm

intervals

Results

11.0ms

256×

body

valid

simplify5.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	6
1	6
0	5

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.3b

localize14.0ms

Local error

Found 1 expressions with local error:

13.3b

(/ x (+ (* x x) 1.0))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `times-frac`
3×	`add-exp-log` `associate-/r` `add-cbrt-cube` `associate-/l`
2×	`associate-/r/`
1×	`pow1` `cbrt-undiv` `frac-2neg` `flip3-+` `div-exp` `clear-num` `flip-+` `div-inv` `add-log-exp`

Counts

1 → 29

Calls

1 calls:

38.0ms

(/ x (+ (* x x) 1.0))

series120.0ms

Counts

1 → 3

Calls

1 calls:

120.0ms

(/ x (+ (* x x) 1.0))

simplify4.3s

Counts

32 → 32

Iterations

Iter	Nodes
done	5287
3	3417
2	709
1	183
0	74

prune218.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize29.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ x (sqrt (+ (* x x) 1.0)))
0.0b	(/ (/ x (sqrt (+ (* x x) 1.0))) (sqrt (+ (* x x) 1.0)))
13.3b	(sqrt (+ (* x x) 1.0))
13.3b	(sqrt (+ (* x x) 1.0))

rewrite213.0ms

Algorithm

rewrite-expression-head

Rules

288×	`times-frac`
164×	`add-sqr-sqrt`
162×	`add-cube-cbrt` `*-un-lft-identity`
156×	`sqrt-prod`
27×	`associate-/l*`
22×	`sqrt-div`
18×	`associate-/r/`
12×	`associate-/r*`
11×	`add-exp-log` `flip3-+` `add-cbrt-cube` `flip-+`
9×	`div-inv`
6×	`pow1`
4×	`cbrt-undiv` `div-exp` `add-log-exp`
2×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num`
1×	`associate-/l/`

Counts

4 → 262

Calls

4 calls:

32.0ms	(/ x (sqrt (+ (* x x) 1.0)))
108.0ms	(/ (/ x (sqrt (+ (* x x) 1.0))) (sqrt (+ (* x x) 1.0)))
20.0ms	(sqrt (+ (* x x) 1.0))
20.0ms	(sqrt (+ (* x x) 1.0))

series526.0ms

Counts

4 → 12

Calls

4 calls:

240.0ms	(/ x (sqrt (+ (* x x) 1.0)))
118.0ms	(/ (/ x (sqrt (+ (* x x) 1.0))) (sqrt (+ (* x x) 1.0)))
78.0ms	(sqrt (+ (* x x) 1.0))
90.0ms	(sqrt (+ (* x x) 1.0))

simplify2.8s

Counts

274 → 274

Iterations

Iter	Nodes
done	5004
2	1947
1	806
0	336

prune1.5s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize62.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ 1 (fabs (cbrt (+ (* x x) 1.0)))) (/ (/ x (sqrt (+ (* x x) 1.0))) (sqrt (cbrt (+ (* x x) 1.0)))))
13.3b	(sqrt (+ (* x x) 1.0))
13.9b	(cbrt (+ (* x x) 1.0))
13.9b	(cbrt (+ (* x x) 1.0))

rewrite449.0ms

Algorithm

rewrite-expression-head

Rules

452×	`times-frac`
320×	`add-sqr-sqrt`
255×	`sqrt-prod`
222×	`associate-r`
214×	`*-un-lft-identity`
204×	`add-cube-cbrt`
87×	`cbrt-prod`
43×	`add-exp-log`
30×	`unswap-sqr`
25×	`add-cbrt-cube`
22×	`sqrt-div`
20×	`associate-/r/`
18×	`div-exp`
13×	`flip3-+` `associate-l` `flip-+`
12×	`prod-exp`
11×	`div-inv`
9×	`cbrt-undiv`
7×	`pow1`
6×	`cbrt-div` `cbrt-unprod`
4×	`add-log-exp`
3×	`rec-exp` `1-exp`
2×	`pow1/3`
1×	`frac-times` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative`

Counts

4 → 336

Calls

4 calls:

341.0ms	(* (/ 1 (fabs (cbrt (+ (* x x) 1.0)))) (/ (/ x (sqrt (+ (* x x) 1.0))) (sqrt (cbrt (+ (* x x) 1.0)))))
20.0ms	(sqrt (+ (* x x) 1.0))
12.0ms	(cbrt (+ (* x x) 1.0))
24.0ms	(cbrt (+ (* x x) 1.0))

series1.3s

Counts

4 → 12

Calls

4 calls:

515.0ms	(* (/ 1 (fabs (cbrt (+ (* x x) 1.0)))) (/ (/ x (sqrt (+ (* x x) 1.0))) (sqrt (cbrt (+ (* x x) 1.0)))))
80.0ms	(sqrt (+ (* x x) 1.0))
348.0ms	(cbrt (+ (* x x) 1.0))
382.0ms	(cbrt (+ (* x x) 1.0))

simplify4.4s

Counts

348 → 348

Iterations

Iter	Nodes
done	5001
1	2203
0	620

prune2.2s

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

localize47.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* x x) x)
0.4b	(/ 1.0 (pow x 5))
0.4b	(/ 1.0 (* (* x x) x))
17.2b	(- (/ 1.0 (pow x 5)) (/ 1.0 (* (* x x) x)))

rewrite220.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt`
27×	`times-frac`
25×	`*-un-lft-identity`
23×	`pow1` `add-exp-log` `add-cube-cbrt`
20×	`add-cbrt-cube`
13×	`unpow-prod-down`
8×	`associate-/r*`
6×	`pow-plus` `div-exp` `prod-exp` `pow-prod-up` `cbrt-unprod` `associate-/l*` `add-log-exp`
5×	`sqr-pow`
4×	`cbrt-undiv` `div-inv` `difference-of-squares`
3×	`associate-r` `pow-prod-down`
2×	`pow2` `frac-2neg` `clear-num` `pow-sqr` `distribute-lft-out--`
1×	`pow-to-exp` `sub-neg` `flip3--` `diff-log` `associate-l` `pow3` `pow-exp` `*-commutative` `frac-sub` `flip--` `unswap-sqr`

Counts

4 → 115

Calls

4 calls:

35.0ms	(* (* x x) x)
18.0ms	(/ 1.0 (pow x 5))
38.0ms	(/ 1.0 (* (* x x) x))
120.0ms	(- (/ 1.0 (pow x 5)) (/ 1.0 (* (* x x) x)))

series493.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(* (* x x) x)
100.0ms	(/ 1.0 (pow x 5))
70.0ms	(/ 1.0 (* (* x x) x))
259.0ms	(- (/ 1.0 (pow x 5)) (/ 1.0 (* (* x x) x)))

simplify2.6s

Counts

127 → 127

Iterations

Iter	Nodes
done	5001
2	1554
1	402
0	173

prune709.0ms

Pruning

4 alts after pruning (0 fresh and 4 done)

Merged error: 0b

regimes171.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 14.9b

bsearch97.0ms

Steps

Iters	Range		Point
6	263824.51516633737	1180206.5730270573	268164.4771045438
9	-6.004472807478775e+52	-4.610656989046551e+47	-2.182351251673565e+51

simplify9.0ms

Iterations

Iter	Nodes
done	28
1	28
0	20

end0.0ms

sample1.2s

Algorithm

intervals

Results

935.0ms

8000×

body

valid