Details

sample24.0ms

Algorithm

intervals

Results

10.0ms

256×

body

valid

simplify4.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	7
1	7
0	5

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.0b

localize12.0ms

Local error

Found 1 expressions with local error:

15.0b

(/ x (fma x x 1.0))

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-sqr-sqrt` `*-un-lft-identity` `times-frac` `add-cube-cbrt`
3×	`associate-/r` `add-cbrt-cube` `add-exp-log` `associate-/l`
1×	`expm1-log1p-u` `pow1` `cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `log1p-expm1-u` `div-inv` `add-log-exp`

Counts

1 → 29

Calls

1 calls:

8.0ms

(/ x (fma x x 1.0))

series136.0ms

Counts

1 → 3

Calls

1 calls:

136.0ms

(/ x (fma x x 1.0))

simplify1.4s

Counts

32 → 32

Iterations

Iter	Nodes
done	5000
3	2280
2	480
1	140
0	68

prune157.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ x (sqrt (fma x x 1.0)))
14.9b	(sqrt (fma x x 1.0))
14.9b	(sqrt (fma x x 1.0))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt`
20×	`*-un-lft-identity` `add-cube-cbrt`
18×	`times-frac` `sqrt-prod`
6×	`associate-/r*`
5×	`pow1` `add-cbrt-cube` `add-exp-log`
3×	`expm1-log1p-u` `log1p-expm1-u` `associate-/l*` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `div-inv`

Counts

3 → 71

Calls

3 calls:

6.0ms	(/ x (sqrt (fma x x 1.0)))
5.0ms	(sqrt (fma x x 1.0))
1.0ms	(sqrt (fma x x 1.0))

series342.0ms

Counts

3 → 9

Calls

3 calls:

197.0ms	(/ x (sqrt (fma x x 1.0)))
79.0ms	(sqrt (fma x x 1.0))
66.0ms	(sqrt (fma x x 1.0))

simplify870.0ms

Counts

80 → 80

Iterations

Iter	Nodes
done	5000
2	947
1	249
0	118

prune457.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize48.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ x (sqrt (sqrt (fma x x 1.0))))
14.9b	(sqrt (fma x x 1.0))
14.9b	(sqrt (fma x x 1.0))
14.9b	(sqrt (fma x x 1.0))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

45×	`sqrt-prod`
32×	`add-sqr-sqrt`
29×	`*-un-lft-identity` `add-cube-cbrt`
27×	`times-frac`
9×	`associate-/r*`
7×	`pow1`
6×	`add-cbrt-cube` `add-exp-log`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-/l*`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `div-inv`

Counts

4 → 98

Calls

4 calls:

13.0ms	(/ x (sqrt (sqrt (fma x x 1.0))))
2.0ms	(sqrt (fma x x 1.0))
2.0ms	(sqrt (fma x x 1.0))
3.0ms	(sqrt (fma x x 1.0))

series597.0ms

Counts

4 → 12

Calls

4 calls:

375.0ms	(/ x (sqrt (sqrt (fma x x 1.0))))
83.0ms	(sqrt (fma x x 1.0))
68.0ms	(sqrt (fma x x 1.0))
71.0ms	(sqrt (fma x x 1.0))

simplify1.3s

Counts

110 → 110

Iterations

Iter	Nodes
done	5000
2	1163
1	317
0	159

prune588.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize29.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ 1.0 (* x x)) x)
0.5b	(/ 1.0 (* x x))
0.6b	(/ 1.0 (pow x 5))
19.4b	(- (/ 1.0 (pow x 5)) (/ (/ 1.0 (* x x)) x))

rewrite260.0ms

Algorithm

rewrite-expression-head

Rules

1376×	`times-frac`
790×	`add-sqr-sqrt`
758×	`*-un-lft-identity`
752×	`add-cube-cbrt`
625×	`prod-diff`
249×	`unpow-prod-down`
133×	`div-inv`
85×	`sqr-pow`
25×	`fma-neg`
23×	`add-exp-log`
20×	`add-cbrt-cube`
13×	`associate-/l*`
12×	`difference-of-squares`
11×	`associate-/r*`
10×	`div-exp`
8×	`cbrt-undiv`
6×	`add-log-exp`
4×	`expm1-log1p-u` `pow1` `log1p-expm1-u`
3×	`clear-num` `frac-2neg`
2×	`prod-exp` `cbrt-unprod` `distribute-lft-out--`
1×	`pow-to-exp` `sub-neg` `flip3--` `diff-log` `pow-exp` `frac-sub` `flip--` `associate-/l/`

Counts

4 → 799

Calls

4 calls:

22.0ms	(/ (/ 1.0 (* x x)) x)
7.0ms	(/ 1.0 (* x x))
6.0ms	(/ 1.0 (pow x 5))
132.0ms	(- (/ 1.0 (pow x 5)) (/ (/ 1.0 (* x x)) x))

series345.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(/ (/ 1.0 (* x x)) x)
28.0ms	(/ 1.0 (* x x))
67.0ms	(/ 1.0 (pow x 5))
201.0ms	(- (/ 1.0 (pow x 5)) (/ (/ 1.0 (* x x)) x))

simplify1.3s

Counts

811 → 811

Iterations

Iter	Nodes
done	5000
1	2185
0	963

prune5.4s

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes43.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 14.8b

bsearch66.0ms

Steps

Iters	Range		Point
9	0.030359728269424062	9645967.64350026	446.32379712242954
2	-7.049573791614887e+27	-5.833600422647533e+27	-6.289590436010292e+27

simplify8.0ms

Iterations

Iter	Nodes
done	32
1	32
0	25

end0.0ms

sample478.0ms

Algorithm

intervals

Results

309.0ms

8000×

body

valid