Details

sample12.0ms

Algorithm

intervals

Results

5.0ms

256×

body

valid

simplify2.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	7
1	7
0	5

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.3b

localize5.0ms

Local error

Found 1 expressions with local error:

15.3b

(/ x (fma x x 1.0))

rewrite5.0ms

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:

4.0ms

(/ x (fma x x 1.0))

series97.0ms

Counts

1 → 3

Calls

1 calls:

97.0ms

(/ x (fma x x 1.0))

simplify1.5s

Counts

32 → 32

Iterations

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

prune201.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (/ x (sqrt (fma x x 1.0))) (sqrt (fma x x 1.0)))
0.0b	(/ x (sqrt (fma x x 1.0)))
15.2b	(sqrt (fma x x 1.0))
15.2b	(sqrt (fma x x 1.0))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

276×	`times-frac`
160×	`add-sqr-sqrt`
158×	`*-un-lft-identity` `add-cube-cbrt`
150×	`sqrt-prod`
25×	`associate-/l*`
12×	`associate-/r*`
11×	`add-cbrt-cube` `add-exp-log`
9×	`div-inv`
6×	`pow1`
4×	`expm1-log1p-u` `cbrt-undiv` `div-exp` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2`
1×	`associate-/l/`

Counts

4 → 248

Calls

4 calls:

19.0ms	(/ (/ x (sqrt (fma x x 1.0))) (sqrt (fma x x 1.0)))
9.0ms	(/ x (sqrt (fma x x 1.0)))
2.0ms	(sqrt (fma x x 1.0))
2.0ms	(sqrt (fma x x 1.0))

series450.0ms

Counts

4 → 12

Calls

4 calls:

113.0ms	(/ (/ x (sqrt (fma x x 1.0))) (sqrt (fma x x 1.0)))
177.0ms	(/ x (sqrt (fma x x 1.0)))
84.0ms	(sqrt (fma x x 1.0))
75.0ms	(sqrt (fma x x 1.0))

simplify1.8s

Counts

260 → 260

Iterations

Iter	Nodes
done	5002
2	2940
1	719
0	304

prune1.1s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize41.0ms

Local error

Found 4 expressions with local error:

15.2b	(sqrt (fma x x 1.0))
15.7b	(cbrt (fma x x 1.0))
15.7b	(cbrt (fma x x 1.0))
15.7b	(cbrt (fma x x 1.0))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod` `add-sqr-sqrt`
8×	`*-un-lft-identity` `add-cube-cbrt`
5×	`pow1`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3` `sqrt-prod`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 54

Calls

4 calls:

2.0ms	(sqrt (fma x x 1.0))
1.0ms	(cbrt (fma x x 1.0))
1.0ms	(cbrt (fma x x 1.0))
1.0ms	(cbrt (fma x x 1.0))

series978.0ms

Counts

4 → 12

Calls

4 calls:

98.0ms	(sqrt (fma x x 1.0))
301.0ms	(cbrt (fma x x 1.0))
294.0ms	(cbrt (fma x x 1.0))
284.0ms	(cbrt (fma x x 1.0))

simplify2.6s

Counts

66 → 66

Iterations

Iter	Nodes
done	5000
3	3849
2	682
1	200
0	90

prune524.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ 1 x) (/ (/ 1.0 x) (* x x)))
0.2b	(/ (/ 1.0 x) (* x x))
0.3b	(/ 1.0 (pow x 5))
17.2b	(+ (- (/ 1 x) (/ (/ 1.0 x) (* x x))) (/ 1.0 (pow x 5)))

rewrite460.0ms

Algorithm

rewrite-expression-head

Rules

969×	`times-frac`
536×	`add-sqr-sqrt`
507×	`*-un-lft-identity`
488×	`add-cube-cbrt`
442×	`prod-diff`
223×	`associate-+l+`
94×	`div-inv`
21×	`add-exp-log`
18×	`add-cbrt-cube` `difference-of-squares`
16×	`associate-/l*`
14×	`fma-def`
13×	`fma-neg`
12×	`unpow-prod-down`
11×	`add-log-exp`
9×	`div-exp`
8×	`associate-/r*`
7×	`cbrt-undiv`
6×	`distribute-lft-out--`
4×	`expm1-log1p-u` `pow1` `log1p-expm1-u` `sqr-pow`
3×	`frac-add` `distribute-lft-out`
2×	`clear-num` `sum-log` `sub-neg` `frac-2neg` `flip3--` `diff-log` `prod-exp` `frac-sub` `cbrt-unprod` `flip--`
1×	`pow-to-exp` `+-commutative` `flip3-+` `pow-exp` `associate-+l-` `flip-+` `associate-/l/`

Counts

4 → 613

Calls

4 calls:

56.0ms	(- (/ 1 x) (/ (/ 1.0 x) (* x x)))
18.0ms	(/ (/ 1.0 x) (* x x))
9.0ms	(/ 1.0 (pow x 5))
306.0ms	(+ (- (/ 1 x) (/ (/ 1.0 x) (* x x))) (/ 1.0 (pow x 5)))

series218.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(- (/ 1 x) (/ (/ 1.0 x) (* x x)))
39.0ms	(/ (/ 1.0 x) (* x x))
56.0ms	(/ 1.0 (pow x 5))
49.0ms	(+ (- (/ 1 x) (/ (/ 1.0 x) (* x x))) (/ 1.0 (pow x 5)))

simplify1.2s

Counts

625 → 625

Iterations

Iter	Nodes
done	5001
1	1340
0	563

prune3.3s

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes52.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 15.1b

bsearch72.0ms

Steps

Iters	Range		Point
8	53640.016154094046	3378812226.2511864	217598.07123922362
10	-4.9624091936815476e+157	-4.725387774062328e+144	-1.3342569343764892e+154

simplify16.0ms

Iterations

Iter	Nodes
done	28
1	28
0	22

end0.0ms

sample339.0ms

Algorithm

intervals

Results

232.0ms

8000×

body

valid