Details

sample45.0ms

Algorithm

intervals

Results

11.0ms	64×	body	640	valid
8.0ms	131×	body	80	valid
6.0ms	44×	body	320	valid
1.0ms	17×	body	160	valid

simplify8.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	12
2	12
1	9
0	6

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.3b

localize17.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ 1.0 (+ x 1.0))
3.6b	(- (/ 1.0 (+ x 1.0)) (/ 1.0 x))

rewrite199.0ms

Algorithm

rewrite-expression-head

Rules

362×	`*-un-lft-identity`
358×	`times-frac`
265×	`add-sqr-sqrt`
253×	`add-cube-cbrt`
234×	`prod-diff`
49×	`distribute-lft-out`
35×	`div-inv`
30×	`associate-/r/`
18×	`fma-neg`
15×	`flip3-+` `flip-+`
8×	`distribute-lft-out--`
4×	`associate-/r*` `add-cbrt-cube` `add-exp-log` `add-log-exp` `difference-of-squares`
3×	`associate-/l*`
2×	`expm1-log1p-u` `pow1` `log1p-expm1-u`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `flip3--` `diff-log` `div-exp` `frac-sub` `flip--`

Counts

2 → 314

Calls

2 calls:

20.0ms	(/ 1.0 (+ x 1.0))
138.0ms	(- (/ 1.0 (+ x 1.0)) (/ 1.0 x))

series173.0ms

Counts

2 → 6

Calls

2 calls:

46.0ms	(/ 1.0 (+ x 1.0))
127.0ms	(- (/ 1.0 (+ x 1.0)) (/ 1.0 x))

simplify2.1s

Counts

320 → 320

Iterations

Iter	Nodes
done	5000
2	3264
1	919
0	387

prune1.2s

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.4b

localize25.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (/ 1.0 (+ x 1.0)))
0.3b	(cbrt (/ 1.0 (+ x 1.0)))
0.3b	(cbrt (/ 1.0 (+ x 1.0)))
19.7b	(- (* (* (cbrt (/ 1.0 (+ x 1.0))) (cbrt (/ 1.0 (+ x 1.0)))) (cbrt (/ 1.0 (+ x 1.0)))) (/ 1.0 x))

rewrite108.0ms

Algorithm

rewrite-expression-head

Rules

54×	`cbrt-prod`
53×	`*-un-lft-identity`
45×	`times-frac`
35×	`add-sqr-sqrt` `add-cube-cbrt`
15×	`cbrt-div`
13×	`prod-diff`
9×	`distribute-lft-out`
7×	`frac-sub`
6×	`associate-/r/` `add-log-exp`
5×	`frac-times` `associate-*l/`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u` `div-inv`
3×	`flip3-+` `pow1/3` `associate-*r/` `flip-+`
1×	`sub-neg` `flip3--` `fma-neg` `diff-log` `flip--`

Counts

4 → 122

Calls

4 calls:

8.0ms	(cbrt (/ 1.0 (+ x 1.0)))
8.0ms	(cbrt (/ 1.0 (+ x 1.0)))
8.0ms	(cbrt (/ 1.0 (+ x 1.0)))
76.0ms	(- (* (* (cbrt (/ 1.0 (+ x 1.0))) (cbrt (/ 1.0 (+ x 1.0)))) (cbrt (/ 1.0 (+ x 1.0)))) (/ 1.0 x))

series762.0ms

Counts

4 → 12

Calls

4 calls:

233.0ms	(cbrt (/ 1.0 (+ x 1.0)))
205.0ms	(cbrt (/ 1.0 (+ x 1.0)))
191.0ms	(cbrt (/ 1.0 (+ x 1.0)))
133.0ms	(- (* (* (cbrt (/ 1.0 (+ x 1.0))) (cbrt (/ 1.0 (+ x 1.0)))) (cbrt (/ 1.0 (+ x 1.0)))) (/ 1.0 x))

simplify2.3s

Counts

134 → 134

Iterations

Iter	Nodes
done	5000
2	3250
1	724
0	279

prune770.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.4b

localize38.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ 1.0 (* x x))
0.5b	(/ 1.0 (* x x))
0.5b	(/ 1 (* x x))
10.5b	(- (/ (/ 1.0 (* x x)) x) (fma (/ 1.0 (* x x)) (/ 1 (* x x)) (/ 1.0 (* x x))))

rewrite122.0ms

Algorithm

rewrite-expression-head

Rules

132×	`times-frac`
99×	`add-sqr-sqrt`
93×	`*-un-lft-identity`
91×	`add-cube-cbrt`
75×	`prod-diff`
25×	`fma-neg` `add-exp-log`
19×	`add-cbrt-cube` `div-inv`
12×	`pow1`
9×	`associate-/l*`
8×	`div-exp`
6×	`cbrt-undiv` `pow-flip` `add-log-exp`
5×	`prod-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`clear-num` `associate-/r*` `frac-2neg` `cbrt-unprod` `difference-of-squares`
2×	`rec-exp` `1-exp`
1×	`pow2` `sub-neg` `pow-plus` `flip3--` `diff-log` `pow-prod-down` `pow-sqr` `pow-prod-up` `fma-udef` `flip--` `associate--r+` `distribute-lft-out--` `inv-pow`

Counts

4 → 199

Calls

4 calls:

8.0ms	(/ 1.0 (* x x))
6.0ms	(/ 1.0 (* x x))
11.0ms	(/ 1 (* x x))
88.0ms	(- (/ (/ 1.0 (* x x)) x) (fma (/ 1.0 (* x x)) (/ 1 (* x x)) (/ 1.0 (* x x))))

series172.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(/ 1.0 (* x x))
36.0ms	(/ 1.0 (* x x))
32.0ms	(/ 1 (* x x))
57.0ms	(- (/ (/ 1.0 (* x x)) x) (fma (/ 1.0 (* x x)) (/ 1 (* x x)) (/ 1.0 (* x x))))

simplify1.9s

Counts

211 → 211

Iterations

Iter	Nodes
done	5001
2	3220
1	620
0	261

prune1.2s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ 1.0 (* x x))
0.5b	(/ 1.0 (* x x))
0.5b	(/ 1 (* x x))
10.5b	(- (/ (/ 1.0 (* x x)) x) (fma (/ 1.0 (* x x)) (/ 1 (* x x)) (/ (/ 1.0 x) x)))

rewrite145.0ms

Algorithm

rewrite-expression-head

Rules

132×	`times-frac`
99×	`add-sqr-sqrt`
93×	`*-un-lft-identity`
91×	`add-cube-cbrt`
75×	`prod-diff`
25×	`fma-neg` `add-exp-log`
19×	`add-cbrt-cube` `div-inv`
12×	`pow1`
9×	`associate-/l*`
8×	`div-exp`
6×	`cbrt-undiv` `pow-flip` `add-log-exp`
5×	`prod-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`clear-num` `associate-/r*` `frac-2neg` `cbrt-unprod` `difference-of-squares`
2×	`rec-exp` `1-exp`
1×	`pow2` `sub-neg` `pow-plus` `flip3--` `diff-log` `pow-prod-down` `pow-sqr` `pow-prod-up` `fma-udef` `flip--` `associate--r+` `distribute-lft-out--` `inv-pow`

Counts

4 → 199

Calls

4 calls:

12.0ms	(/ 1.0 (* x x))
12.0ms	(/ 1.0 (* x x))
16.0ms	(/ 1 (* x x))
89.0ms	(- (/ (/ 1.0 (* x x)) x) (fma (/ 1.0 (* x x)) (/ 1 (* x x)) (/ (/ 1.0 x) x)))

series203.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(/ 1.0 (* x x))
48.0ms	(/ 1.0 (* x x))
32.0ms	(/ 1 (* x x))
76.0ms	(- (/ (/ 1.0 (* x x)) x) (fma (/ 1.0 (* x x)) (/ 1 (* x x)) (/ (/ 1.0 x) x)))

simplify1.8s

Counts

211 → 211

Iterations

Iter	Nodes
done	5002
2	3214
1	620
0	261

prune1.2s

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.0b

regimes58.0ms

Accuracy

99.8% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 26.1b

bsearch120.0ms

Steps

Iters	Range		Point
9	0.030359728269424062	9645967.64350026	8524.530700947043
11	-14746478108.679678	-8.433739504313006e-14	-8014.0951421874715

simplify5.0ms

Iterations

Iter	Nodes
done	30
1	30
0	23

end0.0ms

sample1.3s

Algorithm

intervals

Results

573.0ms	1293×	body	320	valid
296.0ms	1861×	body	640	valid
229.0ms	4203×	body	80	valid
45.0ms	644×	body	160	valid