Details

sample27.0ms

Algorithm

intervals

Results

7.0ms	54×	body	1280	valid
5.0ms	44×	body	640	valid
4.0ms	132×	body	80	valid
2.0ms	19×	body	320	valid
0.0ms	7×	body	160	valid

simplify2.8s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
12	4085
11	1745
10	535
9	183
8	79
7	58
6	39
5	27
4	21
3	19
2	16
1	12
0	7

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.0b

localize14.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ x (+ 1.0 x))
0.0b	(/ (+ 1.0 x) (- x 1.0))
2.7b	(- (/ x (+ 1.0 x)) (/ (+ 1.0 x) (- x 1.0)))

rewrite263.0ms

Algorithm

rewrite-expression-head

Rules

981×	`*-un-lft-identity`
736×	`times-frac`
585×	`add-sqr-sqrt`
468×	`prod-diff`
419×	`add-cube-cbrt`
189×	`distribute-lft-out`
94×	`associate-/r/`
90×	`distribute-lft-out--`
81×	`difference-of-squares`
47×	`div-inv`
29×	`flip3-+` `flip-+`
20×	`flip3--` `flip--`
18×	`fma-neg`
9×	`associate-/r*`
7×	`add-cbrt-cube` `add-exp-log` `associate-/l*`
5×	`add-log-exp`
3×	`expm1-log1p-u` `pow1` `log1p-expm1-u`
2×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `associate-/l/`
1×	`sub-neg` `diff-log` `frac-sub`

Counts

3 → 596

Calls

3 calls:

18.0ms	(/ x (+ 1.0 x))
23.0ms	(/ (+ 1.0 x) (- x 1.0))
138.0ms	(- (/ x (+ 1.0 x)) (/ (+ 1.0 x) (- x 1.0)))

series309.0ms

Counts

3 → 9

Calls

3 calls:

49.0ms	(/ x (+ 1.0 x))
52.0ms	(/ (+ 1.0 x) (- x 1.0))
208.0ms	(- (/ x (+ 1.0 x)) (/ (+ 1.0 x) (- x 1.0)))

simplify2.3s

Counts

605 → 605

Iterations

Iter	Nodes
done	5000
2	4626
1	1268
0	528

prune1.7s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize46.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
0.6b	(cbrt x)
2.7b	(fma (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ 1.0 x)) (cbrt (+ 1.0 x)))) (/ (cbrt x) (cbrt (+ 1.0 x))) (/ (- (+ 1.0 x)) (- x 1.0)))

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`
1×	`fma-udef`

Counts

4 → 49

Calls

4 calls:

1.0ms	(cbrt x)
1.0ms	(cbrt x)
1.0ms	(cbrt x)
0.0ms	(fma (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ 1.0 x)) (cbrt (+ 1.0 x)))) (/ (cbrt x) (cbrt (+ 1.0 x))) (/ (- (+ 1.0 x)) (- x 1.0)))

series1.5s

Counts

4 → 12

Calls

4 calls:

208.0ms	(cbrt x)
270.0ms	(cbrt x)
261.0ms	(cbrt x)
724.0ms	(fma (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ 1.0 x)) (cbrt (+ 1.0 x)))) (/ (cbrt x) (cbrt (+ 1.0 x))) (/ (- (+ 1.0 x)) (- x 1.0)))

simplify671.0ms

Counts

61 → 61

Iterations

Iter	Nodes
done	5001
2	1031
1	270
0	101

prune459.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize25.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- (+ 1.0 x)) (- x 1.0))
0.0b	(/ 1 (+ 1.0 x))
29.6b	(fma x (/ 1 (+ 1.0 x)) (/ (- (+ 1.0 x)) (- x 1.0)))

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

101×	`*-un-lft-identity`
72×	`times-frac`
69×	`add-sqr-sqrt`
43×	`add-cube-cbrt`
24×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
16×	`distribute-lft-out`
15×	`associate-/l*`
13×	`distribute-lft-out--` `difference-of-squares`
9×	`associate-/r*` `add-exp-log`
7×	`add-cbrt-cube`
6×	`neg-mul-1`
4×	`pow1` `associate-/r/`
3×	`expm1-log1p-u` `div-exp` `log1p-expm1-u` `add-log-exp`
2×	`cbrt-undiv` `clear-num` `frac-2neg` `flip3-+` `flip-+` `div-inv` `distribute-neg-frac` `associate-/l/`
1×	`neg-sub0` `rec-exp` `flip3--` `1-exp` `div-sub` `distribute-frac-neg` `fma-udef` `pow-flip` `flip--` `inv-pow`

Counts

3 → 146

Calls

3 calls:

43.0ms	(/ (- (+ 1.0 x)) (- x 1.0))
19.0ms	(/ 1 (+ 1.0 x))
1.0ms	(fma x (/ 1 (+ 1.0 x)) (/ (- (+ 1.0 x)) (- x 1.0)))

series276.0ms

Counts

3 → 9

Calls

3 calls:

52.0ms	(/ (- (+ 1.0 x)) (- x 1.0))
29.0ms	(/ 1 (+ 1.0 x))
195.0ms	(fma x (/ 1 (+ 1.0 x)) (/ (- (+ 1.0 x)) (- x 1.0)))

simplify1.5s

Counts

155 → 155

Iterations

Iter	Nodes
done	5000
2	2202
1	517
0	222

prune462.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize26.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- (+ 1.0 x)) (- x 1.0))
15.0b	(/ x (- (* 1.0 1.0) (* x x)))
29.5b	(fma (/ x (- (* 1.0 1.0) (* x x))) (- 1.0 x) (/ (- (+ 1.0 x)) (- x 1.0)))

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

93×	`*-un-lft-identity`
72×	`times-frac`
69×	`add-sqr-sqrt`
43×	`add-cube-cbrt`
24×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
17×	`difference-of-squares`
15×	`associate-/l*`
13×	`distribute-lft-out--`
12×	`distribute-lft-out`
9×	`associate-/r*`
7×	`add-cbrt-cube` `add-exp-log`
6×	`neg-mul-1`
4×	`associate-/r/`
3×	`expm1-log1p-u` `pow1` `log1p-expm1-u` `add-log-exp`
2×	`cbrt-undiv` `clear-num` `frac-2neg` `flip3--` `div-exp` `div-inv` `flip--` `distribute-neg-frac` `associate-/l/`
1×	`neg-sub0` `flip3-+` `div-sub` `distribute-frac-neg` `flip-+` `fma-udef`

Counts

3 → 142

Calls

3 calls:

49.0ms	(/ (- (+ 1.0 x)) (- x 1.0))
21.0ms	(/ x (- (* 1.0 1.0) (* x x)))
1.0ms	(fma (/ x (- (* 1.0 1.0) (* x x))) (- 1.0 x) (/ (- (+ 1.0 x)) (- x 1.0)))

series335.0ms

Counts

3 → 9

Calls

3 calls:

79.0ms	(/ (- (+ 1.0 x)) (- x 1.0))
86.0ms	(/ x (- (* 1.0 1.0) (* x x)))
169.0ms	(fma (/ x (- (* 1.0 1.0) (* x x))) (- 1.0 x) (/ (- (+ 1.0 x)) (- x 1.0)))

simplify1.6s

Counts

151 → 151

Iterations

Iter	Nodes
done	5000
2	2659
1	602
0	247

prune716.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.0b

regimes78.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 28.8b

bsearch112.0ms

Steps

Iters	Range		Point
9	2205.5689030668646	4825064884.677679	10454.066790945864
10	-185496355225.45163	-22.8286883066892	-13946.27375560417

simplify10.0ms

Iterations

Iter	Nodes
done	40
2	40
1	39
0	25

end0.0ms

sample1.7s

Algorithm

intervals

Results

798.0ms	1659×	body	1280	valid
341.0ms	1242×	body	640	valid
221.0ms	4183×	body	80	valid
81.0ms	629×	body	320	valid
23.0ms	287×	body	160	valid