Details

sample41.0ms

Algorithm

intervals

Results

9.0ms	61×	body	1280	valid
4.0ms	131×	body	80	valid
4.0ms	37×	body	640	valid
1.0ms	14×	body	320	valid
1.0ms	13×	body	160	valid

simplify359.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	7	202
1	12	202
2	16	202
3	19	202
4	21	202
5	27	202
6	39	202
7	58	202
8	75	202
9	96	202
10	222	202
11	329	202
12	340	202
13	346	202
14	350	202
done	350	202

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.9b

localize17.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (+ x 1.0) (- x 1.0))
2.8b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite193.0ms

Algorithm

rewrite-expression-head

Rules

963×	`*-un-lft-identity`
724×	`times-frac`
575×	`add-sqr-sqrt`
468×	`prod-diff`
409×	`add-cube-cbrt`
185×	`distribute-lft-out`
92×	`associate-/r/`
90×	`distribute-lft-out--`
81×	`difference-of-squares`
46×	`div-inv`
28×	`flip3-+` `flip-+`
20×	`flip3--` `flip--`
18×	`fma-neg`
5×	`associate-/r*`
4×	`add-cbrt-cube` `add-exp-log` `associate-/l*` `add-log-exp`
2×	`expm1-log1p-u` `pow1` `log1p-expm1-u` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `diff-log` `div-exp` `frac-sub`

Counts

2 → 561

Calls

2 calls:

20.0ms	(/ (+ x 1.0) (- x 1.0))
115.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series226.0ms

Counts

2 → 6

Calls

2 calls:

51.0ms	(/ (+ x 1.0) (- x 1.0))
175.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify5.2s

Counts

567 → 567

Iterations

Useful iterations: done (5.0s)

Iter	Nodes	Cost
0	502	476430
1	1192	420737
2	2984	382225
done	5003	350012

prune2.2s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 1 (/ (- x 1.0) (+ x 1.0)))
0.0b	(/ (- x 1.0) (+ x 1.0))
2.8b	(- (/ x (+ x 1.0)) (/ 1 (/ (- x 1.0) (+ x 1.0))))

rewrite558.0ms

Algorithm

rewrite-expression-head

Rules

3691×	`times-frac`
3365×	`*-un-lft-identity`
2286×	`add-sqr-sqrt`
1779×	`add-cube-cbrt`
1494×	`prod-diff`
549×	`distribute-lft-out`
305×	`associate-/r/`
247×	`difference-of-squares`
241×	`distribute-lft-out--`
163×	`div-inv`
143×	`flip3-+` `flip-+`
30×	`associate-/r*`
18×	`fma-neg`
16×	`add-exp-log`
10×	`add-cbrt-cube`
8×	`div-exp` `associate-/l*`
5×	`add-log-exp`
4×	`pow1` `cbrt-undiv`
3×	`expm1-log1p-u` `log1p-expm1-u`
2×	`rec-exp` `clear-num` `frac-2neg` `flip3--` `1-exp` `flip--` `associate-/l/`
1×	`sub-neg` `diff-log` `div-sub` `frac-sub` `pow-flip` `inv-pow`

Counts

3 → 1719

Calls

3 calls:

36.0ms	(/ 1 (/ (- x 1.0) (+ x 1.0)))
27.0ms	(/ (- x 1.0) (+ x 1.0))
223.0ms	(- (/ x (+ x 1.0)) (/ 1 (/ (- x 1.0) (+ x 1.0))))

series289.0ms

Counts

3 → 9

Calls

3 calls:

69.0ms	(/ 1 (/ (- x 1.0) (+ x 1.0)))
63.0ms	(/ (- x 1.0) (+ x 1.0))
157.0ms	(- (/ x (+ x 1.0)) (/ 1 (/ (- x 1.0) (+ x 1.0))))

simplify4.6s

Counts

1728 → 1728

Iterations

Useful iterations: done (4.0s)

Iter	Nodes	Cost
0	1399	1879623
1	3332	1457054
done	5001	1336118

prune7.0s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize47.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (/ x (+ x 1.0)))
0.3b	(cbrt (/ x (+ x 1.0)))
7.6b	(fma (* (cbrt (/ x (+ x 1.0))) (cbrt (/ x (+ x 1.0)))) (cbrt (/ x (+ x 1.0))) (- (* (+ x 1.0) (/ 1 (- x 1.0)))))
32.5b	(fma (- (+ x 1.0)) (/ 1 (- x 1.0)) (* (+ x 1.0) (/ 1 (- x 1.0))))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

36×	`cbrt-prod`
32×	`*-un-lft-identity`
24×	`times-frac`
20×	`add-sqr-sqrt` `add-cube-cbrt`
6×	`distribute-lft-out`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `associate-/r/` `log1p-expm1-u` `add-log-exp`
2×	`cbrt-div` `flip3-+` `pow1/3` `flip-+` `fma-udef` `div-inv`

Counts

4 → 78

Calls

4 calls:

8.0ms	(cbrt (/ x (+ x 1.0)))
9.0ms	(cbrt (/ x (+ x 1.0)))
0.0ms	(fma (* (cbrt (/ x (+ x 1.0))) (cbrt (/ x (+ x 1.0)))) (cbrt (/ x (+ x 1.0))) (- (* (+ x 1.0) (/ 1 (- x 1.0)))))
1.0ms	(fma (- (+ x 1.0)) (/ 1 (- x 1.0)) (* (+ x 1.0) (/ 1 (- x 1.0))))

series1.5s

Counts

4 → 12

Calls

4 calls:

202.0ms	(cbrt (/ x (+ x 1.0)))
194.0ms	(cbrt (/ x (+ x 1.0)))
777.0ms	(fma (* (cbrt (/ x (+ x 1.0))) (cbrt (/ x (+ x 1.0)))) (cbrt (/ x (+ x 1.0))) (- (* (+ x 1.0) (/ 1 (- x 1.0)))))
311.0ms	(fma (- (+ x 1.0)) (/ 1 (- x 1.0)) (* (+ x 1.0) (/ 1 (- x 1.0))))

simplify1.9s

Counts

90 → 90

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	185	37114
1	417	32162
2	1275	30596
done	5003	28652

prune704.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize44.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
0.6b	(cbrt x)
29.4b	(fma (/ (* (cbrt x) (cbrt x)) 1) (/ (cbrt x) (+ x 1.0)) (- (/ 1 (/ (- x 1.0) (+ 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)) 1) (/ (cbrt x) (+ x 1.0)) (- (/ 1 (/ (- x 1.0) (+ x 1.0)))))

series1.1s

Counts

4 → 12

Calls

4 calls:

352.0ms	(cbrt x)
299.0ms	(cbrt x)
289.0ms	(cbrt x)
199.0ms	(fma (/ (* (cbrt x) (cbrt x)) 1) (/ (cbrt x) (+ x 1.0)) (- (/ 1 (/ (- x 1.0) (+ x 1.0)))))

simplify2.1s

Counts

61 → 61

Iterations

Useful iterations: 3 (467.0ms)

Iter	Nodes	Cost
0	62	15619
1	134	13023
2	368	12794
3	1133	10530
done	5001	10530

prune306.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

regimes64.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 30.0b

bsearch144.0ms

Steps

Iters	Range		Point
9	0.1909160003853501	166131308.15705827	8600.582868753156
10	-27652538170.40468	-0.18371106458419734	-8089.074957308727

simplify9.0ms

Iterations

Useful iterations: 1 (7.0ms)

Iter	Nodes	Cost
0	27	1016
1	37	937
done	37	937

end0.0ms

sample1.6s

Algorithm

intervals

Results

678.0ms	1221×	body	640	valid
463.0ms	1755×	body	1280	valid
182.0ms	4080×	body	80	valid
130.0ms	646×	body	320	valid
25.0ms	298×	body	160	valid