Details

sample70.0ms

Algorithm

intervals

Results

25.0ms	55×	body	1280	valid
14.0ms	140×	body	80	valid
12.0ms	32×	body	640	valid
4.0ms	16×	body	320	valid
3.0ms	13×	body	160	valid

simplify173.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	231
14	231
13	223
12	191
11	154
10	116
9	79
8	55
7	42
6	32
5	26
4	23
3	22
2	18
1	15
0	7

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.4b

localize20.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ x (+ x 1))
0.0b	(/ (+ x 1) (- x 1))
3.7b	(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))

rewrite159.0ms

Algorithm

rewrite-expression-head

Rules

1284×	`*-un-lft-identity`
984×	`times-frac`
841×	`add-sqr-sqrt`
612×	`prod-diff`
521×	`add-cube-cbrt`
251×	`distribute-lft-out`
158×	`difference-of-squares`
110×	`associate-/r/`
90×	`distribute-lft-out--`
77×	`difference-of-sqr-1`
55×	`div-inv`
37×	`flip3-+` `flip-+`
20×	`flip3--` `flip--`
18×	`fma-neg`
11×	`associate-/r*`
7×	`add-cbrt-cube` `add-exp-log` `associate-/l*`
5×	`add-log-exp`
3×	`expm1-log1p-u` `pow1` `insert-posit16` `log1p-expm1-u`
2×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `associate-/l/`
1×	`sub-neg` `diff-log` `frac-sub`

Counts

3 → 753

Calls

3 calls:

9.0ms	(/ x (+ x 1))
33.0ms	(/ (+ x 1) (- x 1))
83.0ms	(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))

series150.0ms

Counts

3 → 9

Calls

3 calls:

35.0ms	(/ x (+ x 1))
33.0ms	(/ (+ x 1) (- x 1))
82.0ms	(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))

simplify2.1s

Counts

762 → 762

Iterations

Iter	Nodes
done	5002
2	3297
1	1369
0	584

prune2.5s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ x (+ x 1))
0.0b	(/ (+ x 1) (- x 1))
3.7b	(- (/ x (+ x 1)) (* 1 (/ (+ x 1) (- x 1))))

rewrite104.0ms

Algorithm

rewrite-expression-head

Rules

93×	`*-un-lft-identity`
64×	`times-frac`
61×	`add-sqr-sqrt`
41×	`add-cube-cbrt`
18×	`fma-neg` `prod-diff` `distribute-lft-out`
11×	`associate-/r*`
10×	`difference-of-squares`
8×	`associate-/r/`
7×	`add-cbrt-cube` `add-exp-log` `associate-/l*`
6×	`distribute-lft-out--`
5×	`difference-of-sqr-1` `add-log-exp`
4×	`flip3-+` `flip-+` `div-inv`
3×	`expm1-log1p-u` `pow1` `insert-posit16` `log1p-expm1-u`
2×	`cbrt-undiv` `clear-num` `frac-2neg` `flip3--` `div-exp` `flip--` `associate-/l/`
1×	`sub-neg` `diff-log` `associate-*r/` `frac-sub`

Counts

3 → 147

Calls

3 calls:

20.0ms	(/ x (+ x 1))
21.0ms	(/ (+ x 1) (- x 1))
57.0ms	(- (/ x (+ x 1)) (* 1 (/ (+ x 1) (- x 1))))

series226.0ms

Counts

3 → 9

Calls

3 calls:

26.0ms	(/ x (+ x 1))
47.0ms	(/ (+ x 1) (- x 1))
153.0ms	(- (/ x (+ x 1)) (* 1 (/ (+ x 1) (- x 1))))

simplify1.8s

Counts

156 → 156

Iterations

Iter	Nodes
done	5002
2	1682
1	499
0	203

prune593.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize39.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (- (/ x (+ x 1)) (/ (+ x 1) (- x 1))))
0.0b	(/ (+ x 1) (- x 1))
3.7b	(log (exp (- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))))
3.7b	(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))

rewrite604.0ms

Algorithm

rewrite-expression-head

Rules

3683×	`*-un-lft-identity`
2836×	`times-frac`
2412×	`add-sqr-sqrt`
1836×	`prod-diff`
1492×	`add-cube-cbrt`
1228×	`exp-sum`
719×	`distribute-lft-out`
617×	`log-prod`
454×	`difference-of-squares`
316×	`associate-/r/`
260×	`distribute-lft-out--`
221×	`difference-of-sqr-1`
158×	`div-inv`
104×	`flip3-+` `flip-+`
56×	`flip3--` `flip--`
32×	`exp-prod`
18×	`fma-neg`
17×	`log-pow`
9×	`add-log-exp`
7×	`associate-/r*`
6×	`add-cbrt-cube` `add-exp-log`
5×	`pow1`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `associate-/l*`
3×	`sub-neg`
2×	`exp-diff` `diff-log` `rem-exp-log` `associate-/l/`
1×	`cbrt-undiv` `log-div` `clear-num` `frac-2neg` `div-exp` `rem-log-exp` `frac-sub`

Counts

4 → 2006

Calls

4 calls:

179.0ms	(exp (- (/ x (+ x 1)) (/ (+ x 1) (- x 1))))
27.0ms	(/ (+ x 1) (- x 1))
187.0ms	(log (exp (- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))))
99.0ms	(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))

series444.0ms

Counts

4 → 12

Calls

4 calls:

139.0ms	(exp (- (/ x (+ x 1)) (/ (+ x 1) (- x 1))))
42.0ms	(/ (+ x 1) (- x 1))
123.0ms	(log (exp (- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))))
139.0ms	(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))

simplify3.6s

Counts

2018 → 2018

Iterations

Iter	Nodes
done	5000
2	4328
1	2107
0	1293

prune6.2s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize29.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (fma x (/ 1 (+ x 1)) (- (/ (+ x 1) (- x 1)))))
0.0b	(/ (+ x 1) (- x 1))
8.1b	(log (exp (fma x (/ 1 (+ x 1)) (- (/ (+ x 1) (- x 1))))))
27.7b	(fma x (/ 1 (+ x 1)) (- (/ (+ x 1) (- x 1))))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

51×	`*-un-lft-identity`
40×	`add-sqr-sqrt`
28×	`times-frac`
20×	`add-cube-cbrt`
10×	`difference-of-squares`
8×	`distribute-lft-out`
7×	`associate-/r*`
6×	`exp-prod` `add-cbrt-cube` `add-exp-log`
5×	`pow1` `difference-of-sqr-1` `distribute-lft-out--` `add-log-exp`
4×	`expm1-log1p-u` `log-prod` `log-pow` `insert-posit16` `log1p-expm1-u` `associate-/l*`
3×	`fma-udef`
2×	`exp-sum` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `flip3-+` `flip3--` `div-exp` `rem-log-exp` `flip-+` `div-inv` `flip--` `rem-exp-log`

Counts

4 → 103

Calls

4 calls:

2.0ms	(exp (fma x (/ 1 (+ x 1)) (- (/ (+ x 1) (- x 1)))))
19.0ms	(/ (+ x 1) (- x 1))
3.0ms	(log (exp (fma x (/ 1 (+ x 1)) (- (/ (+ x 1) (- x 1))))))
0.0ms	(fma x (/ 1 (+ x 1)) (- (/ (+ x 1) (- x 1))))

series492.0ms

Counts

4 → 12

Calls

4 calls:

175.0ms	(exp (fma x (/ 1 (+ x 1)) (- (/ (+ x 1) (- x 1)))))
52.0ms	(/ (+ x 1) (- x 1))
149.0ms	(log (exp (fma x (/ 1 (+ x 1)) (- (/ (+ x 1) (- x 1))))))
115.0ms	(fma x (/ 1 (+ x 1)) (- (/ (+ x 1) (- x 1))))

simplify3.9s

Counts

115 → 115

Iterations

Iter	Nodes
done	5008
3	3400
2	973
1	362
0	168

prune504.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

regimes60.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 29.6b

bsearch149.0ms

Steps

Iters	Range		Point
9	2842.495256040047	513310621636.50653	11913.338256318099
8	-29345360.474346694	-7508.589471958369	-12354.188123908416

simplify10.0ms

Iterations

Iter	Nodes
done	35
2	35
1	30
0	21

end0.0ms

sample2.2s

Algorithm

intervals

Results

926.0ms	1762×	body	1280	valid
555.0ms	1269×	body	640	valid
376.0ms	4063×	body	80	valid
150.0ms	593×	body	320	valid
52.0ms	313×	body	160	valid