Details

sample26.0ms

Algorithm

intervals

Results

9.0ms	55×	body	1280	valid
5.0ms	140×	body	80	valid
4.0ms	32×	body	640	valid
1.0ms	16×	body	320	valid
1.0ms	13×	body	160	valid

simplify125.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	168
15	168
14	165
13	136
12	114
11	99
10	89
9	69
8	53
7	42
6	32
5	26
4	23
3	22
2	19
1	15
0	7

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.4b

localize13.0ms

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)))

rewrite119.0ms

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))
19.0ms	(/ (+ x 1) (- x 1))
63.0ms	(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))

series159.0ms

Counts

3 → 9

Calls

3 calls:

33.0ms	(/ x (+ x 1))
38.0ms	(/ (+ x 1) (- x 1))
88.0ms	(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))

simplify2.3s

Counts

762 → 762

Iterations

Iter	Nodes
done	5002
2	3248
1	1369
0	584

prune2.3s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize26.0ms

Local error

Found 3 expressions with local error:

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

rewrite303.0ms

Algorithm

rewrite-expression-head

Rules

5198×	`times-frac`
4824×	`*-un-lft-identity`
3607×	`add-sqr-sqrt`
2359×	`add-cube-cbrt`
2124×	`prod-diff`
765×	`distribute-lft-out`
618×	`difference-of-squares`
312×	`distribute-lft-out--`
305×	`difference-of-sqr-1`
278×	`associate-/r/`
273×	`div-inv`
120×	`flip3-+` `flip-+`
20×	`flip3--` `flip--`
19×	`associate-/l*`
18×	`fma-neg`
12×	`add-exp-log`
11×	`associate-/r*`
10×	`add-cbrt-cube`
6×	`div-exp`
5×	`add-log-exp`
4×	`cbrt-undiv`
3×	`expm1-log1p-u` `pow1` `insert-posit16` `log1p-expm1-u`
2×	`clear-num` `frac-2neg`
1×	`sub-neg` `diff-log` `1-exp` `frac-sub` `associate-/l/`

Counts

3 → 2363

Calls

3 calls:

9.0ms	(/ x (+ x 1))
23.0ms	(/ (/ (+ x 1) 1) (- x 1))
101.0ms	(- (/ x (+ x 1)) (/ (/ (+ x 1) 1) (- x 1)))

series517.0ms

Counts

3 → 9

Calls

3 calls:

33.0ms	(/ x (+ x 1))
376.0ms	(/ (/ (+ x 1) 1) (- x 1))
108.0ms	(- (/ x (+ x 1)) (/ (/ (+ x 1) 1) (- x 1)))

simplify3.2s

Counts

2372 → 2372

Iterations

Iter	Nodes
done	5004
1	3854
0	1671

prune6.9s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (+ x 1) (- x 1))
27.7b	(fma x (/ 1 (+ x 1)) (- (/ (+ x 1) (- x 1))))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 69

Calls

2 calls:

31.0ms	(/ (+ x 1) (- x 1))
0.0ms	(fma x (/ 1 (+ x 1)) (- (/ (+ x 1) (- x 1))))

series130.0ms

Counts

2 → 6

Calls

2 calls:

31.0ms	(/ (+ x 1) (- x 1))
99.0ms	(fma x (/ 1 (+ x 1)) (- (/ (+ x 1) (- x 1))))

simplify1.9s

Counts

75 → 75

Iterations

Iter	Nodes
done	5001
3	2512
2	743
1	278
0	122

prune241.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

localize57.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (+ x 1))
0.3b	(* (cbrt (+ x 1)) (cbrt (+ x 1)))
27.7b	(fma (/ 1 (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (/ x (cbrt (+ x 1))) (- (* (/ 1 (- x 1)) (+ x 1))))
30.4b	(fma (- (/ 1 (- x 1))) (+ x 1) (* (/ 1 (- x 1)) (+ x 1)))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

29×	`*-un-lft-identity`
28×	`cbrt-prod`
21×	`add-sqr-sqrt`
14×	`cbrt-div`
13×	`add-cube-cbrt`
11×	`pow1`
9×	`swap-sqr`
7×	`flip3-+` `pow1/3` `associate-r` `associate-l` `flip-+` `distribute-lft-out`
6×	`add-exp-log`
4×	`expm1-log1p-u` `frac-times` `add-cbrt-cube` `insert-posit16` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `associate-l/` `associate-r/` `pow-sqr` `pow-prod-up` `fma-udef`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 95

Calls

4 calls:

4.0ms	(cbrt (+ x 1))
32.0ms	(* (cbrt (+ x 1)) (cbrt (+ x 1)))
0.0ms	(fma (/ 1 (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (/ x (cbrt (+ x 1))) (- (* (/ 1 (- x 1)) (+ x 1))))
0.0ms	(fma (- (/ 1 (- x 1))) (+ x 1) (* (/ 1 (- x 1)) (+ x 1)))

series413.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(cbrt (+ x 1))
50.0ms	(* (cbrt (+ x 1)) (cbrt (+ x 1)))
158.0ms	(fma (/ 1 (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (/ x (cbrt (+ x 1))) (- (* (/ 1 (- x 1)) (+ x 1))))
157.0ms	(fma (- (/ 1 (- x 1))) (+ x 1) (* (/ 1 (- x 1)) (+ x 1)))

simplify2.4s

Counts

107 → 107

Iterations

Iter	Nodes
done	5000
3	3936
2	1214
1	417
0	175

prune517.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

regimes70.0ms

Accuracy

99.9% (0.0b remaining)

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

bsearch124.0ms

Steps

Iters	Range		Point
9	2842.495256040047	513310621636.50653	11033.995023478727
8	-29345360.474346694	-7508.589471958369	-12354.188123908416

simplify14.0ms

Iterations

Iter	Nodes
done	47
2	47
1	44
0	28

end0.0ms

sample1.6s

Algorithm

intervals

Results

846.0ms	1762×	body	1280	valid
306.0ms	4063×	body	80	valid
230.0ms	1269×	body	640	valid
79.0ms	593×	body	320	valid
29.0ms	313×	body	160	valid