Details

sample31.0ms

Algorithm

intervals

Results

9.0ms	58×	body	1280	valid
6.0ms	49×	body	640	valid
4.0ms	121×	body	80	valid
2.0ms	19×	body	320	valid
1.0ms	9×	body	160	valid

simplify2.7s

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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.6b

localize12.0ms

Local error

Found 3 expressions with local error:

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

rewrite173.0ms

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:

8.0ms	(/ x (+ x 1.0))
19.0ms	(/ (+ x 1.0) (- x 1.0))
100.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series221.0ms

Counts

3 → 9

Calls

3 calls:

37.0ms	(/ x (+ x 1.0))
40.0ms	(/ (+ x 1.0) (- x 1.0))
143.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify2.4s

Counts

605 → 605

Iterations

Iter	Nodes
done	5000
2	4599
1	1252
0	523

prune2.0s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize36.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* x x) x)
0.3b	(/ 1.0 (* x x))
0.4b	(/ 3.0 (* (* x x) x))
6.8b	(- (- (/ 3.0 (* (* x x) x))) (+ (/ 3.0 x) (/ 1.0 (* x x))))

rewrite240.0ms

Algorithm

rewrite-expression-head

Rules

98×	`*-un-lft-identity`
72×	`prod-diff`
55×	`add-sqr-sqrt`
52×	`add-cube-cbrt`
37×	`distribute-rgt-neg-in`
36×	`times-frac`
35×	`distribute-lft-neg-in`
23×	`pow1` `add-cbrt-cube` `add-exp-log`
20×	`distribute-lft-out`
18×	`fma-neg`
14×	`add-log-exp`
12×	`div-inv`
7×	`prod-exp` `cbrt-unprod`
6×	`pow-plus` `pow-prod-up` `associate-/l*`
5×	`cbrt-undiv` `neg-mul-1` `div-exp`
4×	`expm1-log1p-u` `diff-log` `log1p-expm1-u` `distribute-lft-out--`
3×	`associate-r` `pow-prod-down` `frac-sub` `distribute-neg-frac`
2×	`pow2` `clear-num` `associate-/r*` `sum-log` `frac-2neg` `neg-log` `pow-sqr`
1×	`associate--l-` `neg-sub0` `sub-neg` `flip3-+` `flip3--` `associate-l` `pow3` `frac-add` `*-commutative` `flip-+` `flip--` `associate--r+` `difference-of-squares` `unswap-sqr`

Counts

4 → 195

Calls

4 calls:

17.0ms	(* (* x x) x)
6.0ms	(/ 1.0 (* x x))
21.0ms	(/ 3.0 (* (* x x) x))
184.0ms	(- (- (/ 3.0 (* (* x x) x))) (+ (/ 3.0 x) (/ 1.0 (* x x))))

series202.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(* (* x x) x)
41.0ms	(/ 1.0 (* x x))
48.0ms	(/ 3.0 (* (* x x) x))
58.0ms	(- (- (/ 3.0 (* (* x x) x))) (+ (/ 3.0 x) (/ 1.0 (* x x))))

simplify2.5s

Counts

207 → 207

Iterations

Iter	Nodes
done	5000
2	4607
1	720
0	254

prune714.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize46.0ms

Local error

Found 4 expressions with local error:

15.5b	(/ (+ x 1.0) (- (* x x) (* 1.0 1.0)))
15.5b	(/ x (- (* x x) (* 1.0 1.0)))
32.3b	(fma (/ x (- (* x x) (* 1.0 1.0))) (- x 1.0) (- (* (+ x 1.0) (/ (+ x 1.0) (- (* x x) (* 1.0 1.0))))))
34.7b	(fma (- (+ x 1.0)) (/ (+ x 1.0) (- (* x x) (* 1.0 1.0))) (* (+ x 1.0) (/ (+ x 1.0) (- (* x x) (* 1.0 1.0)))))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 97

Calls

4 calls:

20.0ms	(/ (+ x 1.0) (- (* x x) (* 1.0 1.0)))
10.0ms	(/ x (- (* x x) (* 1.0 1.0)))
0.0ms	(fma (/ x (- (* x x) (* 1.0 1.0))) (- x 1.0) (- (* (+ x 1.0) (/ (+ x 1.0) (- (* x x) (* 1.0 1.0))))))
0.0ms	(fma (- (+ x 1.0)) (/ (+ x 1.0) (- (* x x) (* 1.0 1.0))) (* (+ x 1.0) (/ (+ x 1.0) (- (* x x) (* 1.0 1.0)))))

series764.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(/ (+ x 1.0) (- (* x x) (* 1.0 1.0)))
87.0ms	(/ x (- (* x x) (* 1.0 1.0)))
226.0ms	(fma (/ x (- (* x x) (* 1.0 1.0))) (- x 1.0) (- (* (+ x 1.0) (/ (+ x 1.0) (- (* x x) (* 1.0 1.0))))))
397.0ms	(fma (- (+ x 1.0)) (/ (+ x 1.0) (- (* x x) (* 1.0 1.0))) (* (+ x 1.0) (/ (+ x 1.0) (- (* x x) (* 1.0 1.0)))))

simplify1.8s

Counts

109 → 109

Iterations

Iter	Nodes
done	5000
2	2293
1	442
0	180

prune575.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

localize26.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ x 1.0) (- x 1.0))
0.0b	(* (+ x 1.0) (+ x 1.0))
0.0b	(/ (- (* x (- x 1.0)) (* (+ x 1.0) (+ x 1.0))) (* (+ x 1.0) (- x 1.0)))
19.0b	(- (* x (- x 1.0)) (* (+ x 1.0) (+ x 1.0)))

rewrite209.0ms

Algorithm

rewrite-expression-head

Rules

54×	`*-un-lft-identity`
46×	`associate-*r/`
42×	`add-sqr-sqrt`
37×	`prod-diff`
36×	`flip3-+` `add-cube-cbrt` `flip-+`
32×	`frac-sub`
28×	`frac-times`
24×	`distribute-rgt-in` `distribute-lft-in` `flip3--` `flip--`
22×	`associate--l+`
18×	`associate-/l/`
14×	`associate-*l/`
13×	`pow1` `add-cbrt-cube` `add-exp-log`
9×	`associate-r`
8×	`associate-l` `associate-/r/`
7×	`distribute-lft-out`
6×	`swap-sqr` `add-log-exp`
5×	`sub-neg`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`times-frac` `prod-exp` `cbrt-unprod` `associate-/l*`
2×	`cbrt-undiv` `div-exp` `pow-prod-down` `*-commutative` `associate--r+` `unswap-sqr`
1×	`pow2` `clear-num` `associate-/r*` `frac-2neg` `pow-plus` `fma-neg` `diff-log` `div-sub` `pow-sqr` `pow-prod-up` `div-inv` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 201

Calls

4 calls:

45.0ms	(* (+ x 1.0) (- x 1.0))
41.0ms	(* (+ x 1.0) (+ x 1.0))
72.0ms	(/ (- (* x (- x 1.0)) (* (+ x 1.0) (+ x 1.0))) (* (+ x 1.0) (- x 1.0)))
36.0ms	(- (* x (- x 1.0)) (* (+ x 1.0) (+ x 1.0)))

series259.0ms

Counts

4 → 12

Calls

4 calls:

106.0ms	(* (+ x 1.0) (- x 1.0))
17.0ms	(* (+ x 1.0) (+ x 1.0))
71.0ms	(/ (- (* x (- x 1.0)) (* (+ x 1.0) (+ x 1.0))) (* (+ x 1.0) (- x 1.0)))
64.0ms	(- (* x (- x 1.0)) (* (+ x 1.0) (+ x 1.0)))

simplify956.0ms

Counts

213 → 213

Iterations

Iter	Nodes
done	5001
1	1141
0	321

prune866.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

regimes40.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 14.6b

bsearch104.0ms

Steps

Iters	Range		Point
11	1126.7541422477805	6.910090022658404e+24	210389.86124830059
7	-6675456248951.233	-154130335284.9803	-6582747193969.391

simplify9.0ms

Iterations

Iter	Nodes
done	43
2	43
1	42
0	27

end0.0ms

sample1.4s

Algorithm

intervals

Results

498.0ms	4187×	body	80	valid
348.0ms	1665×	body	1280	valid
234.0ms	1219×	body	640	valid
105.0ms	611×	body	320	valid
52.0ms	318×	body	160	valid