Details

sample29.0ms

Algorithm

intervals

Results

8.0ms	53×	body	1280	valid
5.0ms	48×	body	640	valid
4.0ms	118×	body	80	valid
3.0ms	26×	body	320	valid
1.0ms	11×	body	160	valid

simplify2.9s

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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.5b

localize25.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ x (+ x 1.0))
0.0b	(/ (+ x 1.0) (- x 1.0))
3.7b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite232.0ms

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:

17.0ms	(/ x (+ x 1.0))
40.0ms	(/ (+ x 1.0) (- x 1.0))
129.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series286.0ms

Counts

3 → 9

Calls

3 calls:

40.0ms	(/ x (+ x 1.0))
53.0ms	(/ (+ x 1.0) (- x 1.0))
193.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify2.7s

Counts

605 → 605

Iterations

Iter	Nodes
done	5000
2	4599
1	1252
0	523

prune2.4s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* x x) x)
0.2b	(/ 3.0 (* (* x x) x))
0.7b	(/ 1.0 (* x x))
5.6b	(- (- (/ 3.0 (* (* x x) x))) (+ (/ 3.0 x) (/ 1.0 (* x x))))

rewrite218.0ms

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:

28.0ms	(* (* x x) x)
16.0ms	(/ 3.0 (* (* x x) x))
6.0ms	(/ 1.0 (* x x))
153.0ms	(- (- (/ 3.0 (* (* x x) x))) (+ (/ 3.0 x) (/ 1.0 (* x x))))

series174.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(* (* x x) x)
66.0ms	(/ 3.0 (* (* x x) x))
30.0ms	(/ 1.0 (* x x))
34.0ms	(- (- (/ 3.0 (* (* x x) x))) (+ (/ 3.0 x) (/ 1.0 (* x x))))

simplify2.7s

Counts

207 → 207

Iterations

Iter	Nodes
done	5000
2	4597
1	720
0	254

prune967.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 1 expressions with local error:

0.0b	(fma x 3.0 (fma (* x x) 1.0 1.0))

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

1×	`add-sqr-sqrt` `expm1-log1p-u` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `fma-udef` `log1p-expm1-u` `add-log-exp`

Counts

1 → 10

Calls

1 calls:

0.0ms

(fma x 3.0 (fma (* x x) 1.0 1.0))

series36.0ms

Counts

1 → 3

Calls

1 calls:

36.0ms

(fma x 3.0 (fma (* x x) 1.0 1.0))

simplify1.1s

Counts

13 → 13

Iterations

Iter	Nodes
done	5000
3	1060
2	151
1	36
0	22

prune58.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (* 1.0 (- (+ (* (* x x) x) x) (* x x))) (/ (+ x 1.0) (- x 1.0)))
0.0b	(/ (+ x 1.0) (- x 1.0))
0.1b	(* (* x x) x)
7.8b	(- (+ (* (* x x) x) x) (* x x))

rewrite340.0ms

Algorithm

rewrite-expression-head

Rules

75×	`*-un-lft-identity`
50×	`add-sqr-sqrt`
41×	`prod-diff`
40×	`times-frac`
30×	`add-cube-cbrt`
23×	`pow1`
19×	`associate--l+`
11×	`add-cbrt-cube` `add-exp-log` `distribute-lft-out` `add-log-exp`
10×	`distribute-lft-out--` `difference-of-squares`
8×	`distribute-rgt-in` `distribute-lft-in`
6×	`pow-plus` `fma-neg` `pow-prod-up`
5×	`associate-/r*` `distribute-lft1-in` `distribute-rgt-out` `flip3--` `flip--`
4×	`expm1-log1p-u` `sub-neg` `associate-/r/` `log1p-expm1-u` `associate-/l*`
3×	`diff-log` `associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`pow2` `associate-*r/` `pow-sqr` `frac-sub` `div-inv` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `sum-log` `frac-2neg` `flip3-+` `distribute-rgt-out--` `div-exp` `associate-l` `pow3` `*-commutative` `flip-+` `unswap-sqr`

Counts

4 → 165

Calls

4 calls:

116.0ms	(- (* 1.0 (- (+ (* (* x x) x) x) (* x x))) (/ (+ x 1.0) (- x 1.0)))
22.0ms	(/ (+ x 1.0) (- x 1.0))
23.0ms	(* (* x x) x)
172.0ms	(- (+ (* (* x x) x) x) (* x x))

series190.0ms

Counts

4 → 12

Calls

4 calls:

75.0ms	(- (* 1.0 (- (+ (* (* x x) x) x) (* x x))) (/ (+ x 1.0) (- x 1.0)))
45.0ms	(/ (+ x 1.0) (- x 1.0))
39.0ms	(* (* x x) x)
31.0ms	(- (+ (* (* x x) x) x) (* x x))

simplify852.0ms

Counts

177 → 177

Iterations

Iter	Nodes
done	5001
1	899
0	307

prune590.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.0b

regimes54.0ms

Accuracy

100% (0.0b remaining)

Error of 0.4b against oracle of 0.4b and baseline of 31.8b

bsearch122.0ms

Steps

Iters	Range		Point
11	1.9534460235190362e-22	53640.016154094046	1.3976806960534893
10	-17239113253358.373	-4.96108325192681e-05	-1.0098163723001696

simplify6.0ms

Iterations

Iter	Nodes
done	34
1	34
0	24

end0.0ms

sample1.1s

Algorithm

intervals

Results

425.0ms	1740×	body	1280	valid
235.0ms	1239×	body	640	valid
179.0ms	4089×	body	80	valid
66.0ms	624×	body	320	valid
23.0ms	308×	body	160	valid