Details

sample43.0ms

Algorithm

intervals

Results

14.0ms	54×	body	1280	valid
11.0ms	50×	body	640	valid
7.0ms	125×	body	80	valid
3.0ms	16×	body	320	valid
1.0ms	11×	body	160	valid

simplify161.0ms

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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.0b

localize21.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (+ x 1) (- x 1))
0.0b	(/ x (+ x 1))
3.0b	(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))

rewrite139.0ms

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:

18.0ms	(/ (+ x 1) (- x 1))
8.0ms	(/ x (+ x 1))
86.0ms	(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))

series145.0ms

Counts

3 → 9

Calls

3 calls:

37.0ms	(/ (+ x 1) (- x 1))
22.0ms	(/ x (+ x 1))
85.0ms	(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))

simplify1.3s

Counts

762 → 762

Iterations

Iter	Nodes
done	2000
2	2000
1	1369
0	584

prune6.9s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b	(* x (* x x))
0.5b	(/ 3 (* x (* x x)))
0.5b	(/ 1 (* x x))
8.8b	(+ (+ (/ 1 (* x x)) (/ 3 x)) (/ 3 (* x (* x x))))

rewrite180.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-exp-log`
26×	`pow1`
23×	`*-un-lft-identity` `add-cbrt-cube`
11×	`add-sqr-sqrt`
10×	`add-cube-cbrt`
9×	`times-frac` `prod-exp` `add-log-exp`
8×	`distribute-lft-out`
7×	`div-exp` `cbrt-unprod`
6×	`fma-def` `pow-prod-up` `div-inv` `pow-flip` `associate-/l*`
5×	`cbrt-undiv`
4×	`expm1-log1p-u` `pow-prod-down` `frac-add` `insert-posit16` `log1p-expm1-u`
3×	`sum-log` `associate-l`
2×	`pow2` `rec-exp` `clear-num` `associate-/r*` `frac-2neg` `flip3-+` `pow-plus` `distribute-rgt-out` `1-exp` `pow-sqr` `flip-+`
1×	`+-commutative` `associate-+l+` `cube-unmult` `associate-r` `*-commutative` `inv-pow` `unswap-sqr`

Counts

4 → 117

Calls

4 calls:

14.0ms	(* x (* x x))
12.0ms	(/ 3 (* x (* x x)))
11.0ms	(/ 1 (* x x))
141.0ms	(+ (+ (/ 1 (* x x)) (/ 3 x)) (/ 3 (* x (* x x))))

series135.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(* x (* x x))
45.0ms	(/ 3 (* x (* x x)))
21.0ms	(/ 1 (* x x))
25.0ms	(+ (+ (/ 1 (* x x)) (/ 3 x)) (/ 3 (* x (* x x))))

simplify800.0ms

Counts

129 → 129

Iterations

Iter	Nodes
done	2001
2	2001
1	483
0	172

prune927.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize33.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (+ (/ 1 x) 3) (/ 3 (* x x)))
0.2b	(* (/ 1 x) (+ (+ (/ 1 x) 3) (/ 3 (* x x))))
0.5b	(/ 3 (* x x))

rewrite187.0ms

Algorithm

rewrite-expression-head

Rules

32×	`*-un-lft-identity`
21×	`add-sqr-sqrt`
17×	`add-exp-log`
14×	`times-frac` `add-cube-cbrt`
13×	`add-cbrt-cube` `associate-l`
12×	`distribute-lft-out`
8×	`add-log-exp`
6×	`flip3-+` `associate-r` `frac-add` `flip-+`
5×	`pow1` `fma-def` `prod-exp` `div-inv`
4×	`frac-times` `div-exp` `associate-*r/`
3×	`expm1-log1p-u` `cbrt-undiv` `sum-log` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `associate-/l*` `unswap-sqr`
1×	`distribute-rgt-in` `+-commutative` `rec-exp` `associate-+l+` `clear-num` `associate-/r` `frac-2neg` `distribute-lft-in` `1-exp` `pow-prod-down` `associate-l/` `*-commutative`

Counts

3 → 101

Calls

3 calls:

46.0ms	(+ (+ (/ 1 x) 3) (/ 3 (* x x)))
123.0ms	(* (/ 1 x) (+ (+ (/ 1 x) 3) (/ 3 (* x x))))
16.0ms	(/ 3 (* x x))

series92.0ms

Counts

3 → 9

Calls

3 calls:

19.0ms	(+ (+ (/ 1 x) 3) (/ 3 (* x x)))
34.0ms	(* (/ 1 x) (+ (+ (/ 1 x) 3) (/ 3 (* x x))))
38.0ms	(/ 3 (* x x))

simplify884.0ms

Counts

110 → 110

Iterations

Iter	Nodes
done	2002
2	2002
1	619
0	176

prune678.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize47.0ms

Local error

Found 4 expressions with local error:

4.5b	(fma (* (cbrt (+ (/ 1 (* x x)) (/ 3 x))) (cbrt (+ (/ 1 (* x x)) (/ 3 x)))) (cbrt (+ (/ 1 (* x x)) (/ 3 x))) (/ 3 (* x (* x x))))
17.0b	(cbrt (+ (/ 1 (* x x)) (/ 3 x)))
17.0b	(cbrt (+ (/ 1 (* x x)) (/ 3 x)))
17.0b	(cbrt (+ (/ 1 (* x x)) (/ 3 x)))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

19×	`*-un-lft-identity`
18×	`cbrt-prod`
9×	`cbrt-div`
7×	`add-sqr-sqrt` `add-cube-cbrt`
6×	`div-inv` `distribute-lft-out`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`flip3-+` `times-frac` `distribute-rgt-out` `pow1/3` `frac-add` `flip-+`
1×	`fma-udef`

Counts

4 → 71

Calls

4 calls:

0.0ms	(fma (* (cbrt (+ (/ 1 (* x x)) (/ 3 x))) (cbrt (+ (/ 1 (* x x)) (/ 3 x)))) (cbrt (+ (/ 1 (* x x)) (/ 3 x))) (/ 3 (* x (* x x))))
13.0ms	(cbrt (+ (/ 1 (* x x)) (/ 3 x)))
12.0ms	(cbrt (+ (/ 1 (* x x)) (/ 3 x)))
13.0ms	(cbrt (+ (/ 1 (* x x)) (/ 3 x)))

series385.0ms

Counts

4 → 12

Calls

4 calls:

212.0ms	(fma (* (cbrt (+ (/ 1 (* x x)) (/ 3 x))) (cbrt (+ (/ 1 (* x x)) (/ 3 x)))) (cbrt (+ (/ 1 (* x x)) (/ 3 x))) (/ 3 (* x (* x x))))
64.0ms	(cbrt (+ (/ 1 (* x x)) (/ 3 x)))
54.0ms	(cbrt (+ (/ 1 (* x x)) (/ 3 x)))
54.0ms	(cbrt (+ (/ 1 (* x x)) (/ 3 x)))

simplify1.0s

Counts

83 → 83

Iterations

Iter	Nodes
done	2004
3	2004
2	1026
1	332
0	124

prune873.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

regimes62.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 31.0b

bsearch166.0ms

Steps

Iters	Range		Point
10	1.8230705747381016e-09	4364471.442644652	6909.881176444165
9	-32298.533864343164	-0.030639508246526274	-8022.341442375084

simplify17.0ms

Iterations

Iter	Nodes
done	65
3	65
2	63
1	50
0	30

end0.0ms

sample2.2s

Algorithm

intervals

Results

752.0ms	1714×	body	1280	valid
748.0ms	1277×	body	640	valid
403.0ms	4052×	body	80	valid
138.0ms	625×	body	320	valid
75.0ms	332×	body	160	valid