Details

sample56.0ms

Algorithm

intervals

Results

25.0ms	70×	body	640	valid
10.0ms	129×	body	80	valid
7.0ms	28×	body	320	valid
5.0ms	14×	body	1280	valid
2.0ms	15×	body	160	valid

simplify274.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	475
9	475
8	357
7	164
6	102
5	81
4	65
3	45
2	35
1	21
0	10

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 10.1b

localize27.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (- x 1))
0.0b	(/ 1 (+ x 1))
0.0b	(- (/ 1 (+ x 1)) (/ 2 x))
2.4b	(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))

rewrite374.0ms

Algorithm

rewrite-expression-head

Rules

743×	`*-un-lft-identity`
715×	`times-frac`
544×	`add-sqr-sqrt`
494×	`add-cube-cbrt`
468×	`prod-diff`
236×	`associate-+l+`
99×	`distribute-lft-out`
72×	`div-inv`
58×	`associate-/r/`
29×	`flip3-+` `flip-+`
22×	`distribute-lft-out--`
20×	`difference-of-squares`
18×	`fma-neg`
13×	`fma-def`
12×	`add-exp-log`
11×	`associate-/r*` `add-log-exp`
8×	`add-cbrt-cube`
6×	`pow1` `associate-/l*`
4×	`expm1-log1p-u` `difference-of-sqr-1` `div-exp` `insert-posit16` `log1p-expm1-u`
3×	`flip3--` `frac-add` `flip--`
2×	`cbrt-undiv` `rec-exp` `clear-num` `sum-log` `sub-neg` `frac-2neg` `diff-log` `1-exp` `frac-sub` `pow-flip` `inv-pow`
1×	`+-commutative` `associate-+l-`

Counts

4 → 648

Calls

4 calls:

18.0ms	(/ 1 (- x 1))
18.0ms	(/ 1 (+ x 1))
55.0ms	(- (/ 1 (+ x 1)) (/ 2 x))
256.0ms	(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))

series198.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(/ 1 (- x 1))
23.0ms	(/ 1 (+ x 1))
25.0ms	(- (/ 1 (+ x 1)) (/ 2 x))
134.0ms	(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))

simplify2.9s

Counts

660 → 660

Iterations

Iter	Nodes
done	5001
2	2873
1	1149
0	495

prune2.0s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.4b

localize31.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (/ 1 (+ x 1)))
0.0b	(sqrt (/ 1 (+ x 1)))
0.1b	(fma (sqrt (/ 1 (+ x 1))) (sqrt (/ 1 (+ x 1))) (/ -2 x))
7.2b	(+ (fma (sqrt (/ 1 (+ x 1))) (sqrt (/ 1 (+ x 1))) (/ -2 x)) (/ 1 (- x 1)))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

38×	`*-un-lft-identity`
36×	`sqrt-prod`
29×	`add-sqr-sqrt`
28×	`times-frac`
21×	`add-cube-cbrt`
8×	`pow1` `distribute-lft-out`
6×	`rem-sqrt-square` `sqrt-pow1` `add-log-exp`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `associate-/r/` `insert-posit16` `log1p-expm1-u`
3×	`fma-def` `flip3-+` `flip-+` `div-inv`
2×	`pow1/2` `sqrt-div` `fma-udef` `pow-flip` `inv-pow`
1×	`+-commutative` `associate-+l+` `sum-log`

Counts

4 → 103

Calls

4 calls:

16.0ms	(sqrt (/ 1 (+ x 1)))
12.0ms	(sqrt (/ 1 (+ x 1)))
1.0ms	(fma (sqrt (/ 1 (+ x 1))) (sqrt (/ 1 (+ x 1))) (/ -2 x))
16.0ms	(+ (fma (sqrt (/ 1 (+ x 1))) (sqrt (/ 1 (+ x 1))) (/ -2 x)) (/ 1 (- x 1)))

series348.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(sqrt (/ 1 (+ x 1)))
47.0ms	(sqrt (/ 1 (+ x 1)))
112.0ms	(fma (sqrt (/ 1 (+ x 1))) (sqrt (/ 1 (+ x 1))) (/ -2 x))
159.0ms	(+ (fma (sqrt (/ 1 (+ x 1))) (sqrt (/ 1 (+ x 1))) (/ -2 x)) (/ 1 (- x 1)))

simplify1.9s

Counts

115 → 115

Iterations

Iter	Nodes
done	5000
3	3084
2	853
1	312
0	148

prune501.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.4b

localize34.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ x 1) x)
0.0b	(/ (fma (fma (+ x 1) -2 x) (+ x -1) (* (+ x 1) x)) (* (* (+ x 1) x) (+ x -1)))
0.0b	(* (* (+ x 1) x) (+ x -1))
31.2b	(fma (fma (+ x 1) -2 x) (+ x -1) (* (+ x 1) x))

rewrite110.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-cbrt-cube` `add-exp-log`
18×	`associate-*l/`
13×	`*-un-lft-identity` `flip3-+` `flip-+`
12×	`add-sqr-sqrt`
11×	`pow1`
9×	`add-cube-cbrt`
8×	`frac-times` `associate-r` `associate-/r/`
7×	`prod-exp` `cbrt-unprod`
5×	`associate-l`
4×	`expm1-log1p-u` `pow-prod-down` `associate-*r/` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `times-frac` `div-exp` `associate-/l*`
2×	`*-commutative` `distribute-lft-out`
1×	`distribute-rgt-in` `difference-of-sqr--1` `clear-num` `associate-/r*` `frac-2neg` `distribute-lft-in` `fma-udef` `div-inv` `unswap-sqr`

Counts

4 → 102

Calls

4 calls:

18.0ms	(* (+ x 1) x)
39.0ms	(/ (fma (fma (+ x 1) -2 x) (+ x -1) (* (+ x 1) x)) (* (* (+ x 1) x) (+ x -1)))
51.0ms	(* (* (+ x 1) x) (+ x -1))
1.0ms	(fma (fma (+ x 1) -2 x) (+ x -1) (* (+ x 1) x))

series808.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(* (+ x 1) x)
379.0ms	(/ (fma (fma (+ x 1) -2 x) (+ x -1) (* (+ x 1) x)) (* (* (+ x 1) x) (+ x -1)))
140.0ms	(* (* (+ x 1) x) (+ x -1))
233.0ms	(fma (fma (+ x 1) -2 x) (+ x -1) (* (+ x 1) x))

simplify2.0s

Counts

114 → 114

Iterations

Iter	Nodes
done	5001
2	2549
1	553
0	173

prune516.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize33.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (+ x 1) x)
0.0b	(* (* (+ x 1) x) (+ x -1))
0.3b	(/ 2 (* (* (+ x 1) x) (+ x -1)))

rewrite126.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-cbrt-cube` `add-exp-log`
18×	`associate-*l/`
13×	`flip3-+` `flip-+`
12×	`*-un-lft-identity`
11×	`add-sqr-sqrt`
10×	`pow1`
8×	`frac-times` `associate-r` `associate-/r/` `add-cube-cbrt`
7×	`prod-exp` `cbrt-unprod`
5×	`associate-l`
4×	`pow-prod-down` `associate-*r/`
3×	`expm1-log1p-u` `cbrt-undiv` `times-frac` `div-exp` `insert-posit16` `log1p-expm1-u` `associate-/l*` `add-log-exp`
2×	`*-commutative` `distribute-lft-out`
1×	`distribute-rgt-in` `difference-of-sqr--1` `clear-num` `associate-/r*` `frac-2neg` `distribute-lft-in` `div-inv` `unswap-sqr`

Counts

3 → 91

Calls

3 calls:

16.0ms	(* (+ x 1) x)
52.0ms	(* (* (+ x 1) x) (+ x -1))
56.0ms	(/ 2 (* (* (+ x 1) x) (+ x -1)))

series311.0ms

Counts

3 → 9

Calls

3 calls:

71.0ms	(* (+ x 1) x)
152.0ms	(* (* (+ x 1) x) (+ x -1))
88.0ms	(/ 2 (* (* (+ x 1) x) (+ x -1)))

simplify2.0s

Counts

100 → 100

Iterations

Iter	Nodes
done	5055
2	2866
1	541
0	165

prune338.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

regimes44.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	15
1	15
0	9

end0.0ms

sample2.6s

Algorithm

intervals

Results

949.0ms	1836×	body	640	valid
602.0ms	555×	body	1280	valid
548.0ms	4243×	body	80	valid
291.0ms	884×	body	320	valid
94.0ms	482×	body	160	valid