Details

sample87.0ms

Algorithm

intervals

Results

32.0ms	62×	body	640	valid
18.0ms	137×	body	80	valid
11.0ms	29×	body	320	valid
8.0ms	13×	body	1280	valid
4.0ms	16×	body	160	valid

simplify290.0ms

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: 10.2b

localize34.0ms

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))
1.2b	(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))

rewrite337.0ms

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:

12.0ms	(/ 1 (- x 1))
9.0ms	(/ 1 (+ x 1))
63.0ms	(- (/ 1 (+ x 1)) (/ 2 x))
235.0ms	(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))

series542.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(/ 1 (- x 1))
17.0ms	(/ 1 (+ x 1))
28.0ms	(- (/ 1 (+ x 1)) (/ 2 x))
482.0ms	(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))

simplify917.0ms

Counts

660 → 660

Iterations

Iter	Nodes
done	2000
1	1149
0	495

prune2.4s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.1b

localize48.0ms

Local error

Found 4 expressions with local error:

0.0b	(* x (+ 1 x))
0.0b	(- x (* 2 (+ 1 x)))
0.1b	(* (* x (+ 1 x)) (- x 1))
30.0b	(fma x (+ 1 x) (* (- x (* 2 (+ 1 x))) (- x 1)))

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt`
26×	`*-un-lft-identity`
21×	`prod-diff` `add-cube-cbrt`
13×	`distribute-rgt-in` `distribute-lft-in`
11×	`pow1` `add-cbrt-cube` `associate-r` `add-exp-log`
10×	`associate-*r/`
6×	`add-log-exp`
4×	`expm1-log1p-u` `frac-times` `flip3-+` `flip3--` `associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `flip-+` `insert-posit16` `log1p-expm1-u` `flip--`
3×	`sub-neg` `fma-neg`
2×	`associate-l/` `-commutative` `associate--r+` `difference-of-squares`
1×	`diff-log` `difference-of-sqr-1` `fma-udef` `distribute-lft-out` `distribute-lft-out--` `unswap-sqr`

Counts

4 → 115

Calls

4 calls:

13.0ms	(* x (+ 1 x))
5.0ms	(- x (* 2 (+ 1 x)))
42.0ms	(* (* x (+ 1 x)) (- x 1))
0.0ms	(fma x (+ 1 x) (* (- x (* 2 (+ 1 x))) (- x 1)))

series385.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(* x (+ 1 x))
38.0ms	(- x (* 2 (+ 1 x)))
113.0ms	(* (* x (+ 1 x)) (- x 1))
183.0ms	(fma x (+ 1 x) (* (- x (* 2 (+ 1 x))) (- x 1)))

simplify678.0ms

Counts

127 → 127

Iterations

Iter	Nodes
done	2000
1	617
0	197

prune659.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.1b

localize52.0ms

Local error

Found 4 expressions with local error:

0.1b	(* x (* x x))
0.1b	(/ 2 (pow x 5))
0.1b	(/ 2 (* x (* x x)))
0.2b	(/ 2 (pow x 7))

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

45×	`times-frac`
40×	`add-sqr-sqrt`
39×	`*-un-lft-identity` `add-cube-cbrt`
28×	`add-exp-log`
24×	`unpow-prod-down`
22×	`add-cbrt-cube`
18×	`pow1`
15×	`associate-/r*`
9×	`div-exp` `associate-/l*`
8×	`sqr-pow`
6×	`prod-exp` `cbrt-unprod`
5×	`cbrt-undiv` `pow-prod-up`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`clear-num` `frac-2neg` `associate-l` `pow-prod-down` `div-inv`
2×	`pow-to-exp` `pow-exp`
1×	`pow2` `pow-plus` `cube-unmult` `associate-r` `pow-sqr` `*-commutative` `unswap-sqr`

Counts

4 → 149

Calls

4 calls:

14.0ms	(* x (* x x))
5.0ms	(/ 2 (pow x 5))
27.0ms	(/ 2 (* x (* x x)))
12.0ms	(/ 2 (pow x 7))

series312.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(* x (* x x))
94.0ms	(/ 2 (pow x 5))
62.0ms	(/ 2 (* x (* x x)))
101.0ms	(/ 2 (pow x 7))

simplify870.0ms

Counts

161 → 161

Iterations

Iter	Nodes
done	2004
2	1526
1	425
0	218

prune728.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0b

localize49.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ 2 (pow x 5))
0.1b	(/ (/ 2 x) (* x x))
0.2b	(/ 2 (pow x 7))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

73×	`times-frac`
49×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
25×	`add-exp-log`
24×	`unpow-prod-down`
19×	`add-cbrt-cube` `associate-/l*`
15×	`associate-/r*`
12×	`div-exp`
8×	`cbrt-undiv` `sqr-pow`
5×	`div-inv`
3×	`expm1-log1p-u` `pow1` `clear-num` `frac-2neg` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`pow-to-exp` `pow-exp` `prod-exp` `cbrt-unprod`
1×	`associate-/l/`

Counts

3 → 145

Calls

3 calls:

5.0ms	(/ 2 (pow x 5))
10.0ms	(/ (/ 2 x) (* x x))
5.0ms	(/ 2 (pow x 7))

series241.0ms

Counts

3 → 9

Calls

3 calls:

69.0ms	(/ 2 (pow x 5))
69.0ms	(/ (/ 2 x) (* x x))
103.0ms	(/ 2 (pow x 7))

simplify965.0ms

Counts

154 → 154

Iterations

Iter	Nodes
done	2000
2	1528
1	495
0	244

prune533.0ms

Pruning

5 alts after pruning (1 fresh and 4 done)

Merged error: 0b

regimes78.0ms

Accuracy

98.6% (0.1b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 9.9b

bsearch202.0ms

Steps

Iters	Range		Point
11	0.0038666078177206752	9.350013159855062e+31	110.41034748839138
10	-121993772661.31783	-0.22068356154967622	-113.60321351793068

simplify11.0ms

Iterations

Iter	Nodes
done	39
1	39
0	30

end0.0ms

sample2.7s

Algorithm

intervals

Results

973.0ms	1924×	body	640	valid
702.0ms	563×	body	1280	valid
457.0ms	4140×	body	80	valid
310.0ms	897×	body	320	valid
92.0ms	479×	body	160	valid