Details

sample72.0ms

Algorithm

intervals

Results

28.0ms	66×	body	640	valid
15.0ms	133×	body	80	valid
12.0ms	38×	body	320	valid
4.0ms	19×	body	160	valid

simplify8.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	18
2	18
1	15
0	7

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.3b

localize23.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 1 (- x 1))
0.0b	(/ 1 (+ x 1))
2.7b	(- (/ 1 (+ x 1)) (/ 1 (- x 1)))

rewrite116.0ms

Algorithm

rewrite-expression-head

Rules

850×	`*-un-lft-identity`
783×	`times-frac`
710×	`add-sqr-sqrt`
486×	`prod-diff`
454×	`add-cube-cbrt`
125×	`difference-of-squares`
98×	`associate-/r/`
94×	`distribute-lft-out`
81×	`distribute-lft-out--`
58×	`difference-of-sqr-1`
52×	`div-inv`
30×	`flip-+`
29×	`flip3-+`
21×	`flip--`
20×	`flip3--`
18×	`fma-neg`
11×	`associate-/r*` `add-exp-log`
7×	`add-cbrt-cube`
6×	`associate-/l*`
5×	`pow1` `add-log-exp`
4×	`div-exp`
3×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
2×	`cbrt-undiv` `rec-exp` `clear-num` `frac-2neg` `1-exp` `pow-flip` `inv-pow`
1×	`sub-neg` `diff-log` `frac-sub`

Counts

3 → 638

Calls

3 calls:

9.0ms	(/ 1 (- x 1))
14.0ms	(/ 1 (+ x 1))
65.0ms	(- (/ 1 (+ x 1)) (/ 1 (- x 1)))

series124.0ms

Counts

3 → 9

Calls

3 calls:

15.0ms	(/ 1 (- x 1))
15.0ms	(/ 1 (+ x 1))
94.0ms	(- (/ 1 (+ x 1)) (/ 1 (- x 1)))

simplify2.2s

Counts

647 → 647

Iterations

Iter	Nodes
done	5000
2	2576
1	1290
0	553

prune1.4s

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.3b

localize47.0ms

Local error

Found 4 expressions with local error:

8.1b	(- (/ 1 (+ x 1)) (/ (+ (fma x x 1) x) (fma x (* x x) -1)))
21.2b	(/ (+ (fma x x 1) x) (fma x (* x x) -1))
21.2b	(/ (+ (fma x x 1) x) (fma x (* x x) -1))
31.9b	(fma (/ -1 (fma x (* x x) -1)) (+ (fma x x 1) x) (/ (+ (fma x x 1) x) (fma x (* x x) -1)))

rewrite150.0ms

Algorithm

rewrite-expression-head

Rules

553×	`*-un-lft-identity`
459×	`times-frac`
319×	`add-sqr-sqrt`
302×	`add-cube-cbrt`
288×	`prod-diff`
117×	`distribute-lft-out`
38×	`div-inv`
34×	`associate-/r/`
19×	`flip3-+` `flip-+`
18×	`fma-neg`
8×	`add-cbrt-cube` `add-exp-log` `associate-/l*`
6×	`associate-/r*` `distribute-lft-out--` `add-log-exp` `difference-of-squares`
4×	`expm1-log1p-u` `pow1` `insert-posit16` `log1p-expm1-u` `associate-/l/`
2×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp`
1×	`sub-neg` `flip3--` `diff-log` `frac-sub` `fma-udef` `flip--`

Counts

4 → 417

Calls

4 calls:

76.0ms	(- (/ 1 (+ x 1)) (/ (+ (fma x x 1) x) (fma x (* x x) -1)))
27.0ms	(/ (+ (fma x x 1) x) (fma x (* x x) -1))
29.0ms	(/ (+ (fma x x 1) x) (fma x (* x x) -1))
1.0ms	(fma (/ -1 (fma x (* x x) -1)) (+ (fma x x 1) x) (/ (+ (fma x x 1) x) (fma x (* x x) -1)))

series634.0ms

Counts

4 → 12

Calls

4 calls:

199.0ms	(- (/ 1 (+ x 1)) (/ (+ (fma x x 1) x) (fma x (* x x) -1)))
68.0ms	(/ (+ (fma x x 1) x) (fma x (* x x) -1))
63.0ms	(/ (+ (fma x x 1) x) (fma x (* x x) -1))
303.0ms	(fma (/ -1 (fma x (* x x) -1)) (+ (fma x x 1) x) (/ (+ (fma x x 1) x) (fma x (* x x) -1)))

simplify2.2s

Counts

429 → 429

Iterations

Iter	Nodes
done	5001
2	2531
1	977
0	411

prune2.0s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.3b

localize31.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* x x) (* x x))
0.2b	(/ -2 (* (* x x) (* x x)))
0.3b	(/ 2 (* x x))
0.4b	(/ 2 (* (* x x) x))

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

115×	`pow1`
48×	`add-cbrt-cube` `add-exp-log`
36×	`pow-prod-up`
23×	`pow-prod-down`
22×	`pow-sqr`
20×	`prod-exp` `cbrt-unprod`
18×	`pow-plus`
13×	`pow2`
10×	`add-sqr-sqrt` `cbrt-undiv` `*-un-lft-identity` `div-exp` `add-cube-cbrt`
9×	`times-frac` `associate-/l*`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`clear-num` `associate-/r*` `frac-2neg` `div-inv`
1×	`swap-sqr` `associate-r` `associate-l` `*-commutative` `unswap-sqr`

Counts

4 → 146

Calls

4 calls:

22.0ms	(* (* x x) (* x x))
25.0ms	(/ -2 (* (* x x) (* x x)))
6.0ms	(/ 2 (* x x))
14.0ms	(/ 2 (* (* x x) x))

series186.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(* (* x x) (* x x))
58.0ms	(/ -2 (* (* x x) (* x x)))
30.0ms	(/ 2 (* x x))
44.0ms	(/ 2 (* (* x x) x))

simplify1.2s

Counts

158 → 158

Iterations

Iter	Nodes
done	5048
2	1793
1	409
0	149

prune407.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ 2 x) x)
0.1b	(* (* x x) (* x x))
0.2b	(/ -2 (* (* x x) (* x x)))
0.4b	(/ 2 (* (* x x) x))

rewrite106.0ms

Algorithm

rewrite-expression-head

Rules

115×	`pow1`
81×	`times-frac`
50×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
48×	`add-cbrt-cube` `add-exp-log`
36×	`pow-prod-up`
23×	`pow-prod-down`
22×	`pow-sqr`
19×	`prod-exp` `cbrt-unprod` `associate-/l*`
18×	`pow-plus`
13×	`pow2`
11×	`cbrt-undiv` `div-exp`
7×	`div-inv`
5×	`associate-/r*`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`clear-num` `frac-2neg`
1×	`swap-sqr` `associate-r` `associate-l` `*-commutative` `unswap-sqr` `associate-/l/`

Counts

4 → 195

Calls

4 calls:

16.0ms	(/ (/ 2 x) x)
42.0ms	(* (* x x) (* x x))
24.0ms	(/ -2 (* (* x x) (* x x)))
18.0ms	(/ 2 (* (* x x) x))

series220.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(/ (/ 2 x) x)
48.0ms	(* (* x x) (* x x))
71.0ms	(/ -2 (* (* x x) (* x x)))
56.0ms	(/ 2 (* (* x x) x))

simplify1.6s

Counts

207 → 207

Iterations

Iter	Nodes
done	5155
2	2097
1	640
0	254

prune701.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0b

regimes48.0ms

Accuracy

99.8% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 29.3b

bsearch131.0ms

Steps

Iters	Range		Point
10	2.618543036730298e-08	12461.173664998358	243.1515967158251
9	-101227.54480913779	-5.532094628653386e-05	-247.204822595503

simplify6.0ms

Iterations

Iter	Nodes
done	41
1	41
0	31

end0.0ms

sample1.8s

Algorithm

intervals

Results

697.0ms	4300×	body	80	valid
610.0ms	1867×	body	640	valid
225.0ms	1187×	body	320	valid
112.0ms	646×	body	160	valid