Details

sample73.0ms

Algorithm

intervals

Results

33.0ms	66×	body	640	valid
15.0ms	133×	body	80	valid
11.0ms	38×	body	320	valid
4.0ms	19×	body	160	valid

simplify7.0ms

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

localize12.0ms

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)))

rewrite281.0ms

Algorithm

rewrite-expression-head

Rules

952×	`*-un-lft-identity`
796×	`add-sqr-sqrt`
783×	`times-frac`
500×	`add-cube-cbrt`
486×	`prod-diff`
145×	`difference-of-squares`
133×	`associate-/r*`
130×	`frac-sub`
107×	`distribute-lft-out`
98×	`associate-/r/`
91×	`distribute-lft-out--`
75×	`associate-/l*`
68×	`difference-of-sqr-1`
52×	`div-inv`
30×	`flip-+`
29×	`flip3-+`
25×	`clear-num` `frac-2neg`
21×	`flip--`
20×	`flip3--`
18×	`fma-neg`
11×	`add-exp-log`
7×	`add-cbrt-cube`
5×	`pow1` `add-log-exp`
4×	`div-exp`
3×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
2×	`cbrt-undiv` `rec-exp` `1-exp` `pow-flip` `inv-pow`
1×	`sub-neg` `diff-log`

Counts

3 → 767

Calls

3 calls:

23.0ms	(/ 1 (- x 1))
19.0ms	(/ 1 (+ x 1))
176.0ms	(- (/ 1 (+ x 1)) (/ 1 (- x 1)))

series163.0ms

Counts

3 → 9

Calls

3 calls:

26.0ms	(/ 1 (- x 1))
29.0ms	(/ 1 (+ x 1))
106.0ms	(- (/ 1 (+ x 1)) (/ 1 (- x 1)))

simplify3.4s

Counts

776 → 776

Iterations

Iter	Nodes
done	5000
2	4555
1	2240
0	818

prune1.9s

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.3b

localize24.0ms

Local error

Found 4 expressions with local error:

2.7b	(- (/ 1 (+ x 1)) (/ (+ x 1) (fma x x -1)))
16.2b	(/ (+ x 1) (fma x x -1))
16.2b	(/ (+ x 1) (fma x x -1))
31.5b	(fma (/ -1 (fma x x -1)) (+ x 1) (/ (+ x 1) (fma x x -1)))

rewrite233.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 536

Calls

4 calls:

129.0ms	(- (/ 1 (+ x 1)) (/ (+ x 1) (fma x x -1)))
32.0ms	(/ (+ x 1) (fma x x -1))
36.0ms	(/ (+ x 1) (fma x x -1))
0.0ms	(fma (/ -1 (fma x x -1)) (+ x 1) (/ (+ x 1) (fma x x -1)))

series488.0ms

Counts

4 → 12

Calls

4 calls:

185.0ms	(- (/ 1 (+ x 1)) (/ (+ x 1) (fma x x -1)))
33.0ms	(/ (+ x 1) (fma x x -1))
46.0ms	(/ (+ x 1) (fma x x -1))
224.0ms	(fma (/ -1 (fma x x -1)) (+ x 1) (/ (+ x 1) (fma x x -1)))

simplify2.1s

Counts

548 → 548

Iterations

Iter	Nodes
done	5001
1	2031
0	675

prune1.8s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.3b

localize45.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* x x) (* x x))
0.2b	(/ -2 (* (* x x) (* x x)))
0.2b	(/ 1 (* (* (* x x) (* x x)) (* x x)))
0.3b	(/ 1 (* x x))

rewrite1.3s

Algorithm

rewrite-expression-head

Rules

3351×	`add-sqr-sqrt`
2049×	`unswap-sqr`
1146×	`times-frac`
1041×	`swap-sqr`
789×	`pow1`
657×	`*-un-lft-identity`
622×	`*-commutative`
621×	`add-cube-cbrt`
609×	`associate-l`
382×	`associate-/r*`
343×	`pow-prod-up`
327×	`associate-r`
193×	`pow-flip`
182×	`add-exp-log`
168×	`pow-prod-down`
146×	`pow-plus`
138×	`pow-sqr`
112×	`prod-exp`
92×	`add-cbrt-cube`
90×	`pow2`
48×	`cbrt-unprod`
31×	`div-exp`
18×	`cbrt-undiv`
13×	`rec-exp` `1-exp`
10×	`pow3`
9×	`associate-/l*`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`clear-num` `frac-2neg` `div-inv`
2×	`inv-pow`

Counts

4 → 1971

Calls

4 calls:

102.0ms	(* (* x x) (* x x))
163.0ms	(/ -2 (* (* x x) (* x x)))
820.0ms	(/ 1 (* (* (* x x) (* x x)) (* x x)))
21.0ms	(/ 1 (* x x))

series215.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(* (* x x) (* x x))
62.0ms	(/ -2 (* (* x x) (* x x)))
71.0ms	(/ 1 (* (* (* x x) (* x x)) (* x x)))
29.0ms	(/ 1 (* x x))

simplify2.8s

Counts

1983 → 1983

Iterations

Iter	Nodes
done	5017
1	3161
0	980

prune2.8s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize43.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* x x) (* x x))
0.1b	(* (* x x) (* x x))
0.2b	(/ -2 (* (* x x) (* x x)))
0.2b	(/ 1 (* (* (* x x) (* x x)) (* x x)))

rewrite1.3s

Algorithm

rewrite-expression-head

Rules

3393×	`add-sqr-sqrt`
2086×	`unswap-sqr`
1101×	`times-frac`
1074×	`swap-sqr`
892×	`pow1`
645×	`*-un-lft-identity`
635×	`*-commutative`
626×	`associate-l`
605×	`add-cube-cbrt`
378×	`pow-prod-up`
367×	`associate-/r*`
342×	`associate-r`
190×	`pow-prod-down`
187×	`pow-flip`
183×	`add-exp-log`
163×	`pow-plus`
159×	`pow-sqr`
117×	`prod-exp`
102×	`pow2`
99×	`add-cbrt-cube`
55×	`cbrt-unprod`
27×	`div-exp`
16×	`cbrt-undiv`
11×	`rec-exp` `1-exp`
10×	`pow3`
6×	`associate-/l*`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`clear-num` `frac-2neg` `div-inv`
1×	`inv-pow`

Counts

4 → 2018

Calls

4 calls:

60.0ms	(* (* x x) (* x x))
74.0ms	(* (* x x) (* x x))
112.0ms	(/ -2 (* (* x x) (* x x)))
876.0ms	(/ 1 (* (* (* x x) (* x x)) (* x x)))

series252.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(* (* x x) (* x x))
45.0ms	(* (* x x) (* x x))
66.0ms	(/ -2 (* (* x x) (* x x)))
67.0ms	(/ 1 (* (* (* x x) (* x x)) (* x x)))

simplify2.7s

Counts

2030 → 2030

Iterations

Iter	Nodes
done	5019
1	2927
0	956

prune3.6s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

regimes48.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 28.4b

bsearch159.0ms

Steps

Iters	Range		Point
10	2.618543036730298e-08	12461.173664998358	223.76966427677394
9	-101227.54480913779	-5.532094628653386e-05	-247.204822595503

simplify5.0ms

Iterations

Iter	Nodes
done	35
1	35
0	26

end0.0ms

sample2.0s

Algorithm

intervals

Results

704.0ms	1867×	body	640	valid
621.0ms	1187×	body	320	valid
421.0ms	4300×	body	80	valid
99.0ms	646×	body	160	valid