Details

sample545.0ms

Algorithm

intervals

Results

363.0ms	115×	body	2560	valid
109.0ms	75×	body	1280	valid
36.0ms	43×	body	640	valid
12.0ms	256×	pre	80	true
10.0ms	16×	body	320	valid
3.0ms	6×	body	160	valid
0.0ms	1×	body	80	valid

simplify5.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	14
2	14
1	10
0	6

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 60.0b

localize10.0ms

Local error

Found 1 expressions with local error:

1.6b	(- (/ 1 x) (/ 1 (tan x)))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

270×	`times-frac`
223×	`add-sqr-sqrt`
215×	`*-un-lft-identity`
199×	`add-cube-cbrt`
182×	`prod-diff`
32×	`div-inv`
13×	`fma-neg` `tan-quot` `associate-/r/`
9×	`difference-of-squares`
7×	`distribute-lft-out--`
3×	`add-log-exp`
1×	`expm1-log1p-u` `pow1` `sub-neg` `flip3--` `add-cbrt-cube` `diff-log` `add-exp-log` `frac-sub` `insert-posit16` `log1p-expm1-u` `flip--`

Counts

1 → 227

Calls

1 calls:

40.0ms

(- (/ 1 x) (/ 1 (tan x)))

series416.0ms

Counts

1 → 3

Calls

1 calls:

416.0ms

(- (/ 1 x) (/ 1 (tan x)))

simplify2.8s

Counts

230 → 230

Iterations

Iter	Nodes
done	5022
3	2953
2	1271
1	723
0	319

prune330.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize34.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma (* x x) 1/45 1/3)
0.0b	(fma 2/945 (pow x 5) (* x (fma (* x x) 1/45 1/3)))
0.4b	(* x (fma (* x x) 1/45 1/3))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

7×	`add-sqr-sqrt`
5×	`pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
4×	`fma-udef`
3×	`expm1-log1p-u` `associate-r` `associate-l` `insert-posit16` `log1p-expm1-u` `add-log-exp`
1×	`distribute-rgt-in` `distribute-lft-in` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

3 → 45

Calls

3 calls:

0.0ms	(fma (* x x) 1/45 1/3)
0.0ms	(fma 2/945 (pow x 5) (* x (fma (* x x) 1/45 1/3)))
12.0ms	(* x (fma (* x x) 1/45 1/3))

series312.0ms

Counts

3 → 9

Calls

3 calls:

99.0ms	(fma (* x x) 1/45 1/3)
74.0ms	(fma 2/945 (pow x 5) (* x (fma (* x x) 1/45 1/3)))
139.0ms	(* x (fma (* x x) 1/45 1/3))

simplify1.9s

Counts

54 → 54

Iterations

Iter	Nodes
done	5009
3	1797
2	412
1	142
0	69

prune279.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.2b

localize34.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (fma (* x x) 1/45 1/3))
0.0b	(sqrt (fma (* x x) 1/45 1/3))
0.4b	(* (* x (sqrt (fma (* x x) 1/45 1/3))) (sqrt (fma (* x x) 1/45 1/3)))
0.4b	(* x (sqrt (fma (* x x) 1/45 1/3)))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt`
13×	`pow1` `sqrt-prod`
12×	`associate-r`
11×	`*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
4×	`expm1-log1p-u` `associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `*-commutative` `unswap-sqr`

Counts

4 → 81

Calls

4 calls:

2.0ms	(sqrt (fma (* x x) 1/45 1/3))
2.0ms	(sqrt (fma (* x x) 1/45 1/3))
35.0ms	(* (* x (sqrt (fma (* x x) 1/45 1/3))) (sqrt (fma (* x x) 1/45 1/3)))
11.0ms	(* x (sqrt (fma (* x x) 1/45 1/3)))

series449.0ms

Counts

4 → 12

Calls

4 calls:

75.0ms	(sqrt (fma (* x x) 1/45 1/3))
75.0ms	(sqrt (fma (* x x) 1/45 1/3))
121.0ms	(* (* x (sqrt (fma (* x x) 1/45 1/3))) (sqrt (fma (* x x) 1/45 1/3)))
177.0ms	(* x (sqrt (fma (* x x) 1/45 1/3)))

simplify2.4s

Counts

93 → 93

Iterations

Iter	Nodes
done	5000
3	4340
2	1092
1	303
0	118

prune451.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.1b

localize40.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (sqrt (fma (* x x) 1/45 1/3)))
0.3b	(* (* (* x (sqrt (fma (* x x) 1/45 1/3))) (sqrt (sqrt (fma (* x x) 1/45 1/3)))) (sqrt (sqrt (fma (* x x) 1/45 1/3))))
0.3b	(* (* x (sqrt (fma (* x x) 1/45 1/3))) (sqrt (sqrt (fma (* x x) 1/45 1/3))))
0.4b	(* x (sqrt (fma (* x x) 1/45 1/3)))

rewrite126.0ms

Algorithm

rewrite-expression-head

Rules

32×	`sqrt-prod`
24×	`associate-r`
22×	`pow1`
21×	`add-sqr-sqrt`
20×	`add-cbrt-cube` `add-exp-log`
15×	`*-un-lft-identity` `add-cube-cbrt`
10×	`pow-prod-down` `prod-exp` `cbrt-unprod`
5×	`associate-l`
4×	`expm1-log1p-u` `sqrt-pow1` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`*-commutative`
2×	`rem-sqrt-square` `pow1/2` `unswap-sqr`

Counts

4 → 104

Calls

4 calls:

2.0ms	(sqrt (sqrt (fma (* x x) 1/45 1/3)))
75.0ms	(* (* (* x (sqrt (fma (* x x) 1/45 1/3))) (sqrt (sqrt (fma (* x x) 1/45 1/3)))) (sqrt (sqrt (fma (* x x) 1/45 1/3))))
40.0ms	(* (* x (sqrt (fma (* x x) 1/45 1/3))) (sqrt (sqrt (fma (* x x) 1/45 1/3))))
8.0ms	(* x (sqrt (fma (* x x) 1/45 1/3)))

series699.0ms

Counts

4 → 12

Calls

4 calls:

137.0ms	(sqrt (sqrt (fma (* x x) 1/45 1/3)))
143.0ms	(* (* (* x (sqrt (fma (* x x) 1/45 1/3))) (sqrt (sqrt (fma (* x x) 1/45 1/3)))) (sqrt (sqrt (fma (* x x) 1/45 1/3))))
272.0ms	(* (* x (sqrt (fma (* x x) 1/45 1/3))) (sqrt (sqrt (fma (* x x) 1/45 1/3))))
146.0ms	(* x (sqrt (fma (* x x) 1/45 1/3)))

simplify1.8s

Counts

116 → 116

Iterations

Iter	Nodes
done	5000
2	2040
1	550
0	218

prune581.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

regimes48.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify5.0ms

Iterations

Iter	Nodes
done	20
1	20
0	16

end0.0ms

sample16.8s

Algorithm

intervals

Results

9.1s	3223×	body	2560	valid
4.9s	2521×	body	1280	valid
1.6s	1251×	body	640	valid
432.0ms	655×	body	320	valid
330.0ms	8000×	pre	80	true
142.0ms	308×	body	160	valid
9.0ms	42×	body	80	valid