Details

sample534.0ms

Algorithm

intervals

Results

295.0ms	102×	body	2560	valid
112.0ms	78×	body	1280	valid
53.0ms	21×	body	320	valid
37.0ms	44×	body	640	valid
12.0ms	256×	pre	80	true
5.0ms	10×	body	160	valid
0.0ms	1×	body	80	valid

simplify6.0ms

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: 59.9b

localize10.0ms

Local error

Found 1 expressions with local error:

3.4b	(- (/ 1 x) (/ 1 (tan x)))

rewrite25.0ms

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:

20.0ms

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

series99.0ms

Counts

1 → 3

Calls

1 calls:

99.0ms

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

simplify989.0ms

Counts

230 → 230

Iterations

Iter	Nodes
done	2000
3	2000
2	1244
1	723
0	319

prune576.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma 2/945 (pow x 5) (fma 1/45 (* (* x x) x) (* x 1/3)))
0.0b	(fma 1/45 (* (* x x) x) (* x 1/3))
0.1b	(* (* x x) x)
0.3b	(* x 1/3)

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

25×	`pow1`
11×	`add-cbrt-cube` `add-exp-log`
10×	`add-sqr-sqrt`
7×	`*-un-lft-identity` `add-cube-cbrt`
6×	`pow-plus` `associate-r` `pow-prod-up`
4×	`expm1-log1p-u` `associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`pow2` `pow-sqr` `*-commutative` `fma-udef` `unswap-sqr`
1×	`pow3`

Counts

4 → 74

Calls

4 calls:

0.0ms	(fma 2/945 (pow x 5) (fma 1/45 (* (* x x) x) (* x 1/3)))
0.0ms	(fma 1/45 (* (* x x) x) (* x 1/3))
27.0ms	(* (* x x) x)
11.0ms	(* x 1/3)

series297.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(fma 2/945 (pow x 5) (fma 1/45 (* (* x x) x) (* x 1/3)))
142.0ms	(fma 1/45 (* (* x x) x) (* x 1/3))
47.0ms	(* (* x x) x)
26.0ms	(* x 1/3)

simplify960.0ms

Counts

86 → 86

Iterations

Iter	Nodes
done	2000
3	2000
2	636
1	222
0	96

prune339.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.2b

localize27.0ms

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)))
0.3b	(* x (fma (* x x) 1/45 1/3))

rewrite6.0ms

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)))
6.0ms	(* x (fma (* x x) 1/45 1/3))

series343.0ms

Counts

3 → 9

Calls

3 calls:

104.0ms	(fma (* x x) 1/45 1/3)
102.0ms	(fma 2/945 (pow x 5) (* x (fma (* x x) 1/45 1/3)))
137.0ms	(* x (fma (* x x) 1/45 1/3))

simplify1.3s

Counts

54 → 54

Iterations

Iter	Nodes
done	2023
4	2023
3	1659
2	374
1	142
0	69

prune296.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.2b

localize39.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt x) (cbrt x))
0.6b	(cbrt x)
0.6b	(cbrt x)
0.6b	(cbrt x)

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`*-un-lft-identity` `add-cube-cbrt`
11×	`pow1`
9×	`pow1/3`
6×	`swap-sqr` `associate-r` `associate-l` `add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `insert-posit16` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 85

Calls

4 calls:

15.0ms	(* (cbrt x) (cbrt x))
1.0ms	(cbrt x)
1.0ms	(cbrt x)
1.0ms	(cbrt x)

series1.1s

Counts

4 → 12

Calls

4 calls:

317.0ms	(* (cbrt x) (cbrt x))
260.0ms	(cbrt x)
245.0ms	(cbrt x)
315.0ms	(cbrt x)

simplify1.0s

Counts

97 → 97

Iterations

Iter	Nodes
done	2002
4	2002
3	1106
2	364
1	141
0	67

prune410.0ms

Pruning

16 alts after pruning (14 fresh and 2 done)

Merged error: 0.1b

regimes76.0ms

Accuracy

0% (0.2b remaining)

Error of 0.4b against oracle of 0.2b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Iterations

Iter	Nodes
done	13
1	13
0	11

end0.0ms

sample13.6s

Algorithm

intervals

Results

7.5s	3276×	body	2560	valid
3.6s	2552×	body	1280	valid
1.6s	1238×	body	640	valid
336.0ms	604×	body	320	valid
261.0ms	8000×	pre	80	true
91.0ms	290×	body	160	valid
7.0ms	40×	body	80	valid