Details

sample406.0ms

Algorithm

intervals

Results

276.0ms	105×	body	2560	valid
77.0ms	86×	body	1280	valid
20.0ms	35×	body	640	valid
13.0ms	256×	pre	80	true
7.0ms	18×	body	320	valid
3.0ms	11×	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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 59.9b

localize10.0ms

Local error

Found 1 expressions with local error:

3.0b	(- (/ 1 x) (/ 1 (tan x)))

rewrite123.0ms

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:

98.0ms

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

series122.0ms

Counts

1 → 3

Calls

1 calls:

122.0ms

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

simplify2.8s

Counts

230 → 230

Iterations

Iter	Nodes
done	5001
3	2848
2	1244
1	723
0	319

prune445.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize31.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma (* x x) 1/45 1/3)
0.1b	(* (pow x 5) 2/945)
0.4b	(fma x (fma (* x x) 1/45 1/3) (* (pow x 5) 2/945))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 50

Calls

3 calls:

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

series228.0ms

Counts

3 → 9

Calls

3 calls:

73.0ms	(fma (* x x) 1/45 1/3)
71.0ms	(* (pow x 5) 2/945)
84.0ms	(fma x (fma (* x x) 1/45 1/3) (* (pow x 5) 2/945))

simplify1.8s

Counts

59 → 59

Iterations

Iter	Nodes
done	5001
3	1684
2	433
1	169
0	87

prune199.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.3b

localize30.0ms

Local error

Found 4 expressions with local error:

0.6b	(* (cbrt (fma x (fma (* x x) 1/45 1/3) (* (pow x 5) 2/945))) (cbrt (fma x (fma (* x x) 1/45 1/3) (* (pow x 5) 2/945))))
0.7b	(cbrt (fma x (fma (* x x) 1/45 1/3) (* (pow x 5) 2/945)))
0.7b	(cbrt (fma x (fma (* x x) 1/45 1/3) (* (pow x 5) 2/945)))
0.7b	(cbrt (fma x (fma (* x x) 1/45 1/3) (* (pow x 5) 2/945)))

rewrite16.0ms

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:

11.0ms	(* (cbrt (fma x (fma (* x x) 1/45 1/3) (* (pow x 5) 2/945))) (cbrt (fma x (fma (* x x) 1/45 1/3) (* (pow x 5) 2/945))))
1.0ms	(cbrt (fma x (fma (* x x) 1/45 1/3) (* (pow x 5) 2/945)))
1.0ms	(cbrt (fma x (fma (* x x) 1/45 1/3) (* (pow x 5) 2/945)))
1.0ms	(cbrt (fma x (fma (* x x) 1/45 1/3) (* (pow x 5) 2/945)))

series788.0ms

Counts

4 → 12

Calls

4 calls:

258.0ms	(* (cbrt (fma x (fma (* x x) 1/45 1/3) (* (pow x 5) 2/945))) (cbrt (fma x (fma (* x x) 1/45 1/3) (* (pow x 5) 2/945))))
153.0ms	(cbrt (fma x (fma (* x x) 1/45 1/3) (* (pow x 5) 2/945)))
202.0ms	(cbrt (fma x (fma (* x x) 1/45 1/3) (* (pow x 5) 2/945)))
174.0ms	(cbrt (fma x (fma (* x x) 1/45 1/3) (* (pow x 5) 2/945)))

simplify1.9s

Counts

97 → 97

Iterations

Iter	Nodes
done	5000
3	2118
2	729
1	317
0	142

prune597.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 0.2b

localize69.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
0.6b	(cbrt x)
0.7b	(cbrt (fma x (fma (* x x) 1/45 1/3) (* (pow x 5) 2/945)))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

12×	`cbrt-prod`
8×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `pow1/3` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`

Counts

4 → 56

Calls

4 calls:

1.0ms	(cbrt x)
1.0ms	(cbrt x)
1.0ms	(cbrt x)
2.0ms	(cbrt (fma x (fma (* x x) 1/45 1/3) (* (pow x 5) 2/945)))

series958.0ms

Counts

4 → 12

Calls

4 calls:

262.0ms	(cbrt x)
265.0ms	(cbrt x)
214.0ms	(cbrt x)
217.0ms	(cbrt (fma x (fma (* x x) 1/45 1/3) (* (pow x 5) 2/945)))

simplify2.2s

Counts

68 → 68

Iterations

Iter	Nodes
done	5000
4	4687
3	1295
2	416
1	189
0	93

prune553.0ms

Pruning

16 alts after pruning (14 fresh and 2 done)

Merged error: 0.2b

regimes141.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.2b and baseline of 0.3b

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	11
1	11
0	10

end0.0ms

sample12.7s

Algorithm

intervals

Results

8.1s	3269×	body	2560	valid
2.7s	2518×	body	1280	valid
1.2s	1232×	body	640	valid
274.0ms	8000×	pre	80	true
207.0ms	623×	body	320	valid
70.0ms	325×	body	160	valid
4.0ms	33×	body	80	valid