Details

sample392.0ms

Algorithm

intervals

Results

251.0ms	103×	body	2560	valid
85.0ms	79×	body	1280	valid
22.0ms	42×	body	640	valid
6.0ms	17×	body	320	valid
5.0ms	256×	pre	80	true
3.0ms	11×	body	160	valid
0.0ms	4×	body	80	valid

simplify9.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	11
2	11
1	8
0	6

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 59.4b

localize17.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ 1.0 (tan x))
2.9b	(- (/ 1.0 x) (/ 1.0 (tan x)))

rewrite115.0ms

Algorithm

rewrite-expression-head

Rules

271×	`times-frac`
220×	`add-sqr-sqrt`
216×	`*-un-lft-identity`
208×	`add-cube-cbrt`
182×	`prod-diff`
31×	`div-inv`
14×	`tan-quot` `associate-/r/`
13×	`fma-neg`
5×	`distribute-lft-out--`
4×	`add-cbrt-cube` `add-exp-log` `add-log-exp` `difference-of-squares`
3×	`associate-/r` `associate-/l`
2×	`expm1-log1p-u` `pow1` `log1p-expm1-u`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `flip3--` `diff-log` `div-exp` `frac-sub` `flip--`

Counts

2 → 249

Calls

2 calls:

6.0ms	(/ 1.0 (tan x))
80.0ms	(- (/ 1.0 x) (/ 1.0 (tan x)))

series188.0ms

Counts

2 → 6

Calls

2 calls:

53.0ms	(/ 1.0 (tan x))
135.0ms	(- (/ 1.0 x) (/ 1.0 (tan x)))

simplify1.9s

Counts

255 → 255

Iterations

Iter	Nodes
done	5001
2	2774
1	843
0	369

prune767.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.4b

localize27.0ms

Local error

Found 2 expressions with local error:

0.0b	(fma 0.022222222222222223 (pow x 3) (* 0.3333333333333333 x))
0.0b	(fma 0.0021164021164021165 (pow x 5) (fma 0.022222222222222223 (pow x 3) (* 0.3333333333333333 x)))

rewrite2.0ms

Algorithm

rewrite-expression-head

Rules

2×	`add-sqr-sqrt` `expm1-log1p-u` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `fma-udef` `log1p-expm1-u` `add-log-exp`

Counts

2 → 20

Calls

2 calls:

0.0ms	(fma 0.022222222222222223 (pow x 3) (* 0.3333333333333333 x))
1.0ms	(fma 0.0021164021164021165 (pow x 5) (fma 0.022222222222222223 (pow x 3) (* 0.3333333333333333 x)))

series218.0ms

Counts

2 → 6

Calls

2 calls:

124.0ms	(fma 0.022222222222222223 (pow x 3) (* 0.3333333333333333 x))
93.0ms	(fma 0.0021164021164021165 (pow x 5) (fma 0.022222222222222223 (pow x 3) (* 0.3333333333333333 x)))

simplify3.4s

Counts

26 → 26

Iterations

Iter	Nodes
done	5000
4	4787
3	744
2	165
1	61
0	34

prune190.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.3b

localize16.0ms

Local error

Found 1 expressions with local error:

0.0b	(fma 0.0021164021164021165 (pow x 5) (* x (fma (* x x) 0.022222222222222223 0.3333333333333333)))

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

1×	`add-sqr-sqrt` `expm1-log1p-u` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `fma-udef` `log1p-expm1-u` `add-log-exp`

Counts

1 → 10

Calls

1 calls:

1.0ms

(fma 0.0021164021164021165 (pow x 5) (* x (fma (* x x) 0.022222222222222223 0.3333333333333333)))

series88.0ms

Counts

1 → 3

Calls

1 calls:

88.0ms

(fma 0.0021164021164021165 (pow x 5) (* x (fma (* x x) 0.022222222222222223 0.3333333333333333)))

simplify2.6s

Counts

13 → 13

Iterations

Iter	Nodes
done	5000
4	3679
3	488
2	117
1	51
0	26

prune118.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.3b

localize25.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (* x (fma (* x x) 0.022222222222222223 0.3333333333333333))) (cbrt (* x (fma (* x x) 0.022222222222222223 0.3333333333333333))))
0.6b	(cbrt (* x (fma (* x x) 0.022222222222222223 0.3333333333333333)))
0.6b	(cbrt (* x (fma (* x x) 0.022222222222222223 0.3333333333333333)))
0.6b	(cbrt (* x (fma (* x x) 0.022222222222222223 0.3333333333333333)))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 66

Calls

4 calls:

11.0ms	(* (cbrt (* x (fma (* x x) 0.022222222222222223 0.3333333333333333))) (cbrt (* x (fma (* x x) 0.022222222222222223 0.3333333333333333))))
3.0ms	(cbrt (* x (fma (* x x) 0.022222222222222223 0.3333333333333333)))
3.0ms	(cbrt (* x (fma (* x x) 0.022222222222222223 0.3333333333333333)))
3.0ms	(cbrt (* x (fma (* x x) 0.022222222222222223 0.3333333333333333)))

series1.5s

Counts

4 → 12

Calls

4 calls:

437.0ms	(* (cbrt (* x (fma (* x x) 0.022222222222222223 0.3333333333333333))) (cbrt (* x (fma (* x x) 0.022222222222222223 0.3333333333333333))))
374.0ms	(cbrt (* x (fma (* x x) 0.022222222222222223 0.3333333333333333)))
336.0ms	(cbrt (* x (fma (* x x) 0.022222222222222223 0.3333333333333333)))
321.0ms	(cbrt (* x (fma (* x x) 0.022222222222222223 0.3333333333333333)))

simplify864.0ms

Counts

78 → 78

Iterations

Iter	Nodes
done	5000
2	1915
1	443
0	164

prune736.0ms

Pruning

16 alts after pruning (14 fresh and 2 done)

Merged error: 0.2b

regimes145.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Iter	Nodes
done	11
1	11
0	10

end0.0ms

sample12.4s

Algorithm

intervals

Results

8.3s	3279×	body	2560	valid
2.5s	2515×	body	1280	valid
628.0ms	1225×	body	640	valid
330.0ms	8000×	pre	80	true
230.0ms	632×	body	320	valid
106.0ms	300×	body	160	valid
5.0ms	49×	body	80	valid