Details

sample819.0ms

Algorithm

intervals

Results

345.0ms	65×	body	2560	valid
237.0ms	84×	body	1280	valid
58.0ms	56×	body	640	valid
19.0ms	27×	body	320	valid
8.0ms	17×	body	160	valid
2.0ms	7×	body	80	valid

simplify18.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	19
3	19
2	17
1	13
0	6

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.7b

localize16.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
2.0b	(- x (tan x))
2.0b	(- x (sin x))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

57×	`add-sqr-sqrt` `*-un-lft-identity`
29×	`add-cube-cbrt`
25×	`times-frac`
18×	`prod-diff`
14×	`distribute-lft-out--` `difference-of-squares`
7×	`add-log-exp`
6×	`fma-neg`
5×	`associate-/r` `add-cbrt-cube` `add-exp-log` `associate-/l`
4×	`flip3--` `flip--`
3×	`expm1-log1p-u` `pow1` `insert-posit16` `log1p-expm1-u`
2×	`sub-neg` `diff-log` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-sub` `div-exp` `div-inv`

Counts

3 → 113

Calls

3 calls:

18.0ms	(/ (- x (sin x)) (- x (tan x)))
5.0ms	(- x (tan x))
7.0ms	(- x (sin x))

series198.0ms

Counts

3 → 9

Calls

3 calls:

87.0ms	(/ (- x (sin x)) (- x (tan x)))
67.0ms	(- x (tan x))
44.0ms	(- x (sin x))

simplify1.2s

Counts

122 → 122

Iterations

Iter	Nodes
done	2007
3	2007
2	1279
1	504
0	212

prune481.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize17.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma 27/2800 (* (* x x) (* x x)) 1/2)
0.1b	(* (* x x) (* x x))
16.6b	(fma 9/40 (* x x) (- (fma 27/2800 (* (* x x) (* x x)) 1/2)))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

114×	`pow1`
36×	`pow-prod-up`
23×	`pow-prod-down`
22×	`pow-sqr`
18×	`pow-plus`
15×	`add-cbrt-cube` `add-exp-log`
13×	`pow2`
8×	`prod-exp` `cbrt-unprod`
3×	`add-sqr-sqrt` `expm1-log1p-u` `*-un-lft-identity` `add-cube-cbrt` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`fma-udef`
1×	`swap-sqr` `associate-r` `associate-l` `*-commutative` `unswap-sqr`

Counts

3 → 88

Calls

3 calls:

0.0ms	(fma 27/2800 (* (* x x) (* x x)) 1/2)
42.0ms	(* (* x x) (* x x))
0.0ms	(fma 9/40 (* x x) (- (fma 27/2800 (* (* x x) (* x x)) 1/2)))

series268.0ms

Counts

3 → 9

Calls

3 calls:

138.0ms	(fma 27/2800 (* (* x x) (* x x)) 1/2)
62.0ms	(* (* x x) (* x x))
68.0ms	(fma 9/40 (* x x) (- (fma 27/2800 (* (* x x) (* x x)) 1/2)))

simplify1.6s

Counts

97 → 97

Iterations

Iter	Nodes
done	2001
4	2001
3	1869
2	486
1	176
0	79

prune280.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize54.0ms

Local error

Found 4 expressions with local error:

2.0b	(- x (tan x))
2.0b	(- x (sin x))
2.0b	(- x (sin x))
2.0b	(- x (sin x))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

40×	`add-sqr-sqrt` `*-un-lft-identity`
36×	`prod-diff`
32×	`add-cube-cbrt`
12×	`fma-neg` `add-log-exp`
4×	`expm1-log1p-u` `pow1` `sub-neg` `flip3--` `add-cbrt-cube` `diff-log` `add-exp-log` `insert-posit16` `log1p-expm1-u` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 116

Calls

4 calls:

10.0ms	(- x (tan x))
12.0ms	(- x (sin x))
12.0ms	(- x (sin x))
12.0ms	(- x (sin x))

series249.0ms

Counts

4 → 12

Calls

4 calls:

74.0ms	(- x (tan x))
61.0ms	(- x (sin x))
43.0ms	(- x (sin x))
71.0ms	(- x (sin x))

simplify1.2s

Counts

128 → 128

Iterations

Iter	Nodes
done	2008
4	2008
3	1653
2	633
1	279
0	129

prune448.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes124.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 31.2b

bsearch223.0ms

Steps

Iters	Range		Point
10	3.4946005567744297e-15	48819.349325626084	0.025242037778536456
9	-6838974.188497498	-0.005838610583870787	-0.028431537088381868

simplify8.0ms

Iterations

Iter	Nodes
done	24
1	24
0	23

end0.0ms

sample16.7s

Algorithm

intervals

Results

7.7s	1668×	body	2560	valid
5.2s	2722×	body	1280	valid
2.5s	1894×	body	640	valid
720.0ms	905×	body	320	valid
265.0ms	484×	body	160	valid
124.0ms	327×	body	80	valid