Details

sample469.0ms

Algorithm

intervals

Results

125.0ms	54×	body	2560	valid
54.0ms	86×	body	1280	valid
23.0ms	67×	body	640	valid
6.0ms	28×	body	320	valid
2.0ms	14×	body	160	valid
1.0ms	7×	body	80	valid

simplify15.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	6	9
1	13	9
2	17	9
3	19	9
done	19	9

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.9b

localize22.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
0.8b	(- x (sin x))
0.8b	(- x (tan x))

rewrite27.0ms

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×	`add-exp-log` `associate-/r` `add-cbrt-cube` `associate-/l`
4×	`flip3--` `flip--`
3×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
2×	`sub-neg` `diff-log` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

3 → 110

Calls

3 calls:

13.0ms	(/ (- x (sin x)) (- x (tan x)))
4.0ms	(- x (sin x))
5.0ms	(- x (tan x))

series175.0ms

Counts

3 → 9

Calls

3 calls:

76.0ms	(/ (- x (sin x)) (- x (tan x)))
31.0ms	(- x (sin x))
68.0ms	(- x (tan x))

simplify674.0ms

Counts

119 → 119

Iterations

Useful iterations: 2 (302.0ms)

Iter	Nodes	Cost
0	209	1823
1	468	1563
2	1408	1384
done	5001	1384

prune239.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma 27/2800 (pow x 4) 1/2)
0.1b	(* 9/40 (pow x 2))
16.6b	(- (* 9/40 (pow x 2)) (fma 27/2800 (pow x 4) 1/2))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt`
8×	`add-exp-log` `associate-r`
7×	`add-cube-cbrt` `*-un-lft-identity`
5×	`add-cbrt-cube` `add-log-exp`
4×	`unpow-prod-down` `unswap-sqr`
3×	`pow1` `expm1-log1p-u` `associate-l` `prod-diff` `prod-exp` `log1p-expm1-u`
2×	`fma-udef` `unpow2` `sqr-pow`
1×	`pow-to-exp` `sub-neg` `flip3--` `fma-neg` `diff-log` `pow-exp` `*-commutative` `flip--` `cbrt-unprod` `associate--r+`

Counts

3 → 58

Calls

3 calls:

0.0ms	(fma 27/2800 (pow x 4) 1/2)
6.0ms	(* 9/40 (pow x 2))
4.0ms	(- (* 9/40 (pow x 2)) (fma 27/2800 (pow x 4) 1/2))

series160.0ms

Counts

3 → 9

Calls

3 calls:

85.0ms	(fma 27/2800 (pow x 4) 1/2)
30.0ms	(* 9/40 (pow x 2))
45.0ms	(- (* 9/40 (pow x 2)) (fma 27/2800 (pow x 4) 1/2))

simplify1.5s

Counts

67 → 67

Iterations

Useful iterations: 3 (544.0ms)

Iter	Nodes	Cost
0	106	845
1	219	700
2	644	642
3	2833	594
done	5000	594

prune154.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (tan x))
0.3b	(- (sqrt x) (sqrt (tan x)))
0.8b	(- x (sin x))
0.8b	(- x (sin x))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

58×	`add-sqr-sqrt`
54×	`prod-diff`
53×	`*-un-lft-identity`
48×	`sqrt-prod`
45×	`add-cube-cbrt`
12×	`fma-neg`
10×	`add-log-exp`
6×	`difference-of-squares`
5×	`pow1`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `distribute-lft-out--`
3×	`sub-neg` `flip3--` `diff-log` `flip--`
1×	`tan-quot` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `sqrt-div`

Counts

4 → 134

Calls

4 calls:

1.0ms	(sqrt (tan x))
8.0ms	(- (sqrt x) (sqrt (tan x)))
3.0ms	(- x (sin x))
4.0ms	(- x (sin x))

series151.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(sqrt (tan x))
51.0ms	(- (sqrt x) (sqrt (tan x)))
37.0ms	(- x (sin x))
31.0ms	(- x (sin x))

simplify1.4s

Counts

146 → 146

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	181	2613
1	366	1807
2	880	1410
3	2997	1348
done	5000	1340

prune345.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes51.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 31.3b

bsearch91.0ms

Steps

Iters	Range		Point
10	3.2824798326487284e-15	0.08347146558812443	0.02869830051678616
9	-5.7596417613087905	-6.7357437175194845e-09	-0.026775790768781334

simplify3.0ms

Iterations

Useful iterations: 1 (1.0ms)

Iter	Nodes	Cost
0	22	38
1	26	30
done	26	30

end0.0ms

sample6.5s

Algorithm

intervals

Results

3.4s	1574×	body	2560	valid
1.9s	2759×	body	1280	valid
665.0ms	1927×	body	640	valid
239.0ms	930×	body	320	valid
72.0ms	457×	body	160	valid
32.0ms	353×	body	80	valid