Details

sample601.0ms

Algorithm

intervals

Results

217.0ms	49×	body	2560	valid
142.0ms	79×	body	1280	valid
107.0ms	72×	body	640	valid
19.0ms	30×	body	320	valid
7.0ms	13×	body	160	valid
4.0ms	13×	body	80	valid

simplify74.0ms

Counts

1 → 1

Iterations

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

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.7b

localize34.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
0.9b	(- x (tan x))
0.9b	(- x (sin x))

rewrite64.0ms

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:

36.0ms	(/ (- x (sin x)) (- x (tan x)))
10.0ms	(- x (tan x))
15.0ms	(- x (sin x))

series261.0ms

Counts

3 → 9

Calls

3 calls:

122.0ms	(/ (- x (sin x)) (- x (tan x)))
75.0ms	(- x (tan x))
64.0ms	(- x (sin x))

simplify3.3s

Counts

122 → 122

Iterations

Iter	Nodes
done	5000
3	4741
2	1279
1	504
0	212

prune418.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sin x) (- x (tan x)))
0.4b	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
0.9b	(- x (tan x))
0.9b	(- x (tan x))

rewrite183.0ms

Algorithm

rewrite-expression-head

Rules

713×	`*-un-lft-identity`
703×	`add-sqr-sqrt`
678×	`times-frac`
459×	`prod-diff`
417×	`add-cube-cbrt`
147×	`distribute-lft-out--`
141×	`difference-of-squares`
92×	`associate-/r/`
49×	`flip3--` `flip--`
46×	`div-inv`
27×	`fma-neg`
10×	`add-log-exp`
6×	`add-cbrt-cube` `add-exp-log`
5×	`associate-/r*`
4×	`expm1-log1p-u` `pow1` `insert-posit16` `log1p-expm1-u`
3×	`sub-neg` `distribute-rgt-out--` `diff-log` `associate-/l*`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `frac-sub` `sub-div`

Counts

4 → 592

Calls

4 calls:

24.0ms	(/ (sin x) (- x (tan x)))
107.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
10.0ms	(- x (tan x))
10.0ms	(- x (tan x))

series497.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(/ (sin x) (- x (tan x)))
266.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
67.0ms	(- x (tan x))
81.0ms	(- x (tan x))

simplify2.3s

Counts

604 → 604

Iterations

Iter	Nodes
done	5000
2	3356
1	1405
0	620

prune2.5s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize47.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sin x) (- x (tan x)))
0.4b	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
0.9b	(- x (tan x))
0.9b	(- x (tan x))

rewrite139.0ms

Algorithm

rewrite-expression-head

Rules

713×	`*-un-lft-identity`
703×	`add-sqr-sqrt`
678×	`times-frac`
459×	`prod-diff`
417×	`add-cube-cbrt`
147×	`distribute-lft-out--`
141×	`difference-of-squares`
92×	`associate-/r/`
49×	`flip3--` `flip--`
46×	`div-inv`
27×	`fma-neg`
10×	`add-log-exp`
6×	`add-cbrt-cube` `add-exp-log`
5×	`associate-/r*`
4×	`expm1-log1p-u` `pow1` `insert-posit16` `log1p-expm1-u`
3×	`sub-neg` `distribute-rgt-out--` `diff-log` `associate-/l*`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `frac-sub` `sub-div`

Counts

4 → 592

Calls

4 calls:

19.0ms	(/ (sin x) (- x (tan x)))
89.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
5.0ms	(- x (tan x))
5.0ms	(- x (tan x))

series499.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(/ (sin x) (- x (tan x)))
256.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
106.0ms	(- x (tan x))
68.0ms	(- x (tan x))

simplify2.6s

Counts

604 → 604

Iterations

Iter	Nodes
done	5000
2	3356
1	1405
0	620

prune3.0s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize48.0ms

Local error

Found 4 expressions with local error:

0.5b	(- (/ (/ (sin x) (cos x)) x) (fma (/ (sin x) (* x x)) (/ (sin x) (cos x)) (/ (sin x) x)))
13.9b	(/ (sin x) (* x x))
13.9b	(/ (sin x) (* x x))
30.0b	(fma (/ (sin x) (* (cos x) (cos x))) (/ (sin x) (* x x)) (- (/ (/ (sin x) (cos x)) x) (fma (/ (sin x) (* x x)) (/ (sin x) (cos x)) (/ (sin x) x))))

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

273×	`times-frac`
200×	`add-sqr-sqrt`
193×	`*-un-lft-identity`
191×	`add-cube-cbrt`
129×	`prod-diff`
43×	`fma-neg`
18×	`div-inv`
14×	`add-cbrt-cube` `add-exp-log`
6×	`associate-/l*` `add-log-exp`
4×	`expm1-log1p-u` `pow1` `cbrt-undiv` `div-exp` `insert-posit16` `log1p-expm1-u`
3×	`difference-of-squares`
2×	`clear-num` `associate-/r*` `frac-2neg` `prod-exp` `cbrt-unprod` `fma-udef`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `associate--r+` `distribute-lft-out--`

Counts

4 → 251

Calls

4 calls:

28.0ms	(- (/ (/ (sin x) (cos x)) x) (fma (/ (sin x) (* x x)) (/ (sin x) (cos x)) (/ (sin x) x)))
21.0ms	(/ (sin x) (* x x))
19.0ms	(/ (sin x) (* x x))
0.0ms	(fma (/ (sin x) (* (cos x) (cos x))) (/ (sin x) (* x x)) (- (/ (/ (sin x) (cos x)) x) (fma (/ (sin x) (* x x)) (/ (sin x) (cos x)) (/ (sin x) x))))

series795.0ms

Counts

4 → 12

Calls

4 calls:

207.0ms	(- (/ (/ (sin x) (cos x)) x) (fma (/ (sin x) (* x x)) (/ (sin x) (cos x)) (/ (sin x) x)))
35.0ms	(/ (sin x) (* x x))
48.0ms	(/ (sin x) (* x x))
504.0ms	(fma (/ (sin x) (* (cos x) (cos x))) (/ (sin x) (* x x)) (- (/ (/ (sin x) (cos x)) x) (fma (/ (sin x) (* x x)) (/ (sin x) (cos x)) (/ (sin x) x))))

simplify2.4s

Counts

263 → 263

Iterations

Iter	Nodes
done	5000
2	2415
1	846
0	376

prune1.9s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

regimes62.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 31.9b

bsearch185.0ms

Steps

Iters	Range		Point
10	2.618543036730298e-08	12461.173664998358	0.029925645760154832
9	-101227.54480913779	-5.532094628653386e-05	-0.02697179057437607

simplify9.0ms

Iterations

Iter	Nodes
done	28
1	28
0	23

end0.0ms

sample14.5s

Algorithm

intervals

Results

6.2s	1612×	body	2560	valid
4.6s	2679×	body	1280	valid
2.1s	1843×	body	640	valid
971.0ms	985×	body	320	valid
243.0ms	503×	body	160	valid
146.0ms	378×	body	80	valid