Details

sample824.0ms

Algorithm

intervals

Results

370.0ms	57×	body	2560	valid
181.0ms	85×	body	1280	valid
61.0ms	66×	body	640	valid
40.0ms	14×	body	160	valid
36.0ms	6×	body	80	valid
16.0ms	28×	body	320	valid

simplify414.0ms

Counts

1 → 1

Iterations

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

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.5b

localize38.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
2.3b	(- x (tan x))
2.4b	(- x (sin x))

rewrite109.0ms

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:

68.0ms	(/ (- x (sin x)) (- x (tan x)))
13.0ms	(- x (tan x))
19.0ms	(- x (sin x))

series263.0ms

Counts

3 → 9

Calls

3 calls:

135.0ms	(/ (- x (sin x)) (- x (tan x)))
75.0ms	(- x (tan x))
53.0ms	(- x (sin x))

simplify2.7s

Counts

122 → 122

Iterations

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

prune476.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma (* x x) 9/40 -1/2)
0.1b	(* (* x x) (* x x))
0.1b	(* -27/2800 (* (* x x) (* x x)))
13.8b	(+ (fma (* x x) 9/40 -1/2) (* -27/2800 (* (* x x) (* x x))))

rewrite184.0ms

Algorithm

rewrite-expression-head

Rules

133×	`pow1`
36×	`pow-prod-down` `pow-prod-up`
34×	`add-cbrt-cube` `add-exp-log`
22×	`pow-sqr`
21×	`prod-exp` `cbrt-unprod`
18×	`pow-plus`
13×	`pow2`
7×	`add-sqr-sqrt`
6×	`*-un-lft-identity` `add-cube-cbrt` `add-log-exp`
4×	`expm1-log1p-u` `associate-l` `insert-posit16` `log1p-expm1-u`
3×	`fma-def`
2×	`associate-r` `*-commutative` `fma-udef` `unswap-sqr`
1×	`+-commutative` `associate-+l+` `sum-log` `flip3-+` `swap-sqr` `flip-+`

Counts

4 → 126

Calls

4 calls:

1.0ms	(fma (* x x) 9/40 -1/2)
41.0ms	(* (* x x) (* x x))
123.0ms	(* -27/2800 (* (* x x) (* x x)))
11.0ms	(+ (fma (* x x) 9/40 -1/2) (* -27/2800 (* (* x x) (* x x))))

series257.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(fma (* x x) 9/40 -1/2)
61.0ms	(* (* x x) (* x x))
54.0ms	(* -27/2800 (* (* x x) (* x x)))
84.0ms	(+ (fma (* x x) 9/40 -1/2) (* -27/2800 (* (* x x) (* x x))))

simplify1.4s

Counts

138 → 138

Iterations

Iter	Nodes
done	5000
2	1188
1	336
0	122

prune406.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sin x) (- x (tan x)))
1.9b	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
2.3b	(- x (tan x))
2.3b	(- x (tan x))

rewrite248.0ms

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:

30.0ms	(/ (sin x) (- x (tan x)))
149.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
7.0ms	(- x (tan x))
7.0ms	(- x (tan x))

series560.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(/ (sin x) (- x (tan x)))
289.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
80.0ms	(- x (tan x))
100.0ms	(- x (tan x))

simplify2.7s

Counts

604 → 604

Iterations

Iter	Nodes
done	5000
2	3356
1	1405
0	620

prune2.5s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize84.0ms

Local error

Found 4 expressions with local error:

0.4b	(- (/ (/ (sin x) (cos x)) x) (fma (/ (sin x) (* x x)) (/ (sin x) (cos x)) (/ (sin x) x)))
17.2b	(/ (sin x) (* x x))
17.2b	(/ (sin x) (* x x))
35.4b	(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))))

rewrite142.0ms

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:

83.0ms	(- (/ (/ (sin x) (cos x)) x) (fma (/ (sin x) (* x x)) (/ (sin x) (cos x)) (/ (sin x) x)))
24.0ms	(/ (sin x) (* x x))
23.0ms	(/ (sin x) (* x x))
1.0ms	(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))))

series823.0ms

Counts

4 → 12

Calls

4 calls:

224.0ms	(- (/ (/ (sin x) (cos x)) x) (fma (/ (sin x) (* x x)) (/ (sin x) (cos x)) (/ (sin x) x)))
58.0ms	(/ (sin x) (* x x))
63.0ms	(/ (sin x) (* x x))
478.0ms	(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))))

simplify2.3s

Counts

263 → 263

Iterations

Iter	Nodes
done	5000
2	2415
1	846
0	376

prune1.9s

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes36.0ms

Accuracy

100% (0.0b remaining)

Error of 0.3b against oracle of 0.3b and baseline of 31.6b

bsearch178.0ms

Steps

Iters	Range		Point
10	1.508099977930646e-06	2590629949647.022	2.4087276690935244
10	-26711381.42537418	-6.803810524357175e-07	-2.4752504163968116

simplify6.0ms

Iterations

Iter	Nodes
done	36
1	36
0	28

end0.0ms

sample12.8s

Algorithm

intervals

Results

5.6s	1608×	body	2560	valid
4.3s	2728×	body	1280	valid
1.9s	1901×	body	640	valid
500.0ms	933×	body	320	valid
132.0ms	469×	body	160	valid
113.0ms	361×	body	80	valid