Details

sample532.0ms

Algorithm

intervals

Results

255.0ms	57×	body	2560	valid
122.0ms	85×	body	1280	valid
47.0ms	66×	body	640	valid
14.0ms	28×	body	320	valid
5.0ms	14×	body	160	valid
3.0ms	6×	body	80	valid

simplify51.0ms

Counts

1 → 1

Iterations

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

prune18.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.7b

localize52.0ms

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))

rewrite107.0ms

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)))
9.0ms	(- x (tan x))
13.0ms	(- x (sin x))

series384.0ms

Counts

3 → 9

Calls

3 calls:

157.0ms	(/ (- x (sin x)) (- x (tan x)))
142.0ms	(- x (tan x))
84.0ms	(- x (sin x))

simplify7.2s

Counts

122 → 122

Iterations

Iter	Nodes
done	5000
3	4764
2	1272
1	503
0	212

prune882.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize48.0ms

Local error

Found 3 expressions with local error:

0.1b	(* (* x x) (* x x))
0.1b	(* (* (* x x) (* x x)) -27/2800)
13.9b	(fma (* x x) 9/40 (* (* (* x x) (* x x)) -27/2800))

rewrite254.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 108

Calls

3 calls:

46.0ms	(* (* x x) (* x x))
197.0ms	(* (* (* x x) (* x x)) -27/2800)
2.0ms	(fma (* x x) 9/40 (* (* (* x x) (* x x)) -27/2800))

series257.0ms

Counts

3 → 9

Calls

3 calls:

65.0ms	(* (* x x) (* x x))
58.0ms	(* (* (* x x) (* x x)) -27/2800)
134.0ms	(fma (* x x) 9/40 (* (* (* x x) (* x x)) -27/2800))

simplify5.3s

Counts

117 → 117

Iterations

Iter	Nodes
done	5002
3	2492
2	753
1	289
0	98

prune486.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize118.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sin x) (* (cos x) (cos x)))
0.2b	(* (cos x) (cos x))
0.4b	(- (/ (/ (sin x) x) (cos x)) (fma (/ (/ (sin x) x) x) (/ (sin x) (cos x)) (/ (sin x) x)))
2.3b	(+ 1 (- (/ (/ (sin x) x) (cos x)) (fma (/ (/ (sin x) x) x) (/ (sin x) (cos x)) (/ (sin x) x))))

rewrite511.0ms

Algorithm

rewrite-expression-head

Rules

468×	`times-frac`
353×	`add-sqr-sqrt`
349×	`*-un-lft-identity`
342×	`add-cube-cbrt`
258×	`prod-diff`
131×	`associate-+r+`
43×	`fma-neg`
29×	`div-inv`
11×	`pow1` `add-cbrt-cube` `add-exp-log` `add-log-exp`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`fma-def` `swap-sqr` `associate-r` `associate-l` `associate-/l*` `difference-of-squares`
2×	`cbrt-undiv` `sum-log` `sub-neg` `diff-log` `div-exp` `prod-exp` `cos-mult` `cbrt-unprod` `distribute-lft-out` `distribute-lft-out--`
1×	`pow2` `+-commutative` `sqr-cos` `clear-num` `associate-+r-` `associate-/r` `frac-2neg` `flip3-+` `pow-plus` `flip3--` `pow-prod-down` `associate-/r/` `pow-sqr` `-commutative` `pow-prod-up` `flip-+` `fma-udef` `flip--` `associate--r+` `unswap-sqr`

Counts

4 → 399

Calls

4 calls:

22.0ms	(/ (sin x) (* (cos x) (cos x)))
26.0ms	(* (cos x) (cos x))
144.0ms	(- (/ (/ (sin x) x) (cos x)) (fma (/ (/ (sin x) x) x) (/ (sin x) (cos x)) (/ (sin x) x)))
226.0ms	(+ 1 (- (/ (/ (sin x) x) (cos x)) (fma (/ (/ (sin x) x) x) (/ (sin x) (cos x)) (/ (sin x) x))))

series809.0ms

Counts

4 → 12

Calls

4 calls:

89.0ms	(/ (sin x) (* (cos x) (cos x)))
28.0ms	(* (cos x) (cos x))
409.0ms	(- (/ (/ (sin x) x) (cos x)) (fma (/ (/ (sin x) x) x) (/ (sin x) (cos x)) (/ (sin x) x)))
284.0ms	(+ 1 (- (/ (/ (sin x) x) (cos x)) (fma (/ (/ (sin x) x) x) (/ (sin x) (cos x)) (/ (sin x) x))))

simplify6.7s

Counts

411 → 411

Iterations

Iter	Nodes
done	5003
2	3426
1	1255
0	543

prune6.3s

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes109.0ms

Accuracy

100% (0.0b remaining)

Error of 0.3b against oracle of 0.3b and baseline of 32.2b

bsearch183.0ms

Steps

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

simplify15.0ms

Iterations

Iter	Nodes
done	36
1	36
0	28

end0.0ms

sample13.2s

Algorithm

intervals

Results

5.9s	1608×	body	2560	valid
4.2s	2728×	body	1280	valid
1.5s	1901×	body	640	valid
893.0ms	933×	body	320	valid
255.0ms	469×	body	160	valid
71.0ms	361×	body	80	valid