Details

sample580.0ms

Algorithm

intervals

Results

261.0ms	54×	body	2560	valid
127.0ms	81×	body	1280	valid
38.0ms	47×	body	640	valid
21.0ms	40×	body	320	valid
6.0ms	18×	body	160	valid
3.0ms	16×	body	80	valid

simplify22.0ms

Counts

1 → 1

Iterations

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

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.6b

localize32.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
1.9b	(- x (tan x))
1.9b	(- x (sin x))

rewrite100.0ms

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)))
10.0ms	(- x (tan x))
14.0ms	(- x (sin x))

series325.0ms

Counts

3 → 9

Calls

3 calls:

142.0ms	(/ (- x (sin x)) (- x (tan x)))
108.0ms	(- x (tan x))
75.0ms	(- x (sin x))

simplify2.6s

Counts

122 → 122

Iterations

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

prune450.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize35.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma (* x x) 9/40 -1/2)
0.1b	(* -27/2800 (* (* x x) (* x x)))
0.2b	(* (* x x) (* x x))
13.1b	(+ (fma (* x x) 9/40 -1/2) (* -27/2800 (* (* x x) (* x x))))

rewrite141.0ms

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:

0.0ms	(fma (* x x) 9/40 -1/2)
85.0ms	(* -27/2800 (* (* x x) (* x x)))
31.0ms	(* (* x x) (* x x))
20.0ms	(+ (fma (* x x) 9/40 -1/2) (* -27/2800 (* (* x x) (* x x))))

series239.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(fma (* x x) 9/40 -1/2)
62.0ms	(* -27/2800 (* (* x x) (* x x)))
41.0ms	(* (* x x) (* x x))
77.0ms	(+ (fma (* x x) 9/40 -1/2) (* -27/2800 (* (* x x) (* x x))))

simplify1.5s

Counts

138 → 138

Iterations

Iter	Nodes
done	5000
2	1192
1	340
0	122

prune298.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize30.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
0.5b	(expm1 (/ (- x (sin x)) (- x (tan x))))
1.9b	(- x (tan x))
1.9b	(- x (sin x))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 125

Calls

4 calls:

38.0ms	(/ (- x (sin x)) (- x (tan x)))
1.0ms	(expm1 (/ (- x (sin x)) (- x (tan x))))
10.0ms	(- x (tan x))
13.0ms	(- x (sin x))

series421.0ms

Counts

4 → 12

Calls

4 calls:

120.0ms	(/ (- x (sin x)) (- x (tan x)))
179.0ms	(expm1 (/ (- x (sin x)) (- x (tan x))))
83.0ms	(- x (tan x))
38.0ms	(- x (sin x))

simplify1.5s

Counts

137 → 137

Iterations

Iter	Nodes
done	5000
2	1690
1	613
0	250

prune499.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (/ (- x (tan x)) (- x (sin x))))
0.5b	(expm1 (/ 1 (/ (- x (tan x)) (- x (sin x)))))
1.9b	(- x (tan x))
1.9b	(- x (sin x))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

193×	`times-frac`
178×	`add-sqr-sqrt` `*-un-lft-identity`
94×	`add-cube-cbrt`
42×	`distribute-lft-out--` `difference-of-squares`
31×	`associate-/r*`
18×	`prod-diff`
15×	`add-exp-log`
9×	`add-cbrt-cube` `associate-/r/`
8×	`add-log-exp`
7×	`div-exp`
6×	`flip3--` `fma-neg` `flip--`
5×	`pow1` `log1p-expm1-u` `div-inv`
4×	`expm1-log1p-u` `insert-posit16`
3×	`cbrt-undiv` `associate-/l*`
2×	`rec-exp` `sub-neg` `diff-log` `1-exp`
1×	`expm1-log1p` `clear-num` `frac-2neg` `pow-flip` `inv-pow` `expm1-udef`

Counts

4 → 221

Calls

4 calls:

28.0ms	(/ 1 (/ (- x (tan x)) (- x (sin x))))
0.0ms	(expm1 (/ 1 (/ (- x (tan x)) (- x (sin x)))))
5.0ms	(- x (tan x))
6.0ms	(- x (sin x))

series366.0ms

Counts

4 → 12

Calls

4 calls:

87.0ms	(/ 1 (/ (- x (tan x)) (- x (sin x))))
159.0ms	(expm1 (/ 1 (/ (- x (tan x)) (- x (sin x)))))
72.0ms	(- x (tan x))
47.0ms	(- x (sin x))

simplify1.9s

Counts

233 → 233

Iterations

Iter	Nodes
done	5004
2	2480
1	968
0	387

prune954.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes92.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 31.5b

bsearch134.0ms

Steps

Iters	Range		Point
8	0.006928851504795399	68.55102067575892	0.029335377355220408
9	-17438.246738609338	-0.0018335887134067947	-0.0287527250874288

simplify5.0ms

Iterations

Iter	Nodes
done	31
1	31
0	27

end0.0ms

sample13.6s

Algorithm

intervals

Results

6.1s	1613×	body	2560	valid
4.6s	2707×	body	1280	valid
1.9s	1838×	body	640	valid
597.0ms	946×	body	320	valid
153.0ms	502×	body	160	valid
68.0ms	394×	body	80	valid