Details

sample480.0ms

Algorithm

intervals

Results

231.0ms	39×	body	640	valid
45.0ms	45×	body	1280	valid
19.0ms	129×	body	80	valid
12.0ms	27×	body	320	valid
4.0ms	16×	body	160	valid

simplify42.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	45
6	45
5	43
4	37
3	29
2	22
1	13
0	7

prune15.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.3b

localize45.0ms

Local error

Found 3 expressions with local error:

0.1b	(fma (tan x) (tan x) 1.0)
0.1b	(/ (fma (- (tan x)) (tan x) 1.0) (fma (tan x) (tan x) 1.0))
0.3b	(fma (- (tan x)) (tan x) 1.0)

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
9×	`times-frac`
5×	`add-cbrt-cube` `add-exp-log`
3×	`expm1-log1p-u` `pow1` `associate-/r` `log1p-expm1-u` `associate-/l` `add-log-exp`
2×	`fma-udef`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `div-inv`

Counts

3 → 49

Calls

3 calls:

0.0ms	(fma (tan x) (tan x) 1.0)
5.0ms	(/ (fma (- (tan x)) (tan x) 1.0) (fma (tan x) (tan x) 1.0))
2.0ms	(fma (- (tan x)) (tan x) 1.0)

series339.0ms

Counts

3 → 9

Calls

3 calls:

63.0ms	(fma (tan x) (tan x) 1.0)
189.0ms	(/ (fma (- (tan x)) (tan x) 1.0) (fma (tan x) (tan x) 1.0))
87.0ms	(fma (- (tan x)) (tan x) 1.0)

simplify1.1s

Counts

58 → 58

Iterations

Iter	Nodes
done	5000
3	1873
2	456
1	161
0	87

prune426.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize36.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (sin x) 2)
0.3b	(pow (sin x) 2)
0.3b	(pow (cos x) 2)
0.3b	(pow (cos x) 2)

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `pow-unpow` `unpow-prod-down` `*-un-lft-identity` `add-cube-cbrt`
8×	`pow1` `add-exp-log`
4×	`expm1-log1p-u` `pow-to-exp` `pow-pow` `add-cbrt-cube` `pow-exp` `log1p-expm1-u` `unpow2` `add-log-exp` `sqr-pow`

Counts

4 → 80

Calls

4 calls:

5.0ms	(pow (sin x) 2)
6.0ms	(pow (sin x) 2)
5.0ms	(pow (cos x) 2)
5.0ms	(pow (cos x) 2)

series102.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(pow (sin x) 2)
21.0ms	(pow (sin x) 2)
31.0ms	(pow (cos x) 2)
19.0ms	(pow (cos x) 2)

simplify1.2s

Counts

92 → 92

Iterations

Iter	Nodes
done	5000
3	2403
2	664
1	194
0	68

prune430.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

localize39.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (fma (tan x) (tan x) 1.0) (fma (- (tan x)) (tan x) 1.0))
0.1b	(/ 1 (/ (fma (tan x) (tan x) 1.0) (fma (- (tan x)) (tan x) 1.0)))
0.1b	(fma (tan x) (tan x) 1.0)
0.3b	(fma (- (tan x)) (tan x) 1.0)

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

84×	`times-frac`
54×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
17×	`add-exp-log`
16×	`associate-/r*`
11×	`add-cbrt-cube`
8×	`div-exp`
6×	`div-inv` `associate-/l*`
5×	`pow1`
4×	`expm1-log1p-u` `cbrt-undiv` `log1p-expm1-u` `add-log-exp`
2×	`rec-exp` `clear-num` `frac-2neg` `1-exp` `fma-udef`
1×	`associate-/r/` `pow-flip` `inv-pow`

Counts

4 → 127

Calls

4 calls:

8.0ms	(/ (fma (tan x) (tan x) 1.0) (fma (- (tan x)) (tan x) 1.0))
16.0ms	(/ 1 (/ (fma (tan x) (tan x) 1.0) (fma (- (tan x)) (tan x) 1.0)))
0.0ms	(fma (tan x) (tan x) 1.0)
1.0ms	(fma (- (tan x)) (tan x) 1.0)

series568.0ms

Counts

4 → 12

Calls

4 calls:

196.0ms	(/ (fma (tan x) (tan x) 1.0) (fma (- (tan x)) (tan x) 1.0))
221.0ms	(/ 1 (/ (fma (tan x) (tan x) 1.0) (fma (- (tan x)) (tan x) 1.0)))
63.0ms	(fma (tan x) (tan x) 1.0)
87.0ms	(fma (- (tan x)) (tan x) 1.0)

simplify970.0ms

Counts

139 → 139

Iterations

Iter	Nodes
done	5001
2	1711
1	435
0	191

prune605.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize33.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
0.2b	(- 1.0 (* (tan x) (tan x)))
0.3b	(* (tan x) (tan x))
0.3b	(* (tan x) (tan x))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt`
23×	`*-un-lft-identity` `add-cube-cbrt`
18×	`pow1`
12×	`times-frac`
10×	`add-cbrt-cube` `add-exp-log`
8×	`tan-quot`
6×	`swap-sqr` `associate-r` `associate-l` `add-log-exp`
5×	`difference-of-squares`
4×	`expm1-log1p-u` `log1p-expm1-u` `associate-/l*`
3×	`associate-/r*` `fma-neg` `prod-diff`
2×	`pow2` `frac-times` `pow-plus` `flip3--` `pow-prod-down` `associate-l/` `prod-exp` `associate-r/` `associate-/r/` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `flip--` `unswap-sqr` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `flip3-+` `diff-log` `div-sub` `div-exp` `flip-+` `div-inv`

Counts

4 → 119

Calls

4 calls:

23.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
7.0ms	(- 1.0 (* (tan x) (tan x)))
13.0ms	(* (tan x) (tan x))
15.0ms	(* (tan x) (tan x))

series284.0ms

Counts

4 → 12

Calls

4 calls:

136.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
54.0ms	(- 1.0 (* (tan x) (tan x)))
56.0ms	(* (tan x) (tan x))
37.0ms	(* (tan x) (tan x))

simplify1.5s

Counts

131 → 131

Iterations

Iter	Nodes
done	5001
2	1700
1	376
0	151

prune548.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 0.0b

regimes604.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	12
1	12
0	11

end0.0ms

sample4.5s

Algorithm

intervals

Results

1.9s	1519×	body	1280	valid
1.3s	1213×	body	640	valid
491.0ms	4310×	body	80	valid
405.0ms	632×	body	320	valid
200.0ms	326×	body	160	valid