Details

sample1.6s

Algorithm

intervals

Results

945.0ms	62×	body	640	valid
161.0ms	48×	body	2560	valid
100.0ms	89×	body	1280	valid
11.0ms	27×	body	320	valid
6.0ms	18×	body	160	valid
2.0ms	12×	body	80	valid

simplify18.0ms

Counts

1 → 1

Iterations

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

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.6b

localize20.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
1.7b	(- x (tan x))
1.7b	(- x (sin x))

rewrite125.0ms

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` `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 → 110

Calls

3 calls:

85.0ms	(/ (- x (sin x)) (- x (tan x)))
13.0ms	(- x (tan x))
18.0ms	(- x (sin x))

series240.0ms

Counts

3 → 9

Calls

3 calls:

104.0ms	(/ (- x (sin x)) (- x (tan x)))
80.0ms	(- x (tan x))
56.0ms	(- x (sin x))

simplify1.6s

Counts

119 → 119

Iterations

Iter	Nodes
done	5002
2	2273
1	502
0	209

prune587.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize32.0ms

Local error

Found 3 expressions with local error:

0.1b	(fma 9/40 (* x x) -1/2)
0.1b	(* (pow x 4) 27/2800)
14.8b	(- (fma 9/40 (* x x) -1/2) (* (pow x 4) 27/2800))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt`
8×	`*-un-lft-identity` `add-exp-log` `add-cube-cbrt`
7×	`associate-l`
5×	`add-cbrt-cube` `add-log-exp`
4×	`unpow-prod-down`
3×	`expm1-log1p-u` `pow1` `fma-neg` `associate-r` `prod-diff` `prod-exp` `log1p-expm1-u` `unswap-sqr`
2×	`fma-udef` `sqr-pow`
1×	`pow-to-exp` `sub-neg` `flip3--` `diff-log` `pow-exp` `associate--l+` `*-commutative` `cbrt-unprod` `flip--`

Counts

3 → 58

Calls

3 calls:

1.0ms	(fma 9/40 (* x x) -1/2)
19.0ms	(* (pow x 4) 27/2800)
14.0ms	(- (fma 9/40 (* x x) -1/2) (* (pow x 4) 27/2800))

series177.0ms

Counts

3 → 9

Calls

3 calls:

69.0ms	(fma 9/40 (* x x) -1/2)
44.0ms	(* (pow x 4) 27/2800)
63.0ms	(- (fma 9/40 (* x x) -1/2) (* (pow x 4) 27/2800))

simplify763.0ms

Counts

67 → 67

Iterations

Iter	Nodes
done	5000
2	900
1	215
0	98

prune282.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize52.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (cos x) 2)
0.5b	(- (/ (/ (sin x) (cos x)) x) (fma (/ (sin x) (cos x)) (/ (sin x) (* x x)) (/ (sin x) x)))
14.4b	(/ (sin x) (* x x))
14.4b	(/ (sin x) (* x x))

rewrite167.0ms

Algorithm

rewrite-expression-head

Rules

273×	`times-frac`
202×	`add-sqr-sqrt`
195×	`*-un-lft-identity`
193×	`add-cube-cbrt`
129×	`prod-diff`
43×	`fma-neg`
18×	`div-inv`
15×	`add-exp-log`
14×	`add-cbrt-cube`
6×	`associate-/l*` `add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `cbrt-undiv` `div-exp` `log1p-expm1-u`
3×	`pow-unpow` `unpow-prod-down` `difference-of-squares`
2×	`clear-num` `associate-/r*` `frac-2neg` `prod-exp` `cbrt-unprod`
1×	`pow-to-exp` `sub-neg` `pow-pow` `flip3--` `diff-log` `pow-exp` `fma-udef` `flip--` `associate--r+` `distribute-lft-out--` `unpow2` `sqr-pow`

Counts

4 → 257

Calls

4 calls:

5.0ms	(pow (cos x) 2)
83.0ms	(- (/ (/ (sin x) (cos x)) x) (fma (/ (sin x) (cos x)) (/ (sin x) (* x x)) (/ (sin x) x)))
26.0ms	(/ (sin x) (* x x))
20.0ms	(/ (sin x) (* x x))

series354.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(pow (cos x) 2)
226.0ms	(- (/ (/ (sin x) (cos x)) x) (fma (/ (sin x) (cos x)) (/ (sin x) (* x x)) (/ (sin x) x)))
67.0ms	(/ (sin x) (* x x))
37.0ms	(/ (sin x) (* x x))

simplify1.8s

Counts

269 → 269

Iterations

Iter	Nodes
done	5000
2	4225
1	927
0	375

prune1.5s

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes118.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 31.4b

bsearch125.0ms

Steps

Iters	Range		Point
9	5.1798647897020696e-05	160.65039477392645	0.02964489669427243
8	-0.9341403346610884	-0.003292329160956242	-0.029656023299900573

simplify5.0ms

Iterations

Iter	Nodes
done	25
1	25
0	21

end0.0ms

sample13.6s

Algorithm

intervals

Results

6.4s	1636×	body	2560	valid
3.7s	2687×	body	1280	valid
2.3s	1902×	body	640	valid
526.0ms	923×	body	320	valid
214.0ms	504×	body	160	valid
119.0ms	348×	body	80	valid