Details

sample439.0ms

Algorithm

intervals

Results

135.0ms	42×	body	2560	valid
98.0ms	86×	body	1280	valid
76.0ms	18×	body	160	valid
39.0ms	68×	body	640	valid
13.0ms	33×	body	320	valid
2.0ms	9×	body	80	valid

simplify15.0ms

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: 29.2b

localize21.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
0.8b	(- x (tan x))
0.8b	(- x (sin x))

rewrite448.0ms

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:

21.0ms	(/ (- x (sin x)) (- x (tan x)))
7.0ms	(- x (tan x))
414.0ms	(- x (sin x))

series250.0ms

Counts

3 → 9

Calls

3 calls:

106.0ms	(/ (- x (sin x)) (- x (tan x)))
93.0ms	(- x (tan x))
51.0ms	(- x (sin x))

simplify1.7s

Counts

119 → 119

Iterations

Iter	Nodes
done	5002
2	2273
1	502
0	209

prune499.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize55.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ (sin x) (cos x)) x)
0.1b	(/ (/ (sin x) (cos x)) x)
0.6b	(- (/ (/ (sin x) (cos x)) x) (fma (/ (sin x) (cos x)) (/ (sin x) (* x x)) (/ (sin x) x)))
12.4b	(/ (sin x) (* x x))

rewrite171.0ms

Algorithm

rewrite-expression-head

Rules

420×	`times-frac`
282×	`add-sqr-sqrt`
275×	`*-un-lft-identity`
273×	`add-cube-cbrt`
129×	`prod-diff`
43×	`fma-neg`
29×	`associate-/l*`
27×	`div-inv`
19×	`add-cbrt-cube` `add-exp-log`
8×	`cbrt-undiv` `div-exp`
7×	`associate-/r*`
6×	`add-log-exp`
4×	`expm1-log1p-u` `pow1` `log1p-expm1-u`
3×	`clear-num` `frac-2neg` `difference-of-squares`
2×	`associate-/l/`
1×	`sub-neg` `flip3--` `diff-log` `prod-exp` `cbrt-unprod` `fma-udef` `flip--` `associate--r+` `distribute-lft-out--`

Counts

4 → 358

Calls

4 calls:

26.0ms	(/ (/ (sin x) (cos x)) x)
17.0ms	(/ (/ (sin x) (cos x)) x)
80.0ms	(- (/ (/ (sin x) (cos x)) x) (fma (/ (sin x) (cos x)) (/ (sin x) (* x x)) (/ (sin x) x)))
10.0ms	(/ (sin x) (* x x))

series372.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(/ (/ (sin x) (cos x)) x)
62.0ms	(/ (/ (sin x) (cos x)) x)
196.0ms	(- (/ (/ (sin x) (cos x)) x) (fma (/ (sin x) (cos x)) (/ (sin x) (* x x)) (/ (sin x) x)))
57.0ms	(/ (sin x) (* x x))

simplify2.4s

Counts

370 → 370

Iterations

Iter	Nodes
done	5000
2	4276
1	909
0	384

prune2.9s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma 9/40 (* x x) -1/2)
0.1b	(* (* 27/2800 (* x x)) (* x x))
0.2b	(* 27/2800 (* x x))
16.3b	(- (fma 9/40 (* x x) -1/2) (* (* 27/2800 (* x x)) (* x x)))

rewrite101.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 82

Calls

4 calls:

1.0ms	(fma 9/40 (* x x) -1/2)
70.0ms	(* (* 27/2800 (* x x)) (* x x))
19.0ms	(* 27/2800 (* x x))
7.0ms	(- (fma 9/40 (* x x) -1/2) (* (* 27/2800 (* x x)) (* x x)))

series239.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(fma 9/40 (* x x) -1/2)
51.0ms	(* (* 27/2800 (* x x)) (* x x))
40.0ms	(* 27/2800 (* x x))
78.0ms	(- (fma 9/40 (* x x) -1/2) (* (* 27/2800 (* x x)) (* x x)))

simplify2.0s

Counts

94 → 94

Iterations

Iter	Nodes
done	5001
2	2063
1	311
0	110

prune365.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes70.0ms

Accuracy

100% (0.0b remaining)

Error of 0.3b against oracle of 0.3b and baseline of 31.9b

bsearch208.0ms

Steps

Iters	Range		Point
11	1.9534460235190362e-22	53640.016154094046	2.424314253224005
10	-17239113253358.373	-4.96108325192681e-05	-2.41224692961804

simplify11.0ms

Iterations

Iter	Nodes
done	36
1	36
0	27

end0.0ms

sample13.5s

Algorithm

intervals

Results

6.6s	1666×	body	2560	valid
4.0s	2699×	body	1280	valid
1.9s	1879×	body	640	valid
433.0ms	944×	body	320	valid
227.0ms	474×	body	160	valid
63.0ms	338×	body	80	valid