Details

sample668.0ms

Algorithm

intervals

Results

245.0ms	89×	body	1280	valid
156.0ms	48×	body	2560	valid
76.0ms	62×	body	640	valid
11.0ms	27×	body	320	valid
6.0ms	18×	body	160	valid
2.0ms	12×	body	80	valid

simplify21.0ms

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

localize18.0ms

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))

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` `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:

74.0ms	(/ (- x (sin x)) (- x (tan x)))
6.0ms	(- x (tan x))
10.0ms	(- x (sin x))

series286.0ms

Counts

3 → 9

Calls

3 calls:

119.0ms	(/ (- x (sin x)) (- x (tan x)))
115.0ms	(- x (tan x))
51.0ms	(- x (sin x))

simplify1.6s

Counts

119 → 119

Iterations

Iter	Nodes
done	5002
2	2273
1	502
0	209

prune514.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sin x) (- x (tan x)))
1.7b	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
1.7b	(- x (tan x))
1.7b	(- x (tan x))

rewrite221.0ms

Algorithm

rewrite-expression-head

Rules

713×	`*-un-lft-identity`
703×	`add-sqr-sqrt`
678×	`times-frac`
459×	`prod-diff`
417×	`add-cube-cbrt`
147×	`distribute-lft-out--`
141×	`difference-of-squares`
92×	`associate-/r/`
49×	`flip3--` `flip--`
46×	`div-inv`
27×	`fma-neg`
10×	`add-log-exp`
6×	`add-cbrt-cube` `add-exp-log`
5×	`associate-/r*`
4×	`expm1-log1p-u` `pow1` `log1p-expm1-u`
3×	`sub-neg` `distribute-rgt-out--` `diff-log` `associate-/l*`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `frac-sub` `sub-div`

Counts

4 → 588

Calls

4 calls:

21.0ms	(/ (sin x) (- x (tan x)))
112.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
5.0ms	(- x (tan x))
5.0ms	(- x (tan x))

series528.0ms

Counts

4 → 12

Calls

4 calls:

118.0ms	(/ (sin x) (- x (tan x)))
260.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
61.0ms	(- x (tan x))
89.0ms	(- x (tan x))

simplify3.0s

Counts

600 → 600

Iterations

Iter	Nodes
done	5000
2	4814
1	1405
0	617

prune3.0s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

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))

rewrite46.0ms

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:

32.0ms	(/ (- x (sin x)) (- x (tan x)))
5.0ms	(- x (tan x))
6.0ms	(- x (sin x))

series284.0ms

Counts

3 → 9

Calls

3 calls:

135.0ms	(/ (- x (sin x)) (- x (tan x)))
103.0ms	(- x (tan x))
46.0ms	(- x (sin x))

simplify1.6s

Counts

119 → 119

Iterations

Iter	Nodes
done	5002
2	2273
1	502
0	209

prune436.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize29.0ms

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

rewrite123.0ms

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:

0.0ms	(fma 9/40 (* x x) -1/2)
84.0ms	(* (* 27/2800 (* x x)) (* x x))
26.0ms	(* 27/2800 (* x x))
11.0ms	(- (fma 9/40 (* x x) -1/2) (* (* 27/2800 (* x x)) (* x x)))

series242.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(fma 9/40 (* x x) -1/2)
56.0ms	(* (* 27/2800 (* x x)) (* x x))
56.0ms	(* 27/2800 (* x x))
61.0ms	(- (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

prune291.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes126.0ms

Accuracy

100% (0.0b remaining)

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

bsearch103.0ms

Steps

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

simplify6.0ms

Iterations

Iter	Nodes
done	25
1	25
0	20

end0.0ms

sample13.0s

Algorithm

intervals

Results

5.8s	1636×	body	2560	valid
3.6s	2687×	body	1280	valid
2.4s	1902×	body	640	valid
627.0ms	923×	body	320	valid
234.0ms	504×	body	160	valid
125.0ms	348×	body	80	valid