Details

sample481.0ms

Algorithm

intervals

Results

161.0ms	48×	body	2560	valid
115.0ms	92×	body	1280	valid
107.0ms	65×	body	640	valid
12.0ms	28×	body	320	valid
4.0ms	14×	body	160	valid
2.0ms	9×	body	80	valid

simplify24.0ms

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: 31.5b

localize27.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
1.6b	(- x (tan x))
1.6b	(- x (sin x))

rewrite98.0ms

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:

27.0ms	(/ (- x (sin x)) (- x (tan x)))
14.0ms	(- x (tan x))
52.0ms	(- x (sin x))

series283.0ms

Counts

3 → 9

Calls

3 calls:

145.0ms	(/ (- x (sin x)) (- x (tan x)))
85.0ms	(- x (tan x))
53.0ms	(- x (sin x))

simplify1.5s

Counts

119 → 119

Iterations

Iter	Nodes
done	5002
2	2273
1	502
0	209

prune491.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
1.6b	(- x (sin x))
1.7b	(/ (- x (sin x)) (fma (* (cbrt x) (cbrt x)) (cbrt x) (- (tan x))))
29.1b	(fma (* (cbrt x) (cbrt x)) (cbrt x) (- (tan x)))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt` `*-un-lft-identity`
22×	`add-cube-cbrt`
15×	`times-frac`
9×	`prod-diff`
6×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
5×	`associate-/l*` `distribute-lft-out--` `difference-of-squares`
4×	`expm1-log1p-u` `pow1` `log1p-expm1-u`
3×	`cbrt-prod` `associate-/r*` `fma-neg`
2×	`flip3--` `flip--` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `pow1/3` `diff-log` `div-sub` `div-exp` `fma-udef` `div-inv`

Counts

4 → 91

Calls

4 calls:

1.0ms	(cbrt x)
11.0ms	(- x (sin x))
35.0ms	(/ (- x (sin x)) (fma (* (cbrt x) (cbrt x)) (cbrt x) (- (tan x))))
0.0ms	(fma (* (cbrt x) (cbrt x)) (cbrt x) (- (tan x)))

series1.6s

Counts

4 → 12

Calls

4 calls:

239.0ms	(cbrt x)
56.0ms	(- x (sin x))
801.0ms	(/ (- x (sin x)) (fma (* (cbrt x) (cbrt x)) (cbrt x) (- (tan x))))
506.0ms	(fma (* (cbrt x) (cbrt x)) (cbrt x) (- (tan x)))

simplify1.2s

Counts

103 → 103

Iterations

Iter	Nodes
done	5000
2	1445
1	363
0	168

prune469.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sin x) (- x (tan x)))
1.4b	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
1.6b	(- x (tan x))
1.6b	(- x (tan x))

rewrite217.0ms

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)))
119.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
5.0ms	(- x (tan x))
5.0ms	(- x (tan x))

series539.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(/ (sin x) (- x (tan x)))
277.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
91.0ms	(- x (tan x))
90.0ms	(- x (tan x))

simplify2.1s

Counts

600 → 600

Iterations

Iter	Nodes
done	5000
2	4814
1	1405
0	617

prune2.4s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize25.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma (pow x 4) 27/2800 1/2)
0.1b	(* 9/40 (* x x))
16.1b	(- (* 9/40 (* x x)) (fma (pow x 4) 27/2800 1/2))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 50

Calls

3 calls:

0.0ms	(fma (pow x 4) 27/2800 1/2)
13.0ms	(* 9/40 (* x x))
26.0ms	(- (* 9/40 (* x x)) (fma (pow x 4) 27/2800 1/2))

series285.0ms

Counts

3 → 9

Calls

3 calls:

150.0ms	(fma (pow x 4) 27/2800 1/2)
48.0ms	(* 9/40 (* x x))
86.0ms	(- (* 9/40 (* x x)) (fma (pow x 4) 27/2800 1/2))

simplify1.5s

Counts

59 → 59

Iterations

Iter	Nodes
done	5002
2	1333
1	235
0	91

prune230.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.0b

regimes61.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 31.8b

bsearch138.0ms

Steps

Iters	Range		Point
9	7.294142785006675e-07	13.800596953327334	0.030608973476154103
7	-0.10952899301968014	-0.00181011214377754	-0.03200837114588731

simplify5.0ms

Iterations

Iter	Nodes
done	26
1	26
0	22

end0.0ms

sample13.6s

Algorithm

intervals

Results

6.7s	1679×	body	2560	valid
4.3s	2685×	body	1280	valid
1.5s	1884×	body	640	valid
381.0ms	902×	body	320	valid
198.0ms	354×	body	80	valid
146.0ms	496×	body	160	valid