Details

sample1.0s

Algorithm

intervals

Results

626.0ms	38×	body	2560	valid
164.0ms	99×	body	1280	valid
67.0ms	59×	body	640	valid
52.0ms	17×	body	80	valid
18.0ms	26×	body	320	valid
8.0ms	17×	body	160	valid

simplify27.0ms

Counts

1 → 1

Iterations

Iter	Nodes
4	19
3	19
2	17
1	13
0	6

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.3b

localize33.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
2.0b	(- x (tan x))
2.0b	(- x (sin x))

rewrite57.0ms

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` `insert-posit16` `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 → 113

Calls

3 calls:

19.0ms	(/ (- x (sin x)) (- x (tan x)))
5.0ms	(- x (tan x))
29.0ms	(- x (sin x))

series286.0ms

Counts

3 → 9

Calls

3 calls:

131.0ms	(/ (- x (sin x)) (- x (tan x)))
91.0ms	(- x (tan x))
64.0ms	(- x (sin x))

simplify1.5s

Counts

122 → 122

Iterations

Iter	Nodes
3	4396
2	1293
1	504
0	212

prune1.0s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize47.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
2.0b	(- x (sin x))
15.9b	(- (* (* (cbrt x) (cbrt x)) (cbrt x)) (tan x))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt` `*-un-lft-identity`
14×	`add-cube-cbrt`
12×	`prod-diff`
8×	`add-log-exp`
6×	`cbrt-prod`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `fma-neg` `add-exp-log` `insert-posit16` `log1p-expm1-u`
2×	`sub-neg` `flip3--` `pow1/3` `diff-log` `flip--`
1×	`distribute-lft-out--` `difference-of-squares`

Counts

4 → 76

Calls

4 calls:

1.0ms	(cbrt x)
1.0ms	(cbrt x)
13.0ms	(- x (sin x))
44.0ms	(- (* (* (cbrt x) (cbrt x)) (cbrt x)) (tan x))

series674.0ms

Counts

4 → 12

Calls

4 calls:

241.0ms	(cbrt x)
253.0ms	(cbrt x)
53.0ms	(- x (sin x))
127.0ms	(- (* (* (cbrt x) (cbrt x)) (cbrt x)) (tan x))

simplify3.0s

Counts

88 → 88

Iterations

Iter	Nodes
4	5825
3	1960
2	761
1	322
0	145

prune754.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
2.0b	(- x (tan x))
2.0b	(- x (sin x))
3.5b	(log (/ (- x (sin x)) (- x (tan x))))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

89×	`add-sqr-sqrt` `*-un-lft-identity`
50×	`times-frac`
41×	`add-cube-cbrt`
31×	`log-prod`
24×	`distribute-lft-out--` `difference-of-squares`
18×	`prod-diff`
9×	`add-exp-log`
8×	`add-log-exp`
6×	`add-cbrt-cube` `fma-neg`
5×	`pow1` `associate-/r` `flip3--` `flip--` `associate-/l`
4×	`expm1-log1p-u` `associate-/r/` `insert-posit16` `log1p-expm1-u`
2×	`sub-neg` `diff-log` `div-exp` `rem-log-exp` `div-inv` `associate-/l/`
1×	`cbrt-undiv` `log-div` `clear-num` `frac-2neg` `div-sub` `log-pow`

Counts

4 → 158

Calls

4 calls:

18.0ms	(/ (- x (sin x)) (- x (tan x)))
5.0ms	(- x (tan x))
6.0ms	(- x (sin x))
7.0ms	(log (/ (- x (sin x)) (- x (tan x))))

series432.0ms

Counts

4 → 12

Calls

4 calls:

110.0ms	(/ (- x (sin x)) (- x (tan x)))
99.0ms	(- x (tan x))
54.0ms	(- x (sin x))
169.0ms	(log (/ (- x (sin x)) (- x (tan x))))

simplify2.6s

Counts

170 → 170

Iterations

Iter	Nodes
3	7520
2	1746
1	669
0	283

prune1.7s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(- 9/40 (* 27/2800 (* x x)))
0.0b	(- (* (* x x) (- 9/40 (* 27/2800 (* x x)))) 1/2)
0.1b	(* (* x x) (- 9/40 (* 27/2800 (* x x))))
0.4b	(* 27/2800 (* x x))

rewrite68.0ms

Algorithm

rewrite-expression-head

Rules

18×	`prod-diff`
15×	`add-sqr-sqrt`
14×	`pow1` `add-cbrt-cube` `add-exp-log`
13×	`*-un-lft-identity` `add-cube-cbrt`
10×	`distribute-rgt-in` `distribute-lft-in` `associate--l+`
8×	`add-log-exp`
6×	`sub-neg` `pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`expm1-log1p-u` `fma-neg` `associate-r` `associate-l` `insert-posit16` `log1p-expm1-u`
3×	`flip3--` `flip--`
2×	`diff-log` `associate-r/` `-commutative` `unswap-sqr`

Counts

4 → 106

Calls

4 calls:

5.0ms	(- 9/40 (* 27/2800 (* x x)))
22.0ms	(- (* (* x x) (- 9/40 (* 27/2800 (* x x)))) 1/2)
26.0ms	(* (* x x) (- 9/40 (* 27/2800 (* x x))))
13.0ms	(* 27/2800 (* x x))

series386.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(- 9/40 (* 27/2800 (* x x)))
80.0ms	(- (* (* x x) (- 9/40 (* 27/2800 (* x x)))) 1/2)
162.0ms	(* (* x x) (- 9/40 (* 27/2800 (* x x))))
51.0ms	(* 27/2800 (* x x))

simplify2.3s

Counts

118 → 118

Iterations

Iter	Nodes
3	3581
2	1268
1	453
0	160

prune861.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

regimes101.0ms

Accuracy

99.7% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 31.7b

bsearch162.0ms

Steps

Iters	Range		Point
7	0.10106394179147121	1.6697130628152668	1.5588973207876802
8	-174.255226838109	-0.11981472621416538	-4.638405512419418

simplify8.0ms

Iterations

Iter	Nodes
2	27
1	27
0	22

end0.0ms

sample16.9s

Algorithm

intervals

Results

7.3s	1662×	body	2560	valid
5.7s	2702×	body	1280	valid
2.2s	1866×	body	640	valid
810.0ms	934×	body	320	valid
548.0ms	447×	body	160	valid
100.0ms	389×	body	80	valid