Details

sample1.1s

Algorithm

intervals

Results

377.0ms	55×	body	2560	valid
321.0ms	89×	body	1280	valid
206.0ms	56×	body	640	valid
33.0ms	43×	body	320	valid
6.0ms	7×	body	160	valid
1.0ms	6×	body	80	valid

simplify31.0ms

Counts

1 → 1

Iterations

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

prune58.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.4b

localize79.0ms

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))

rewrite140.0ms

Algorithm

rewrite-expression-head

Rules

43×	`add-sqr-sqrt` `*-un-lft-identity`
25×	`times-frac`
15×	`add-cube-cbrt`
14×	`distribute-lft-out--` `difference-of-squares`
7×	`add-log-exp`
5×	`associate-/r` `add-cbrt-cube` `add-exp-log` `associate-/l`
4×	`flip3--` `flip--`
3×	`pow1` `insert-posit16`
2×	`sub-neg` `diff-log` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-sub` `div-exp` `div-inv`

Counts

3 → 83

Calls

3 calls:

73.0ms	(/ (- x (sin x)) (- x (tan x)))
12.0ms	(- x (tan x))
50.0ms	(- x (sin x))

series264.0ms

Counts

3 → 9

Calls

3 calls:

94.0ms	(/ (- x (sin x)) (- x (tan x)))
96.0ms	(- x (tan x))
73.0ms	(- x (sin x))

simplify1.4s

Counts

92 → 92

Iterations

Iter	Nodes
3	3119
2	973
1	373
0	160

prune762.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize28.0ms

Local error

Found 2 expressions with local error:

0.1b	(* (* x x) (- 9/40 (* 27/2800 (* x x))))
0.2b	(* 27/2800 (* x x))

rewrite77.0ms

Algorithm

rewrite-expression-head

Rules

12×	`pow1` `add-cbrt-cube` `add-exp-log`
6×	`add-sqr-sqrt` `pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`-un-lft-identity` `associate-r` `associate-l*` `add-cube-cbrt`
2×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `associate-r/` `-commutative` `insert-posit16` `add-log-exp` `unswap-sqr`
1×	`flip3--` `flip--`

Counts

2 → 46

Calls

2 calls:

50.0ms	(* (* x x) (- 9/40 (* 27/2800 (* x x))))
26.0ms	(* 27/2800 (* x x))

series194.0ms

Counts

2 → 6

Calls

2 calls:

142.0ms	(* (* x x) (- 9/40 (* 27/2800 (* x x))))
52.0ms	(* 27/2800 (* x x))

simplify864.0ms

Counts

52 → 52

Iterations

Iter	Nodes
3	2105
2	638
1	234
0	80

prune472.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize58.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ (sin x) (* x x)) (/ (sin x) (cos x)))
0.2b	(/ (/ (sin x) x) (cos x))
1.7b	(- 1 (/ (sin x) x))
15.6b	(/ (sin x) (* x x))

rewrite79.0ms

Algorithm

rewrite-expression-head

Rules

96×	`times-frac`
75×	`add-sqr-sqrt`
61×	`*-un-lft-identity`
57×	`add-cube-cbrt`
35×	`add-cbrt-cube` `add-exp-log`
16×	`associate-/l*`
13×	`associate-r`
12×	`cbrt-undiv` `div-exp`
9×	`prod-exp` `cbrt-unprod`
8×	`div-inv`
7×	`associate-l`
6×	`pow1` `add-log-exp`
4×	`associate-/r*` `insert-posit16` `difference-of-squares` `unswap-sqr`
2×	`clear-num` `frac-2neg`
1×	`frac-times` `sub-neg` `flip3--` `diff-log` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative` `flip--` `distribute-lft-out--` `associate-/l/`

Counts

4 → 160

Calls

4 calls:

35.0ms	(* (/ (sin x) (* x x)) (/ (sin x) (cos x)))
15.0ms	(/ (/ (sin x) x) (cos x))
8.0ms	(- 1 (/ (sin x) x))
17.0ms	(/ (sin x) (* x x))

series264.0ms

Counts

4 → 12

Calls

4 calls:

85.0ms	(* (/ (sin x) (* x x)) (/ (sin x) (cos x)))
72.0ms	(/ (/ (sin x) x) (cos x))
57.0ms	(- 1 (/ (sin x) x))
51.0ms	(/ (sin x) (* x x))

simplify1.1s

Counts

172 → 172

Iterations

Iter	Nodes
2	2858
1	768
0	299

prune2.1s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

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

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

61×	`add-sqr-sqrt` `*-un-lft-identity`
40×	`times-frac`
30×	`sqrt-prod`
25×	`add-cube-cbrt`
18×	`distribute-lft-out--` `difference-of-squares`
10×	`add-log-exp`
8×	`associate-/r*`
6×	`add-cbrt-cube` `add-exp-log`
5×	`flip3--` `flip--` `associate-/l*`
4×	`pow1` `insert-posit16`
3×	`sub-neg` `diff-log`
2×	`sqrt-div` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-sub` `div-exp` `div-inv`

Counts

4 → 116

Calls

4 calls:

19.0ms	(/ (- x (sin x)) (sqrt (- x (tan x))))
5.0ms	(- x (tan x))
9.0ms	(- x (tan x))
6.0ms	(- x (sin x))

series372.0ms

Counts

4 → 12

Calls

4 calls:

170.0ms	(/ (- x (sin x)) (sqrt (- x (tan x))))
70.0ms	(- x (tan x))
86.0ms	(- x (tan x))
46.0ms	(- x (sin x))

simplify2.4s

Counts

128 → 128

Iterations

Iter	Nodes
3	5769
2	1631
1	568
0	239

prune1.2s

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.0b

regimes43.0ms

Accuracy

99.6% (0.1b remaining)

Error of 0.3b against oracle of 0.2b and baseline of 31.2b

bsearch180.0ms

Steps

Iters	Range		Point
10	1.4996160052323843e-06	45385424.466692075	7.937565998741664
10	-8.26555774309129e+15	-0.755072844465923	-2.4051902967603365

simplify6.0ms

Iterations

Iter	Nodes
2	37
1	37
0	29

end0.0ms

sample17.2s

Algorithm

intervals

Results

7.6s	1602×	body	2560	valid
6.0s	2775×	body	1280	valid
2.1s	1927×	body	640	valid
866.0ms	918×	body	320	valid
245.0ms	446×	body	160	valid
86.0ms	332×	body	80	valid