Details

sample673.0ms

Algorithm

intervals

Results

244.0ms	57×	body	2560	valid
170.0ms	94×	body	1280	valid
162.0ms	58×	body	640	valid
21.0ms	27×	body	320	valid
8.0ms	13×	body	160	valid
2.0ms	7×	body	80	valid

simplify30.0ms

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: 32.8b

localize65.0ms

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))

rewrite57.0ms

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:

28.0ms	(/ (- x (sin x)) (- x (tan x)))
9.0ms	(- x (tan x))
15.0ms	(- x (sin x))

series295.0ms

Counts

3 → 9

Calls

3 calls:

127.0ms	(/ (- x (sin x)) (- x (tan x)))
97.0ms	(- x (tan x))
70.0ms	(- x (sin x))

simplify1.3s

Counts

92 → 92

Iterations

Iter	Nodes
3	3119
2	973
1	373
0	160

prune781.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 3 expressions with local error:

0.0b	(- 9/40 (* 27/2800 (* x x)))
0.1b	(* (* x x) (- 9/40 (* 27/2800 (* x x))))
0.2b	(* 27/2800 (* x x))

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 59

Calls

3 calls:

7.0ms	(- 9/40 (* 27/2800 (* x x)))
37.0ms	(* (* x x) (- 9/40 (* 27/2800 (* x x))))
27.0ms	(* 27/2800 (* x x))

series251.0ms

Counts

3 → 9

Calls

3 calls:

77.0ms	(- 9/40 (* 27/2800 (* x x)))
133.0ms	(* (* x x) (- 9/40 (* 27/2800 (* x x))))
40.0ms	(* 27/2800 (* x x))

simplify764.0ms

Counts

68 → 68

Iterations

Iter	Nodes
3	2326
2	747
1	263
0	89

prune532.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize56.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sin x) (cos x))
0.2b	(/ (/ (sin x) x) (cos x))
0.8b	(- 1 (/ (sin x) x))
16.2b	(/ (sin x) (* x x))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

89×	`times-frac`
64×	`add-sqr-sqrt`
60×	`*-un-lft-identity`
56×	`add-cube-cbrt`
19×	`associate-/l*`
16×	`add-cbrt-cube` `add-exp-log`
7×	`associate-/r*` `div-inv`
6×	`cbrt-undiv` `div-exp` `add-log-exp`
4×	`pow1` `insert-posit16` `difference-of-squares`
3×	`clear-num` `frac-2neg`
1×	`quot-tan` `sub-neg` `flip3--` `diff-log` `prod-exp` `cbrt-unprod` `flip--` `distribute-lft-out--` `associate-/l/`

Counts

4 → 140

Calls

4 calls:

16.0ms	(/ (sin x) (cos x))
15.0ms	(/ (/ (sin x) x) (cos x))
8.0ms	(- 1 (/ (sin x) x))
15.0ms	(/ (sin x) (* x x))

series208.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(/ (sin x) (cos x))
78.0ms	(/ (/ (sin x) x) (cos x))
44.0ms	(- 1 (/ (sin x) x))
54.0ms	(/ (sin x) (* x x))

simplify4.3s

Counts

152 → 152

Iterations

Iter	Nodes
3	8150
2	1768
1	590
0	263

prune1.9s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

localize39.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sin x) (sin x))
0.8b	(- (* x x) (* (sin x) (sin x)))
0.8b	(- x (tan x))
16.8b	(/ (- (* x x) (* (sin x) (sin x))) (* (- x (tan x)) (+ x (sin x))))

rewrite79.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
12×	`*-un-lft-identity`
11×	`pow1` `add-cbrt-cube` `add-exp-log`
10×	`add-cube-cbrt`
8×	`associate-/r/` `add-log-exp`
6×	`flip3--` `flip--`
4×	`frac-times` `times-frac` `insert-posit16` `associate-/l*` `difference-of-squares`
3×	`flip3-+` `swap-sqr` `associate-r` `associate-l` `flip-+`
2×	`cbrt-undiv` `sub-neg` `diff-log` `div-exp` `associate-l/` `prod-exp` `associate-r/` `cbrt-unprod` `sqr-sin` `associate-/l/`
1×	`pow2` `clear-num` `associate-/r` `frac-2neg` `pow-plus` `div-sub` `pow-prod-down` `pow-sqr` `-commutative` `pow-prod-up` `div-inv` `sin-mult` `distribute-lft-out--` `associate--r-` `unswap-sqr`

Counts

4 → 93

Calls

4 calls:

18.0ms	(* (sin x) (sin x))
15.0ms	(- (* x x) (* (sin x) (sin x)))
11.0ms	(- x (tan x))
34.0ms	(/ (- (* x x) (* (sin x) (sin x))) (* (- x (tan x)) (+ x (sin x))))

series459.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(* (sin x) (sin x))
118.0ms	(- (* x x) (* (sin x) (sin x)))
67.0ms	(- x (tan x))
236.0ms	(/ (- (* x x) (* (sin x) (sin x))) (* (- x (tan x)) (+ x (sin x))))

simplify967.0ms

Counts

105 → 105

Iterations

Iter	Nodes
2	2843
1	618
0	204

prune1.0s

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.0b

regimes75.0ms

Accuracy

99.1% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 31.6b

bsearch208.0ms

Steps

Iters	Range		Point
11	1.0334628320549359e-08	2.7368728718549235e+26	2.4570066373596267
9	-128555.04713805256	-0.18430940072566707	-2.446923987498581

simplify6.0ms

Iterations

Iter	Nodes
2	37
1	37
0	29

end0.0ms

sample15.2s

Algorithm

intervals

Results

6.3s	1597×	body	2560	valid
5.0s	2785×	body	1280	valid
2.4s	1900×	body	640	valid
924.0ms	924×	body	320	valid
242.0ms	456×	body	160	valid
77.0ms	338×	body	80	valid