Details

sample1.2s

Algorithm

intervals

Results

841.0ms	46×	body	1280	valid
117.0ms	51×	body	640	valid
32.0ms	133×	body	80	valid
16.0ms	20×	body	320	valid
4.0ms	6×	body	160	valid

simplify66.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	44
5	44
4	39
3	31
2	24
1	15
0	7

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize61.0ms

Local error

Found 4 expressions with local error:

0.1b	(- 1 (* (tan x) (tan x)))
0.2b	(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
0.3b	(* (tan x) (tan x))
0.3b	(* (tan x) (tan x))

rewrite116.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
29×	`*-un-lft-identity`
24×	`add-cube-cbrt`
18×	`pow1`
15×	`times-frac`
10×	`add-cbrt-cube` `add-exp-log` `difference-of-squares`
8×	`tan-quot`
6×	`swap-sqr` `associate-r` `associate-l` `add-log-exp`
5×	`associate-/l*`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`associate-/r*` `fma-neg` `prod-diff`
2×	`pow2` `frac-times` `pow-plus` `flip3--` `pow-prod-down` `associate-l/` `prod-exp` `associate-r/` `associate-/r/` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `flip--` `unswap-sqr` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `flip3-+` `diff-log` `div-sub` `div-exp` `flip-+` `div-inv`

Counts

4 → 128

Calls

4 calls:

11.0ms	(- 1 (* (tan x) (tan x)))
31.0ms	(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
30.0ms	(* (tan x) (tan x))
33.0ms	(* (tan x) (tan x))

series342.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(- 1 (* (tan x) (tan x)))
155.0ms	(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
53.0ms	(* (tan x) (tan x))
75.0ms	(* (tan x) (tan x))

simplify1.1s

Counts

140 → 140

Iterations

Iter	Nodes
done	2004
3	2004
2	1114
1	399
0	157

prune1.2s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize29.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ 1 (tan x))
0.2b	(- 1 (tan x))
0.2b	(/ (- 1 (tan x)) (fma (tan x) (tan x) 1))
0.2b	(* (+ 1 (tan x)) (/ (- 1 (tan x)) (fma (tan x) (tan x) 1)))

rewrite100.0ms

Algorithm

rewrite-expression-head

Rules

63×	`add-sqr-sqrt`
62×	`*-un-lft-identity`
37×	`times-frac`
34×	`add-cube-cbrt`
22×	`associate-r`
16×	`difference-of-squares`
11×	`add-cbrt-cube` `add-exp-log`
9×	`prod-diff`
8×	`distribute-lft-out--` `add-log-exp`
6×	`pow1` `associate-/l*`
4×	`expm1-log1p-u` `associate-l` `insert-posit16` `log1p-expm1-u`
3×	`associate-/r*` `fma-def` `flip3-+` `fma-neg` `flip-+`
2×	`frac-times` `cbrt-undiv` `flip3--` `div-exp` `associate-*l/` `prod-exp` `cbrt-unprod` `div-inv` `flip--` `distribute-lft-out` `unswap-sqr` `associate-/l/`
1×	`+-commutative` `clear-num` `sum-log` `sub-neg` `frac-2neg` `diff-log` `div-sub` `pow-prod-down` `associate-r/` `-commutative`

Counts

4 → 142

Calls

4 calls:

5.0ms	(+ 1 (tan x))
11.0ms	(- 1 (tan x))
26.0ms	(/ (- 1 (tan x)) (fma (tan x) (tan x) 1))
57.0ms	(* (+ 1 (tan x)) (/ (- 1 (tan x)) (fma (tan x) (tan x) 1)))

series292.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(+ 1 (tan x))
35.0ms	(- 1 (tan x))
68.0ms	(/ (- 1 (tan x)) (fma (tan x) (tan x) 1))
170.0ms	(* (+ 1 (tan x)) (/ (- 1 (tan x)) (fma (tan x) (tan x) 1)))

simplify1.3s

Counts

154 → 154

Iterations

Iter	Nodes
done	2000
3	2000
2	1711
1	525
0	208

prune1.4s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (tan x) (tan x))
0.3b	(* (tan x) (tan x))
0.3b	(* (tan x) (tan x))
0.4b	(- (/ 1 (+ 1 (* (tan x) (tan x)))) (/ (* (tan x) (tan x)) (+ 1 (* (tan x) (tan x)))))

rewrite143.0ms

Algorithm

rewrite-expression-head

Rules

143×	`times-frac`
136×	`add-sqr-sqrt`
135×	`prod-diff`
124×	`*-un-lft-identity`
116×	`add-cube-cbrt`
54×	`associate-/r/`
30×	`div-inv`
27×	`flip3-+` `flip-+`
25×	`pow1`
15×	`fma-neg`
12×	`tan-quot`
10×	`add-cbrt-cube` `add-exp-log`
9×	`swap-sqr` `associate-r` `associate-l`
6×	`add-log-exp` `difference-of-squares`
5×	`distribute-rgt-out--`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`pow2` `frac-times` `pow-plus` `pow-prod-down` `associate-l/` `prod-exp` `associate-r/` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `unswap-sqr`
2×	`distribute-lft-out--`
1×	`sub-neg` `flip3--` `diff-log` `frac-sub` `flip--` `sub-div`

Counts

4 → 273

Calls

4 calls:

29.0ms	(* (tan x) (tan x))
15.0ms	(* (tan x) (tan x))
14.0ms	(* (tan x) (tan x))
75.0ms	(- (/ 1 (+ 1 (* (tan x) (tan x)))) (/ (* (tan x) (tan x)) (+ 1 (* (tan x) (tan x)))))

series290.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(* (tan x) (tan x))
60.0ms	(* (tan x) (tan x))
38.0ms	(* (tan x) (tan x))
146.0ms	(- (/ 1 (+ 1 (* (tan x) (tan x)))) (/ (* (tan x) (tan x)) (+ 1 (* (tan x) (tan x)))))

simplify1.5s

Counts

285 → 285

Iterations

Iter	Nodes
done	2000
3	2000
2	1891
1	765
0	313

prune3.0s

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 0.0b

localize45.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (tan x) (tan x))
0.3b	(* (tan x) (tan x))
0.3b	(* (tan x) (tan x))
0.4b	(* (* (tan x) (tan x)) (* (tan x) (tan x)))

rewrite218.0ms

Algorithm

rewrite-expression-head

Rules

136×	`pow1`
44×	`tan-quot`
39×	`pow-prod-up`
26×	`pow-prod-down`
25×	`pow-sqr`
22×	`add-sqr-sqrt` `add-cbrt-cube` `add-exp-log`
21×	`pow-plus`
20×	`frac-times`
16×	`pow2` `*-un-lft-identity` `add-cube-cbrt`
14×	`associate-l/` `associate-r/`
11×	`prod-exp` `cbrt-unprod`
10×	`swap-sqr` `associate-r` `associate-l`
4×	`expm1-log1p-u` `*-commutative` `insert-posit16` `log1p-expm1-u` `add-log-exp` `unswap-sqr`

Counts

4 → 174

Calls

4 calls:

19.0ms	(* (tan x) (tan x))
29.0ms	(* (tan x) (tan x))
31.0ms	(* (tan x) (tan x))
137.0ms	(* (* (tan x) (tan x)) (* (tan x) (tan x)))

series236.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(* (tan x) (tan x))
63.0ms	(* (tan x) (tan x))
41.0ms	(* (tan x) (tan x))
71.0ms	(* (* (tan x) (tan x)) (* (tan x) (tan x)))

simplify1.1s

Counts

186 → 186

Iterations

Iter	Nodes
done	2000
3	2000
2	901
1	324
0	112

prune1.9s

Pruning

12 alts after pruning (9 fresh and 3 done)

Merged error: 0.0b

regimes316.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	12
1	12
0	8

end0.0ms

sample5.9s

Algorithm

intervals

Results

2.6s	1521×	body	1280	valid
1.8s	1284×	body	640	valid
825.0ms	4276×	body	80	valid
453.0ms	631×	body	320	valid
119.0ms	288×	body	160	valid