Details

sample354.0ms

Algorithm

intervals

Results

108.0ms	52×	body	640	valid
72.0ms	43×	body	1280	valid
36.0ms	131×	body	80	valid
15.0ms	19×	body	320	valid
6.0ms	11×	body	160	valid

simplify55.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	38
5	38
4	36
3	28
2	23
1	15
0	7

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize34.0ms

Local error

Found 4 expressions with local error:

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

rewrite97.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-sqr-sqrt`
27×	`*-un-lft-identity`
22×	`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×	`insert-posit16`
3×	`associate-/r*`
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 → 114

Calls

4 calls:

30.0ms	(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
5.0ms	(- 1 (* (tan x) (tan x)))
16.0ms	(* (tan x) (tan x))
42.0ms	(* (tan x) (tan x))

series278.0ms

Counts

4 → 12

Calls

4 calls:

121.0ms	(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
56.0ms	(- 1 (* (tan x) (tan x)))
40.0ms	(* (tan x) (tan x))
60.0ms	(* (tan x) (tan x))

simplify1.2s

Counts

126 → 126

Iterations

Iter	Nodes
done	2002
3	2002
2	964
1	376
0	144

prune573.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

localize41.0ms

Local error

Found 4 expressions with local error:

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

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

123×	`times-frac`
87×	`add-sqr-sqrt`
83×	`*-un-lft-identity`
70×	`add-cube-cbrt`
26×	`difference-of-squares`
21×	`associate-/r*`
19×	`pow1` `add-exp-log`
13×	`add-cbrt-cube`
9×	`associate-/r/`
8×	`tan-quot`
7×	`div-exp`
6×	`swap-sqr` `associate-r` `associate-l` `add-log-exp`
5×	`flip3--` `div-inv` `flip--`
4×	`insert-posit16`
3×	`cbrt-undiv` `associate-/l*`
2×	`pow2` `frac-times` `rec-exp` `pow-plus` `1-exp` `pow-prod-down` `associate-l/` `prod-exp` `associate-r/` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `unswap-sqr`
1×	`clear-num` `sub-neg` `frac-2neg` `diff-log` `pow-flip` `inv-pow`

Counts

4 → 182

Calls

4 calls:

16.0ms	(/ 1 (/ (+ 1 (* (tan x) (tan x))) (- 1 (* (tan x) (tan x)))))
5.0ms	(- 1 (* (tan x) (tan x)))
18.0ms	(* (tan x) (tan x))
29.0ms	(* (tan x) (tan x))

series246.0ms

Counts

4 → 12

Calls

4 calls:

111.0ms	(/ 1 (/ (+ 1 (* (tan x) (tan x))) (- 1 (* (tan x) (tan x)))))
41.0ms	(- 1 (* (tan x) (tan x)))
57.0ms	(* (tan x) (tan x))
37.0ms	(* (tan x) (tan x))

simplify1.5s

Counts

194 → 194

Iterations

Iter	Nodes
done	2011
3	2011
2	1660
1	714
0	272

prune743.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize33.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (tan x) (tan x))
0.2b	(* (tan x) (tan x))
0.2b	(* (tan x) (tan x))
0.3b	(* (* (tan x) (tan x)) (* (tan x) (tan x)))

rewrite202.0ms

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×	`*-commutative` `insert-posit16` `add-log-exp` `unswap-sqr`

Counts

4 → 166

Calls

4 calls:

31.0ms	(* (tan x) (tan x))
23.0ms	(* (tan x) (tan x))
15.0ms	(* (tan x) (tan x))
128.0ms	(* (* (tan x) (tan x)) (* (tan x) (tan x)))

series188.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(* (tan x) (tan x))
38.0ms	(* (tan x) (tan x))
55.0ms	(* (tan x) (tan x))
63.0ms	(* (* (tan x) (tan x)) (* (tan x) (tan x)))

simplify1.5s

Counts

178 → 178

Iterations

Iter	Nodes
done	2009
4	2009
3	1922
2	954
1	318
0	108

prune702.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.1b

localize57.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin x) (sin x))
0.2b	(* (sin x) (sin x))
0.3b	(* (cos x) (cos x))
0.3b	(* (cos x) (cos x))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

32×	`pow1`
28×	`add-sqr-sqrt`
20×	`*-un-lft-identity` `add-cube-cbrt`
12×	`add-cbrt-cube` `swap-sqr` `associate-r` `associate-l` `add-exp-log`
4×	`pow2` `pow-plus` `pow-prod-down` `prod-exp` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `insert-posit16` `add-log-exp` `unswap-sqr`
2×	`sqr-cos` `cos-mult` `sqr-sin` `sin-mult`

Counts

4 → 112

Calls

4 calls:

12.0ms	(* (sin x) (sin x))
12.0ms	(* (sin x) (sin x))
10.0ms	(* (cos x) (cos x))
14.0ms	(* (cos x) (cos x))

series100.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(* (sin x) (sin x))
27.0ms	(* (sin x) (sin x))
17.0ms	(* (cos x) (cos x))
22.0ms	(* (cos x) (cos x))

simplify1.5s

Counts

124 → 124

Iterations

Iter	Nodes
done	2001
4	2001
3	1169
2	566
1	210
0	79

prune482.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.1b

regimes355.0ms

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	9

end0.0ms

sample5.7s

Algorithm

intervals

Results

2.4s	1522×	body	1280	valid
1.3s	4258×	body	80	valid
1.2s	1229×	body	640	valid
443.0ms	658×	body	320	valid
183.0ms	333×	body	160	valid