Details

sample229.0ms

Algorithm

intervals

Results

36.0ms	41×	body	1280	valid
26.0ms	40×	body	640	valid
25.0ms	154×	body	80	valid
8.0ms	15×	body	320	valid
2.0ms	6×	body	160	valid

simplify150.0ms

Counts

1 → 1

Iterations

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

prune102.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

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))

rewrite139.0ms

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:

47.0ms	(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
11.0ms	(- 1 (* (tan x) (tan x)))
36.0ms	(* (tan x) (tan x))
38.0ms	(* (tan x) (tan x))

series304.0ms

Counts

4 → 12

Calls

4 calls:

141.0ms	(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
35.0ms	(- 1 (* (tan x) (tan x)))
58.0ms	(* (tan x) (tan x))
70.0ms	(* (tan x) (tan x))

simplify2.4s

Counts

126 → 126

Iterations

Iter	Nodes
done	5070
3	3113
2	964
1	376
0	144

prune508.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.0b

localize34.0ms

Local error

Found 4 expressions with local error:

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

rewrite311.0ms

Algorithm

rewrite-expression-head

Rules

240×	`pow1`
74×	`pow-prod-up`
72×	`tan-quot`
48×	`pow-prod-down`
46×	`pow-sqr`
38×	`pow-plus`
36×	`frac-times`
32×	`add-cbrt-cube` `add-exp-log`
28×	`pow2`
24×	`associate-l/` `associate-r/`
18×	`prod-exp` `cbrt-unprod`
16×	`add-sqr-sqrt`
12×	`*-un-lft-identity` `add-cube-cbrt`
8×	`swap-sqr` `associate-r` `associate-l`
4×	`*-commutative` `insert-posit16` `add-log-exp` `unswap-sqr`

Counts

4 → 216

Calls

4 calls:

31.0ms	(* (tan x) (tan x))
30.0ms	(* (tan x) (tan x))
123.0ms	(* (* (tan x) (tan x)) (* (tan x) (tan x)))
112.0ms	(* (* (tan x) (tan x)) (* (tan x) (tan x)))

series265.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(* (tan x) (tan x))
47.0ms	(* (tan x) (tan x))
82.0ms	(* (* (tan x) (tan x)) (* (tan x) (tan x)))
85.0ms	(* (* (tan x) (tan x)) (* (tan x) (tan x)))

simplify2.4s

Counts

228 → 228

Iterations

Iter	Nodes
done	5000
3	1922
2	954
1	318
0	108

prune740.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize36.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 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))

rewrite122.0ms

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:

37.0ms	(/ 1 (/ (+ 1 (* (tan x) (tan x))) (- 1 (* (tan x) (tan x)))))
10.0ms	(- 1 (* (tan x) (tan x)))
35.0ms	(* (tan x) (tan x))
31.0ms	(* (tan x) (tan x))

series252.0ms

Counts

4 → 12

Calls

4 calls:

109.0ms	(/ 1 (/ (+ 1 (* (tan x) (tan x))) (- 1 (* (tan x) (tan x)))))
36.0ms	(- 1 (* (tan x) (tan x)))
44.0ms	(* (tan x) (tan x))
62.0ms	(* (tan x) (tan x))

simplify1.6s

Counts

194 → 194

Iterations

Iter	Nodes
done	5004
2	1660
1	714
0	272

prune708.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

localize53.0ms

Local error

Found 4 expressions with local error:

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

rewrite89.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 88

Calls

4 calls:

23.0ms	(/ (* (sin x) (tan x)) (cos x))
11.0ms	(- 1 (/ (* (sin x) (tan x)) (cos x)))
13.0ms	(* (sin x) (tan x))
37.0ms	(* (tan x) (tan x))

series267.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(/ (* (sin x) (tan x)) (cos x))
81.0ms	(- 1 (/ (* (sin x) (tan x)) (cos x)))
59.0ms	(* (sin x) (tan x))
43.0ms	(* (tan x) (tan x))

simplify2.8s

Counts

100 → 100

Iterations

Iter	Nodes
done	5660
3	3735
2	951
1	349
0	138

prune516.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

regimes709.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify5.0ms

Iterations

Iter	Nodes
done	20
1	20
0	14

end0.0ms

sample4.1s

Algorithm

intervals

Results

2.0s	1501×	body	1280	valid
1.1s	1261×	body	640	valid
495.0ms	4281×	body	80	valid
300.0ms	629×	body	320	valid
90.0ms	328×	body	160	valid