Details

sample213.0ms

Algorithm

intervals

Results

61.0ms	35×	body	640	valid
35.0ms	41×	body	1280	valid
22.0ms	145×	body	80	valid
11.0ms	27×	body	320	valid
3.0ms	8×	body	160	valid

simplify27.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	39
5	39
4	36
3	28
2	23
1	15
0	7

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize16.0ms

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))

rewrite63.0ms

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:

14.0ms	(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
5.0ms	(- 1 (* (tan x) (tan x)))
14.0ms	(* (tan x) (tan x))
27.0ms	(* (tan x) (tan x))

series215.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
35.0ms	(- 1 (* (tan x) (tan x)))
35.0ms	(* (tan x) (tan x))
53.0ms	(* (tan x) (tan x))

simplify1.9s

Counts

126 → 126

Iterations

Iter	Nodes
done	5002
2	2277
1	392
0	144

prune492.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize42.0ms

Local error

Found 4 expressions with local error:

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

rewrite109.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 107

Calls

4 calls:

9.0ms	(- 1 (tan x))
9.0ms	(+ 1 (tan x))
61.0ms	(* (+ 1 (tan x)) (/ (- 1 (tan x)) (+ 1 (* (tan x) (tan x)))))
28.0ms	(* (tan x) (tan x))

series274.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(- 1 (tan x))
29.0ms	(+ 1 (tan x))
156.0ms	(* (+ 1 (tan x)) (/ (- 1 (tan x)) (+ 1 (* (tan x) (tan x)))))
56.0ms	(* (tan x) (tan x))

simplify2.9s

Counts

119 → 119

Iterations

Iter	Nodes
done	5000
2	3568
1	535
0	185

prune428.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.0b

localize53.0ms

Local error

Found 4 expressions with local error:

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

rewrite88.0ms

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` `associate-l/` `prod-exp` `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-r/` `pow-sqr` `pow-prod-up` `div-inv` `flip--` `associate-/l` `distribute-lft-out--` `associate-/l/`

Counts

4 → 88

Calls

4 calls:

25.0ms	(* (tan x) (sin x))
17.0ms	(- 1 (/ (* (tan x) (sin x)) (cos x)))
25.0ms	(/ (* (tan x) (sin x)) (cos x))
20.0ms	(* (tan x) (tan x))

series300.0ms

Counts

4 → 12

Calls

4 calls:

75.0ms	(* (tan x) (sin x))
75.0ms	(- 1 (/ (* (tan x) (sin x)) (cos x)))
104.0ms	(/ (* (tan x) (sin x)) (cos x))
46.0ms	(* (tan x) (tan x))

simplify1.9s

Counts

100 → 100

Iterations

Iter	Nodes
done	5001
2	2226
1	351
0	138

prune521.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.0b

localize56.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (cos x) (* (tan x) (sin x)))
0.2b	(- 1 (/ 1 (/ (cos x) (* (tan x) (sin x)))))
0.2b	(* (tan x) (tan x))
0.3b	(/ 1 (/ (cos x) (* (tan x) (sin x))))

rewrite140.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 134

Calls

4 calls:

29.0ms	(/ (cos x) (* (tan x) (sin x)))
67.0ms	(- 1 (/ 1 (/ (cos x) (* (tan x) (sin x)))))
22.0ms	(* (tan x) (tan x))
19.0ms	(/ 1 (/ (cos x) (* (tan x) (sin x))))

series312.0ms

Counts

4 → 12

Calls

4 calls:

113.0ms	(/ (cos x) (* (tan x) (sin x)))
63.0ms	(- 1 (/ 1 (/ (cos x) (* (tan x) (sin x)))))
34.0ms	(* (tan x) (tan x))
102.0ms	(/ 1 (/ (cos x) (* (tan x) (sin x))))

simplify2.4s

Counts

146 → 146

Iterations

Iter	Nodes
done	5001
2	3540
1	543
0	206

prune681.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 0.0b

regimes407.0ms

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	16
1	16
0	12

end0.0ms

sample6.0s

Algorithm

intervals

Results

2.6s	1509×	body	1280	valid
1.4s	4234×	body	80	valid
1.3s	1338×	body	640	valid
449.0ms	600×	body	320	valid
132.0ms	319×	body	160	valid