Details

sample283.0ms

Algorithm

intervals

Results

109.0ms	143×	body	80	valid
38.0ms	39×	body	1280	valid
27.0ms	41×	body	640	valid
8.0ms	17×	body	320	valid
5.0ms	16×	body	160	valid

simplify68.0ms

Counts

1 → 1

Iterations

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

prune39.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b	(- 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))

rewrite72.0ms

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:

5.0ms	(- 1 (* (tan x) (tan x)))
17.0ms	(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
16.0ms	(* (tan x) (tan x))
32.0ms	(* (tan x) (tan x))

series210.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(- 1 (* (tan x) (tan x)))
86.0ms	(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
34.0ms	(* (tan x) (tan x))
48.0ms	(* (tan x) (tan x))

simplify977.0ms

Counts

126 → 126

Iterations

Iter	Nodes
done	2000
3	2000
2	950
1	374
0	144

prune1.1s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.1b

localize28.0ms

Local error

Found 4 expressions with local error:

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

rewrite92.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 109

Calls

4 calls:

19.0ms	(/ (* (+ 1 (tan x)) (- 1 (tan x))) (+ 1 (* (tan x) (tan x))))
5.0ms	(+ 1 (tan x))
38.0ms	(* (+ 1 (tan x)) (- 1 (tan x)))
28.0ms	(* (tan x) (tan x))

series332.0ms

Counts

4 → 12

Calls

4 calls:

169.0ms	(/ (* (+ 1 (tan x)) (- 1 (tan x))) (+ 1 (* (tan x) (tan x))))
31.0ms	(+ 1 (tan x))
79.0ms	(* (+ 1 (tan x)) (- 1 (tan x)))
53.0ms	(* (tan x) (tan x))

simplify990.0ms

Counts

121 → 121

Iterations

Iter	Nodes
done	2002
2	2002
1	529
0	181

prune1.2s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize22.0ms

Local error

Found 4 expressions with local error:

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

rewrite143.0ms

Algorithm

rewrite-expression-head

Rules

57×	`times-frac`
41×	`add-sqr-sqrt` `*-un-lft-identity`
34×	`add-cube-cbrt`
33×	`associate-/r/`
29×	`add-exp-log`
21×	`frac-times`
17×	`add-cbrt-cube`
16×	`flip3-+` `flip-+`
15×	`associate-/r*` `flip3--` `flip--`
14×	`pow1`
12×	`div-exp`
11×	`associate-l/` `associate-r/`
9×	`associate-r`
7×	`associate-l`
6×	`add-log-exp`
5×	`cbrt-undiv` `prod-exp` `div-inv`
4×	`tan-quot` `insert-posit16`
3×	`rec-exp` `1-exp` `swap-sqr` `cbrt-unprod` `associate-/l*`
2×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `pow-prod-down` `*-commutative` `distribute-lft-out` `difference-of-squares` `unswap-sqr`
1×	`pow2` `+-commutative` `clear-num` `sum-log` `frac-2neg` `pow-plus` `pow-sqr` `pow-prod-up` `pow-flip` `distribute-lft-out--` `inv-pow`

Counts

4 → 166

Calls

4 calls:

48.0ms	(/ 1 (/ (+ 1 (* (tan x) (tan x))) (* (+ 1 (tan x)) (- 1 (tan x)))))
8.0ms	(+ 1 (tan x))
48.0ms	(* (+ 1 (tan x)) (- 1 (tan x)))
30.0ms	(* (tan x) (tan x))

series305.0ms

Counts

4 → 12

Calls

4 calls:

151.0ms	(/ 1 (/ (+ 1 (* (tan x) (tan x))) (* (+ 1 (tan x)) (- 1 (tan x)))))
23.0ms	(+ 1 (tan x))
74.0ms	(* (+ 1 (tan x)) (- 1 (tan x)))
58.0ms	(* (tan x) (tan x))

simplify1.2s

Counts

178 → 178

Iterations

Iter	Nodes
done	2001
2	2001
1	775
0	284

prune2.2s

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 0.0b

localize31.0ms

Local error

Found 4 expressions with local error:

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

rewrite109.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 228

Calls

4 calls:

34.0ms	(/ (+ 1 (tan x)) (/ (+ 1 (* (tan x) (tan x))) (- 1 (tan x))))
50.0ms	(/ (+ 1 (* (tan x) (tan x))) (- 1 (tan x)))
4.0ms	(+ 1 (tan x))
16.0ms	(* (tan x) (tan x))

series348.0ms

Counts

4 → 12

Calls

4 calls:

191.0ms	(/ (+ 1 (tan x)) (/ (+ 1 (* (tan x) (tan x))) (- 1 (tan x))))
94.0ms	(/ (+ 1 (* (tan x) (tan x))) (- 1 (tan x)))
18.0ms	(+ 1 (tan x))
44.0ms	(* (tan x) (tan x))

simplify1.2s

Counts

240 → 240

Iterations

Iter	Nodes
done	2000
2	2000
1	882
0	325

prune2.5s

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 0.0b

regimes403.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
done	15
1	15
0	10

end0.0ms

sample6.1s

Algorithm

intervals

Results

2.7s	1502×	body	1280	valid
1.7s	1267×	body	640	valid
979.0ms	4312×	body	80	valid
416.0ms	624×	body	320	valid
117.0ms	295×	body	160	valid