Details

sample230.0ms

Algorithm

intervals

Results

49.0ms	47×	body	1280	valid
31.0ms	40×	body	640	valid
19.0ms	138×	body	80	valid
9.0ms	19×	body	320	valid
4.0ms	12×	body	160	valid

simplify103.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	37
5	37
4	34
3	26
2	21
1	13
0	7

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize39.0ms

Local error

Found 4 expressions with local error:

0.2b	(- 1.0 (* (tan x) (tan x)))
0.2b	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
0.3b	(* (tan x) (tan x))
0.3b	(* (tan x) (tan x))

rewrite112.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt`
21×	`*-un-lft-identity` `add-cube-cbrt`
18×	`pow1`
12×	`times-frac`
10×	`add-cbrt-cube` `add-exp-log`
8×	`tan-quot`
6×	`swap-sqr` `associate-r` `associate-l` `add-log-exp`
5×	`difference-of-squares`
4×	`associate-/l*`
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 → 105

Calls

4 calls:

8.0ms	(- 1.0 (* (tan x) (tan x)))
43.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
26.0ms	(* (tan x) (tan x))
28.0ms	(* (tan x) (tan x))

series335.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(- 1.0 (* (tan x) (tan x)))
131.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
63.0ms	(* (tan x) (tan x))
78.0ms	(* (tan x) (tan x))

simplify1.3s

Counts

117 → 117

Iterations

Iter	Nodes
done	5000
2	1536
1	350
0	138

prune588.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (+ 1.0 (* (tan x) (tan x))))
0.2b	(* (- 1.0 (* (tan x) (tan x))) (/ 1 (+ 1.0 (* (tan x) (tan x)))))
0.3b	(* (tan x) (tan x))
0.3b	(* (tan x) (tan x))

rewrite118.0ms

Algorithm

rewrite-expression-head

Rules

40×	`add-sqr-sqrt`
29×	`*-un-lft-identity`
28×	`add-cube-cbrt`
21×	`pow1` `associate-r` `add-exp-log`
20×	`times-frac`
15×	`add-cbrt-cube`
10×	`associate-l`
8×	`tan-quot`
6×	`swap-sqr` `prod-exp`
5×	`unswap-sqr`
4×	`frac-times` `div-exp` `associate-*l/` `associate-/r/` `cbrt-unprod` `add-log-exp`
3×	`associate-/r` `pow-prod-down` `associate-r/` `-commutative` `associate-/l`
2×	`pow2` `cbrt-undiv` `rec-exp` `flip3-+` `pow-plus` `flip3--` `1-exp` `pow-sqr` `pow-prod-up` `flip-+` `div-inv` `flip--`
1×	`clear-num` `frac-2neg` `un-div-inv` `pow-flip` `inv-pow` `difference-of-squares`

Counts

4 → 132

Calls

4 calls:

14.0ms	(/ 1 (+ 1.0 (* (tan x) (tan x))))
60.0ms	(* (- 1.0 (* (tan x) (tan x))) (/ 1 (+ 1.0 (* (tan x) (tan x)))))
24.0ms	(* (tan x) (tan x))
15.0ms	(* (tan x) (tan x))

series315.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(/ 1 (+ 1.0 (* (tan x) (tan x))))
127.0ms	(* (- 1.0 (* (tan x) (tan x))) (/ 1 (+ 1.0 (* (tan x) (tan x)))))
65.0ms	(* (tan x) (tan x))
45.0ms	(* (tan x) (tan x))

simplify3.2s

Counts

144 → 144

Iterations

Iter	Nodes
done	5000
2	3121
1	442
0	169

prune754.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize55.0ms

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

rewrite98.0ms

Algorithm

rewrite-expression-head

Rules

32×	`pow1`
28×	`add-sqr-sqrt`
20×	`*-un-lft-identity` `add-cube-cbrt`
16×	`tan-quot`
12×	`add-cbrt-cube` `swap-sqr` `associate-r` `associate-l` `add-exp-log`
4×	`pow2` `frac-times` `pow-plus` `pow-prod-down` `associate-l/` `prod-exp` `associate-r/` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `add-log-exp` `unswap-sqr`

Counts

4 → 112

Calls

4 calls:

23.0ms	(* (tan x) (tan x))
24.0ms	(* (tan x) (tan x))
24.0ms	(* (tan x) (tan x))
24.0ms	(* (tan x) (tan x))

series203.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(* (tan x) (tan x))
49.0ms	(* (tan x) (tan x))
55.0ms	(* (tan x) (tan x))
52.0ms	(* (tan x) (tan x))

simplify8.3s

Counts

124 → 124

Iterations

Iter	Nodes
done	5000
3	4667
2	563
1	124
0	49

prune650.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize59.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (+ (* (tan x) (tan x)) 1.0) (+ (* (tan x) (tan x)) 1.0))
0.3b	(* (tan x) (tan x))
0.3b	(* (tan x) (tan x))
0.3b	(* (tan x) (tan x))

rewrite128.0ms

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` `tan-quot` `add-exp-log`
7×	`frac-times`
6×	`flip3-+` `flip-+`
5×	`associate-l/` `associate-r/`
4×	`pow2` `pow-plus` `pow-prod-down` `prod-exp` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `add-log-exp` `unswap-sqr`
1×	`distribute-rgt-in` `distribute-lft-in`

Counts

4 → 119

Calls

4 calls:

74.0ms	(* (+ (* (tan x) (tan x)) 1.0) (+ (* (tan x) (tan x)) 1.0))
16.0ms	(* (tan x) (tan x))
19.0ms	(* (tan x) (tan x))
12.0ms	(* (tan x) (tan x))

series212.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(* (+ (* (tan x) (tan x)) 1.0) (+ (* (tan x) (tan x)) 1.0))
39.0ms	(* (tan x) (tan x))
43.0ms	(* (tan x) (tan x))
61.0ms	(* (tan x) (tan x))

simplify1.6s

Counts

131 → 131

Iterations

Iter	Nodes
done	5001
2	1937
1	344
0	107

prune727.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

regimes439.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	21
1	21
0	15

end0.0ms

sample4.1s

Algorithm

intervals

Results

1.7s	1465×	body	1280	valid
975.0ms	4287×	body	80	valid
870.0ms	1308×	body	640	valid
209.0ms	598×	body	320	valid
77.0ms	342×	body	160	valid