Details

sample324.0ms

Algorithm

intervals

Results

81.0ms	30×	body	640	valid
78.0ms	51×	body	1280	valid
31.0ms	139×	body	80	valid
21.0ms	27×	body	320	valid
5.0ms	9×	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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize17.0ms

Local error

Found 4 expressions with local error:

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

rewrite79.0ms

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:

9.0ms	(- 1 (* (tan x) (tan x)))
17.0ms	(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
14.0ms	(* (tan x) (tan x))
34.0ms	(* (tan x) (tan x))

series260.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(- 1 (* (tan x) (tan x)))
115.0ms	(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
33.0ms	(* (tan x) (tan x))
54.0ms	(* (tan x) (tan x))

simplify722.0ms

Counts

126 → 126

Iterations

Iter	Nodes
done	2000
2	950
1	374
0	144

prune570.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize48.0ms

Local error

Found 4 expressions with local error:

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

rewrite77.0ms

Algorithm

rewrite-expression-head

Rules

66×	`add-sqr-sqrt`
58×	`times-frac`
52×	`*-un-lft-identity` `add-cube-cbrt`
22×	`add-cbrt-cube` `add-exp-log`
18×	`pow1`
16×	`swap-sqr` `associate-r` `associate-l`
6×	`cbrt-undiv` `associate-/r` `div-exp` `div-inv` `associate-/l`
5×	`prod-exp` `cbrt-unprod` `unswap-sqr`
4×	`tan-quot` `insert-posit16` `add-log-exp`
2×	`pow2` `frac-times` `quot-tan` `clear-num` `frac-2neg` `pow-plus` `pow-prod-down` `associate-l/` `associate-r/` `pow-sqr` `*-commutative` `pow-prod-up`

Counts

4 → 155

Calls

4 calls:

8.0ms	(/ (sin x) (cos x))
15.0ms	(/ (sin x) (cos x))
37.0ms	(* (/ (sin x) (cos x)) (/ (sin x) (cos x)))
15.0ms	(* (tan x) (tan x))

series160.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(/ (sin x) (cos x))
33.0ms	(/ (sin x) (cos x))
61.0ms	(* (/ (sin x) (cos x)) (/ (sin x) (cos x)))
39.0ms	(* (tan x) (tan x))

simplify841.0ms

Counts

167 → 167

Iterations

Iter	Nodes
done	2000
2	1719
1	520
0	167

prune1.2s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize44.0ms

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)))

rewrite171.0ms

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:

14.0ms	(* (tan x) (tan x))
14.0ms	(* (tan x) (tan x))
64.0ms	(* (* (tan x) (tan x)) (* (tan x) (tan x)))
75.0ms	(* (* (tan x) (tan x)) (* (tan x) (tan x)))

series192.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(* (tan x) (tan x))
37.0ms	(* (tan x) (tan x))
55.0ms	(* (* (tan x) (tan x)) (* (tan x) (tan x)))
56.0ms	(* (* (tan x) (tan x)) (* (tan x) (tan x)))

simplify1.3s

Counts

228 → 228

Iterations

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

prune808.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

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

rewrite87.0ms

Algorithm

rewrite-expression-head

Rules

138×	`times-frac`
100×	`add-sqr-sqrt`
96×	`*-un-lft-identity`
80×	`add-cube-cbrt`
32×	`difference-of-squares`
26×	`associate-/r*`
21×	`add-exp-log`
19×	`pow1`
15×	`add-cbrt-cube`
11×	`associate-/r/`
8×	`div-exp` `tan-quot`
6×	`swap-sqr` `associate-r` `associate-l` `div-inv` `associate-/l*`
5×	`flip3--` `flip--`
4×	`cbrt-undiv` `insert-posit16` `add-log-exp`
2×	`pow2` `frac-times` `rec-exp` `clear-num` `frac-2neg` `pow-plus` `1-exp` `pow-prod-down` `associate-l/` `prod-exp` `associate-r/` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `unswap-sqr` `associate-/l/`
1×	`flip3-+` `flip-+` `pow-flip` `inv-pow`

Counts

4 → 207

Calls

4 calls:

40.0ms	(/ (+ 1 (* (tan x) (tan x))) (- 1 (* (tan x) (tan x))))
17.0ms	(/ 1 (/ (+ 1 (* (tan x) (tan x))) (- 1 (* (tan x) (tan x)))))
14.0ms	(* (tan x) (tan x))
14.0ms	(* (tan x) (tan x))

series309.0ms

Counts

4 → 12

Calls

4 calls:

118.0ms	(/ (+ 1 (* (tan x) (tan x))) (- 1 (* (tan x) (tan x))))
106.0ms	(/ 1 (/ (+ 1 (* (tan x) (tan x))) (- 1 (* (tan x) (tan x)))))
45.0ms	(* (tan x) (tan x))
40.0ms	(* (tan x) (tan x))

simplify1.2s

Counts

219 → 219

Iterations

Iter	Nodes
done	2001
2	1819
1	752
0	284

prune762.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

regimes252.0ms

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	11
1	11
0	8

end0.0ms

sample6.2s

Algorithm

intervals

Results

2.6s	1537×	body	1280	valid
1.7s	1235×	body	640	valid
1.0s	4274×	body	80	valid
514.0ms	662×	body	320	valid
121.0ms	292×	body	160	valid