Details

sample392.0ms

Algorithm

intervals

Results

165.0ms	43×	body	1280	valid
62.0ms	52×	body	640	valid
32.0ms	131×	body	80	valid
13.0ms	19×	body	320	valid
4.0ms	11×	body	160	valid

simplify32.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	44
5	44
4	39
3	31
2	24
1	15
0	7

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize55.0ms

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))

rewrite78.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
29×	`*-un-lft-identity`
24×	`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×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`associate-/r*` `fma-neg` `prod-diff`
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 → 128

Calls

4 calls:

15.0ms	(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
5.0ms	(- 1 (* (tan x) (tan x)))
26.0ms	(* (tan x) (tan x))
29.0ms	(* (tan x) (tan x))

series273.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
66.0ms	(- 1 (* (tan x) (tan x)))
38.0ms	(* (tan x) (tan x))
67.0ms	(* (tan x) (tan x))

simplify1.3s

Counts

140 → 140

Iterations

Iter	Nodes
done	2016
3	2016
2	1102
1	401
0	157

prune1.2s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 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))

rewrite80.0ms

Algorithm

rewrite-expression-head

Rules

123×	`times-frac`
89×	`add-sqr-sqrt`
85×	`*-un-lft-identity`
72×	`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×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`cbrt-undiv` `fma-neg` `prod-diff` `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 → 196

Calls

4 calls:

22.0ms	(/ 1 (/ (+ 1 (* (tan x) (tan x))) (- 1 (* (tan x) (tan x)))))
5.0ms	(- 1 (* (tan x) (tan x)))
18.0ms	(* (tan x) (tan x))
30.0ms	(* (tan x) (tan x))

series244.0ms

Counts

4 → 12

Calls

4 calls:

111.0ms	(/ 1 (/ (+ 1 (* (tan x) (tan x))) (- 1 (* (tan x) (tan x)))))
40.0ms	(- 1 (* (tan x) (tan x)))
43.0ms	(* (tan x) (tan x))
49.0ms	(* (tan x) (tan x))

simplify1.8s

Counts

208 → 208

Iterations

Iter	Nodes
done	2006
3	2006
2	1729
1	735
0	283

prune2.0s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize31.0ms

Local error

Found 4 expressions with local error:

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

rewrite151.0ms

Algorithm

rewrite-expression-head

Rules

136×	`pow1`
44×	`tan-quot`
39×	`pow-prod-up`
26×	`pow-prod-down`
25×	`pow-sqr`
22×	`add-sqr-sqrt` `add-cbrt-cube` `add-exp-log`
21×	`pow-plus`
20×	`frac-times`
16×	`pow2` `*-un-lft-identity` `add-cube-cbrt`
14×	`associate-l/` `associate-r/`
11×	`prod-exp` `cbrt-unprod`
10×	`swap-sqr` `associate-r` `associate-l`
4×	`expm1-log1p-u` `*-commutative` `insert-posit16` `log1p-expm1-u` `add-log-exp` `unswap-sqr`

Counts

4 → 174

Calls

4 calls:

16.0ms	(* (tan x) (tan x))
28.0ms	(* (tan x) (tan x))
14.0ms	(* (tan x) (tan x))
90.0ms	(* (* (tan x) (tan x)) (* (tan x) (tan x)))

series211.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(* (tan x) (tan x))
38.0ms	(* (tan x) (tan x))
56.0ms	(* (tan x) (tan x))
60.0ms	(* (* (tan x) (tan x)) (* (tan x) (tan x)))

simplify1.0s

Counts

186 → 186

Iterations

Iter	Nodes
done	2000
3	2000
2	901
1	324
0	112

prune1.7s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.1b

localize30.0ms

Local error

Found 4 expressions with local error:

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

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

210×	`*-un-lft-identity`
204×	`times-frac`
158×	`add-sqr-sqrt`
98×	`add-cube-cbrt`
40×	`difference-of-squares`
30×	`associate-/r*`
26×	`distribute-lft-out`
20×	`distribute-lft-out--`
13×	`associate-/r/`
11×	`add-cbrt-cube` `add-exp-log`
9×	`prod-diff`
8×	`add-log-exp`
7×	`flip3--` `div-inv` `flip--` `associate-/l*`
4×	`expm1-log1p-u` `pow1` `cbrt-undiv` `div-exp` `insert-posit16` `log1p-expm1-u`
3×	`fma-def` `fma-neg`
2×	`clear-num` `frac-2neg` `flip3-+` `flip-+` `associate-/l/`
1×	`+-commutative` `sum-log` `sub-neg` `diff-log`

Counts

4 → 236

Calls

4 calls:

5.0ms	(- 1 (tan x))
9.0ms	(/ (fma (tan x) (tan x) 1) (- 1 (tan x)))
38.0ms	(/ (+ 1 (tan x)) (/ (fma (tan x) (tan x) 1) (- 1 (tan x))))
10.0ms	(+ 1 (tan x))

series313.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(- 1 (tan x))
90.0ms	(/ (fma (tan x) (tan x) 1) (- 1 (tan x)))
168.0ms	(/ (+ 1 (tan x)) (/ (fma (tan x) (tan x) 1) (- 1 (tan x))))
32.0ms	(+ 1 (tan x))

simplify1.1s

Counts

248 → 248

Iterations

Iter	Nodes
done	2000
2	2000
1	820
0	324

prune2.6s

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 0.1b

regimes422.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	14
1	14
0	11

end0.0ms

sample6.1s

Algorithm

intervals

Results

2.7s	1522×	body	1280	valid
1.8s	1229×	body	640	valid
808.0ms	4258×	body	80	valid
529.0ms	658×	body	320	valid
142.0ms	333×	body	160	valid