Details

sample305.0ms

Algorithm

intervals

Results

21.0ms	47×	body	1280	valid
14.0ms	51×	body	640	valid
8.0ms	126×	body	80	valid
4.0ms	22×	body	320	valid
1.0ms	10×	body	160	valid

simplify30.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (8.0ms)

Iter	Nodes	Cost
0	7	15
1	13	15
2	22	14
3	29	14
4	37	14
5	42	14
6	44	14
done	44	14

prune7.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.3b

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
0.2b	(- 1.0 (* (tan x) (tan x)))
0.3b	(* (tan x) (tan x))
0.3b	(* (tan x) (tan x))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt`
23×	`add-cube-cbrt` `*-un-lft-identity`
18×	`pow1`
12×	`times-frac`
10×	`add-exp-log` `add-cbrt-cube`
8×	`tan-quot`
6×	`swap-sqr` `associate-r` `associate-l` `add-log-exp`
5×	`difference-of-squares`
4×	`expm1-log1p-u` `log1p-expm1-u` `associate-/l*`
3×	`fma-neg` `prod-diff` `associate-/r*`
2×	`pow2` `frac-times` `flip3--` `pow-plus` `associate-r/` `pow-prod-down` `associate-l/` `prod-exp` `associate-/r/` `pow-sqr` `*-commutative` `pow-prod-up` `flip--` `cbrt-unprod` `associate-/l/` `unswap-sqr`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `flip3-+` `diff-log` `div-sub` `div-exp` `clear-num` `flip-+` `div-inv`

Counts

4 → 119

Calls

4 calls:

8.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
2.0ms	(- 1.0 (* (tan x) (tan x)))
5.0ms	(* (tan x) (tan x))
7.0ms	(* (tan x) (tan x))

series206.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
33.0ms	(- 1.0 (* (tan x) (tan x)))
38.0ms	(* (tan x) (tan x))
42.0ms	(* (tan x) (tan x))

simplify515.0ms

Counts

131 → 131

Iterations

Useful iterations: 2 (109.0ms)

Iter	Nodes	Cost
0	151	1789
1	339	1638
2	1141	1453
done	5000	1453

prune288.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (cos x) 2)
0.2b	(pow (cos x) 2)
0.3b	(pow (sin x) 2)
0.3b	(pow (sin x) 2)

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `add-cube-cbrt` `unpow-prod-down` `pow-unpow` `*-un-lft-identity`
8×	`pow1` `add-exp-log`
4×	`expm1-log1p-u` `pow-to-exp` `pow-pow` `pow-exp` `add-cbrt-cube` `log1p-expm1-u` `unpow2` `add-log-exp` `sqr-pow`

Counts

4 → 80

Calls

4 calls:

1.0ms	(pow (cos x) 2)
1.0ms	(pow (cos x) 2)
1.0ms	(pow (sin x) 2)
2.0ms	(pow (sin x) 2)

series75.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(pow (cos x) 2)
17.0ms	(pow (cos x) 2)
19.0ms	(pow (sin x) 2)
20.0ms	(pow (sin x) 2)

simplify1.3s

Counts

92 → 92

Iterations

Useful iterations: 2 (55.0ms)

Iter	Nodes	Cost
0	68	616
1	149	530
2	472	466
3	1509	466
done	5000	466

prune258.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma (tan x) (tan x) 1.0)
0.2b	(- 1.0 (* (tan x) (tan x)))
0.2b	(/ 1 (/ (fma (tan x) (tan x) 1.0) (- 1.0 (* (tan x) (tan x)))))
0.3b	(* (tan x) (tan x))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

102×	`times-frac`
76×	`add-sqr-sqrt`
61×	`add-cube-cbrt` `*-un-lft-identity`
18×	`associate-/r*`
17×	`add-exp-log`
13×	`difference-of-squares`
12×	`pow1`
11×	`add-cbrt-cube`
9×	`associate-/r/`
7×	`div-exp`
6×	`add-log-exp`
5×	`flip3--` `flip--` `div-inv`
4×	`tan-quot` `expm1-log1p-u` `log1p-expm1-u`
3×	`cbrt-undiv` `fma-neg` `swap-sqr` `associate-r` `associate-l` `prod-diff` `associate-/l*`
2×	`rec-exp` `1-exp`
1×	`pow2` `frac-times` `sub-neg` `pow-flip` `frac-2neg` `pow-plus` `diff-log` `associate-r/` `pow-prod-down` `associate-l/` `prod-exp` `clear-num` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `fma-udef` `inv-pow` `unswap-sqr`

Counts

4 → 159

Calls

4 calls:

0.0ms	(fma (tan x) (tan x) 1.0)
2.0ms	(- 1.0 (* (tan x) (tan x)))
8.0ms	(/ 1 (/ (fma (tan x) (tan x) 1.0) (- 1.0 (* (tan x) (tan x)))))
8.0ms	(* (tan x) (tan x))

series216.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(fma (tan x) (tan x) 1.0)
35.0ms	(- 1.0 (* (tan x) (tan x)))
106.0ms	(/ 1 (/ (fma (tan x) (tan x) 1.0) (- 1.0 (* (tan x) (tan x)))))
32.0ms	(* (tan x) (tan x))

simplify1.3s

Counts

171 → 171

Iterations

Useful iterations: 2 (236.0ms)

Iter	Nodes	Cost
0	270	3573
1	585	3269
2	2219	2917
done	5000	2917

prune319.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize12.0ms

Local error

Found 4 expressions with local error:

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

rewrite108.0ms

Algorithm

rewrite-expression-head

Rules

294×	`times-frac`
268×	`add-sqr-sqrt`
206×	`*-un-lft-identity`
150×	`add-cube-cbrt`
77×	`associate-r`
52×	`difference-of-squares`
38×	`sqrt-prod`
36×	`add-exp-log`
30×	`associate-/r*`
26×	`distribute-lft-out--`
20×	`add-cbrt-cube`
18×	`prod-diff` `associate-/r/`
15×	`div-exp`
10×	`div-inv`
9×	`flip3--` `flip--`
7×	`pow1` `cbrt-undiv` `prod-exp`
6×	`fma-neg` `associate-/l*` `add-log-exp`
5×	`unswap-sqr`
4×	`expm1-log1p-u` `rec-exp` `1-exp` `associate-l` `log1p-expm1-u`
3×	`cbrt-unprod`
2×	`frac-times` `frac-2neg` `flip3-+` `associate-*l/` `clear-num` `flip-+`
1×	`sub-neg` `pow-flip` `diff-log` `associate-r/` `pow-prod-down` `un-div-inv` `-commutative` `distribute-lft-out` `inv-pow`

Counts

4 → 319

Calls

4 calls:

16.0ms	(/ 1 (/ (fma (tan x) (tan x) 1.0) (- (sqrt 1.0) (tan x))))
57.0ms	(* (+ (tan x) (sqrt 1.0)) (/ 1 (/ (fma (tan x) (tan x) 1.0) (- (sqrt 1.0) (tan x)))))
6.0ms	(- (sqrt 1.0) (tan x))
11.0ms	(/ (fma (tan x) (tan x) 1.0) (- (sqrt 1.0) (tan x)))

series466.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(/ 1 (/ (fma (tan x) (tan x) 1.0) (- (sqrt 1.0) (tan x))))
203.0ms	(* (+ (tan x) (sqrt 1.0)) (/ 1 (/ (fma (tan x) (tan x) 1.0) (- (sqrt 1.0) (tan x)))))
39.0ms	(- (sqrt 1.0) (tan x))
122.0ms	(/ (fma (tan x) (tan x) 1.0) (- (sqrt 1.0) (tan x)))

simplify2.3s

Counts

331 → 331

Iterations

Useful iterations: 2 (414.0ms)

Iter	Nodes	Cost
0	404	8023
1	1001	7126
2	4080	6037
done	5000	6037

prune636.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

regimes107.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	26
1	13	26
2	15	26
done	15	26

end0.0ms

sample1.6s

Algorithm

intervals

Results

680.0ms	1521×	body	1280	valid
370.0ms	1285×	body	640	valid
241.0ms	4286×	body	80	valid
120.0ms	606×	body	320	valid
40.0ms	302×	body	160	valid