Details

sample370.0ms

Algorithm

intervals

Results

26.0ms	61×	body	1280	valid
10.0ms	36×	body	640	valid
9.0ms	135×	body	80	valid
3.0ms	18×	body	320	valid
1.0ms	6×	body	160	valid

simplify40.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	13	9
1	22	9
2	29	9
3	37	9
4	43	9
5	45	9
6	45	9
done	45	9

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize12.0ms

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))

rewrite68.0ms

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:

10.0ms	(- 1.0 (* (tan x) (tan x)))
20.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
15.0ms	(* (tan x) (tan x))
18.0ms	(* (tan x) (tan x))

series216.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(- 1.0 (* (tan x) (tan x)))
101.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
33.0ms	(* (tan x) (tan x))
44.0ms	(* (tan x) (tan x))

simplify43.0ms

Counts

131 → 131

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	338	1007
1	1243	917
2	5001	882
done	5001	882

prune290.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize10.0ms

Local error

Found 4 expressions with local error:

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

rewrite127.0ms

Algorithm

rewrite-expression-head

Rules

204×	`times-frac`
186×	`*-un-lft-identity`
174×	`add-sqr-sqrt`
96×	`add-cube-cbrt`
38×	`difference-of-squares`
30×	`associate-/r*`
26×	`distribute-lft-out`
22×	`sqrt-prod`
19×	`distribute-lft-out--`
13×	`add-exp-log` `associate-/r/` `add-cbrt-cube`
11×	`pow1`
7×	`div-inv` `associate-/l*`
6×	`flip3--` `fma-def` `flip--` `add-log-exp`
4×	`tan-quot` `cbrt-undiv` `expm1-log1p-u` `div-exp` `log1p-expm1-u` `associate-/l/`
3×	`flip3-+` `swap-sqr` `associate-r` `associate-l` `flip-+`
2×	`frac-2neg` `clear-num`
1×	`+-commutative` `pow2` `frac-times` `pow-plus` `associate-r/` `pow-prod-down` `associate-l/` `prod-exp` `sum-log` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `unswap-sqr`

Counts

4 → 238

Calls

4 calls:

10.0ms	(+ (sqrt 1.0) (tan x))
50.0ms	(/ (+ (sqrt 1.0) (tan x)) (/ (+ 1.0 (* (tan x) (tan x))) (- (sqrt 1.0) (tan x))))
39.0ms	(/ (+ 1.0 (* (tan x) (tan x))) (- (sqrt 1.0) (tan x)))
15.0ms	(* (tan x) (tan x))

series374.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(+ (sqrt 1.0) (tan x))
192.0ms	(/ (+ (sqrt 1.0) (tan x)) (/ (+ 1.0 (* (tan x) (tan x))) (- (sqrt 1.0) (tan x))))
111.0ms	(/ (+ 1.0 (* (tan x) (tan x))) (- (sqrt 1.0) (tan x)))
37.0ms	(* (tan x) (tan x))

simplify120.0ms

Counts

250 → 250

Iterations

Useful iterations: 2 (88.0ms)

Iter	Nodes	Cost
0	758	4210
1	3856	3784
2	5001	3760
done	5001	3760

prune559.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite83.0ms

Algorithm

rewrite-expression-head

Rules

22×	`*-un-lft-identity`
16×	`add-sqr-sqrt`
15×	`add-exp-log` `add-cbrt-cube`
14×	`add-cube-cbrt`
12×	`fma-def`
11×	`pow1`
8×	`add-log-exp`
6×	`sqrt-prod`
5×	`flip3-+` `associate-/r/` `flip-+`
4×	`tan-quot` `cbrt-undiv` `expm1-log1p-u` `times-frac` `div-exp` `log1p-expm1-u` `distribute-lft-out` `associate-/l*`
3×	`frac-times` `associate-r/` `swap-sqr` `associate-r` `associate-l*` `prod-exp` `cbrt-unprod`
2×	`+-commutative` `associate-*l/` `sum-log` `associate-/l/`
1×	`pow2` `frac-2neg` `pow-plus` `pow-prod-down` `clear-num` `associate-/r` `pow-sqr` `-commutative` `pow-prod-up` `div-inv` `unswap-sqr`

Counts

4 → 104

Calls

4 calls:

9.0ms	(+ (sqrt 1.0) (tan x))
9.0ms	(+ (sqrt 1.0) (tan x))
46.0ms	(/ (+ (sqrt 1.0) (tan x)) (* (/ (fma (tan x) (tan x) 1.0) (- 1.0 (* (tan x) (tan x)))) (+ (sqrt 1.0) (tan x))))
15.0ms	(* (tan x) (tan x))

series216.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(+ (sqrt 1.0) (tan x))
38.0ms	(+ (sqrt 1.0) (tan x))
112.0ms	(/ (+ (sqrt 1.0) (tan x)) (* (/ (fma (tan x) (tan x) 1.0) (- 1.0 (* (tan x) (tan x)))) (+ (sqrt 1.0) (tan x))))
33.0ms	(* (tan x) (tan x))

simplify58.0ms

Counts

116 → 116

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	411	1009
1	2091	817
2	5003	717
done	5003	717

prune311.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 4 expressions with local error:

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

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 93

Calls

4 calls:

0.0ms	(fma (tan x) (tan x) 1.0)
13.0ms	(- (* (sqrt 1.0) (sqrt 1.0)) (* (tan x) (tan x)))
31.0ms	(/ (- (* (sqrt 1.0) (sqrt 1.0)) (* (tan x) (tan x))) (fma (tan x) (tan x) 1.0))
15.0ms	(* (tan x) (tan x))

series323.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(fma (tan x) (tan x) 1.0)
71.0ms	(- (* (sqrt 1.0) (sqrt 1.0)) (* (tan x) (tan x)))
176.0ms	(/ (- (* (sqrt 1.0) (sqrt 1.0)) (* (tan x) (tan x))) (fma (tan x) (tan x) 1.0))
33.0ms	(* (tan x) (tan x))

simplify48.0ms

Counts

105 → 105

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	367	1024
1	1626	900
2	5001	887
done	5001	887

prune265.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

regimes74.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	11
1	9	11
done	9	11

end0.0ms

sample1.6s

Algorithm

intervals

Results

682.0ms	1556×	body	1280	valid
364.0ms	1285×	body	640	valid
240.0ms	4264×	body	80	valid
117.0ms	623×	body	320	valid
39.0ms	272×	body	160	valid