Details

sample352.0ms

Algorithm

intervals

Results

19.0ms	45×	body	1280	valid
12.0ms	44×	body	640	valid
9.0ms	133×	body	80	valid
4.0ms	23×	body	320	valid
1.0ms	11×	body	160	valid

simplify14.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	13	9
1	21	9
2	26	9
3	34	9
4	37	9
5	37	9
done	37	9

prune27.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- 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))

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt`
21×	`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×	`associate-/l*`
3×	`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 → 105

Calls

4 calls:

21.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
5.0ms	(- 1.0 (* (tan x) (tan x)))
15.0ms	(* (tan x) (tan x))
17.0ms	(* (tan x) (tan x))

series211.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
39.0ms	(- 1.0 (* (tan x) (tan x)))
33.0ms	(* (tan x) (tan x))
44.0ms	(* (tan x) (tan x))

simplify43.0ms

Counts

117 → 117

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	314	909
1	1157	838
2	5001	824
done	5001	824

prune235.0ms

Pruning

11 alts after pruning (11 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)) (- (sqrt 1.0) (tan x))) (+ 1.0 (* (tan x) (tan x))))
0.2b	(+ (sqrt 1.0) (tan x))
0.3b	(* (+ (sqrt 1.0) (tan x)) (- (sqrt 1.0) (tan x)))
0.3b	(* (tan x) (tan x))

rewrite110.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
18×	`*-un-lft-identity`
13×	`pow1` `add-exp-log` `add-cbrt-cube`
12×	`add-cube-cbrt`
9×	`frac-times` `associate-r`
8×	`flip3-+` `flip-+` `associate-/l/`
7×	`associate-l`
6×	`flip3--` `flip--` `add-log-exp`
5×	`associate-r/` `associate-l/`
4×	`tan-quot`
3×	`times-frac` `swap-sqr` `prod-exp` `associate-/r*` `cbrt-unprod`
2×	`cbrt-undiv` `distribute-rgt-in` `sub-neg` `distribute-lft-in` `div-exp` `pow-prod-down` `associate-/r/` `*-commutative` `distribute-lft-out` `difference-of-squares` `unswap-sqr`
1×	`+-commutative` `pow2` `frac-2neg` `pow-plus` `clear-num` `sum-log` `sqrt-prod` `pow-sqr` `pow-prod-up` `div-inv` `associate-/l*` `distribute-lft-out--`

Counts

4 → 105

Calls

4 calls:

31.0ms	(/ (* (+ (sqrt 1.0) (tan x)) (- (sqrt 1.0) (tan x))) (+ 1.0 (* (tan x) (tan x))))
10.0ms	(+ (sqrt 1.0) (tan x))
49.0ms	(* (+ (sqrt 1.0) (tan x)) (- (sqrt 1.0) (tan x)))
17.0ms	(* (tan x) (tan x))

series360.0ms

Counts

4 → 12

Calls

4 calls:

191.0ms	(/ (* (+ (sqrt 1.0) (tan x)) (- (sqrt 1.0) (tan x))) (+ 1.0 (* (tan x) (tan x))))
33.0ms	(+ (sqrt 1.0) (tan x))
103.0ms	(* (+ (sqrt 1.0) (tan x)) (- (sqrt 1.0) (tan x)))
33.0ms	(* (tan x) (tan x))

simplify76.0ms

Counts

117 → 117

Iterations

Useful iterations: 2 (67.0ms)

Iter	Nodes	Cost
0	517	1120
1	2851	938
2	5001	923
done	5001	923

prune266.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.1b

localize9.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ (+ 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))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

102×	`times-frac`
80×	`add-sqr-sqrt`
63×	`add-cube-cbrt` `*-un-lft-identity`
19×	`pow1` `add-exp-log`
18×	`associate-/r*`
13×	`add-cbrt-cube` `difference-of-squares`
9×	`associate-/r/`
8×	`tan-quot`
7×	`div-exp`
6×	`swap-sqr` `associate-r` `associate-l` `add-log-exp`
5×	`flip3--` `flip--` `div-inv`
3×	`cbrt-undiv` `associate-/l*`
2×	`pow2` `frac-times` `rec-exp` `pow-plus` `1-exp` `associate-r/` `pow-prod-down` `associate-l/` `prod-exp` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `unswap-sqr`
1×	`sub-neg` `pow-flip` `frac-2neg` `diff-log` `clear-num` `inv-pow`

Counts

4 → 165

Calls

4 calls:

18.0ms	(/ 1 (/ (+ 1.0 (* (tan x) (tan x))) (- 1.0 (* (tan x) (tan x)))))
5.0ms	(- 1.0 (* (tan x) (tan x)))
17.0ms	(* (tan x) (tan x))
15.0ms	(* (tan x) (tan x))

series198.0ms

Counts

4 → 12

Calls

4 calls:

96.0ms	(/ 1 (/ (+ 1.0 (* (tan x) (tan x))) (- 1.0 (* (tan x) (tan x)))))
33.0ms	(- 1.0 (* (tan x) (tan x)))
32.0ms	(* (tan x) (tan x))
37.0ms	(* (tan x) (tan x))

simplify71.0ms

Counts

177 → 177

Iterations

Useful iterations: 2 (55.0ms)

Iter	Nodes	Cost
0	545	2150
1	2567	1968
2	5001	1866
done	5001	1866

prune275.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.1b

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (tan x) (- (tan x) (sqrt 1.0)))
0.3b	(* (/ (+ (pow (sqrt 1.0) 3) (pow (tan x) 3)) (+ (* (tan x) (- (tan x) (sqrt 1.0))) 1.0)) (- (sqrt 1.0) (tan x)))
0.3b	(* (tan x) (tan x))
0.4b	(pow (tan x) 3)

rewrite274.0ms

Algorithm

rewrite-expression-head

Rules

61×	`*-un-lft-identity`
44×	`add-sqr-sqrt`
39×	`associate-l`
28×	`times-frac`
27×	`add-cube-cbrt`
16×	`pow1`
15×	`unpow-prod-down` `cube-prod` `associate-r` `distribute-lft-out`
14×	`add-exp-log` `add-cbrt-cube`
8×	`tan-quot`
5×	`frac-times` `associate-*r/`
4×	`distribute-rgt-in` `sub-neg` `flip3--` `distribute-lft-in` `prod-exp` `flip--` `cbrt-unprod` `add-log-exp` `difference-of-squares` `unswap-sqr`
3×	`pow-unpow` `swap-sqr` `pow-prod-down` `associate-l/` `sum-cubes` `-commutative`
2×	`sqrt-prod` `associate-/r/` `distribute-lft-out--`
1×	`cbrt-undiv` `cube-div` `pow2` `cube-mult` `pow-to-exp` `pow-pow` `flip3-+` `pow-plus` `unpow3` `div-exp` `pow-exp` `pow-sqr` `pow-prod-up` `flip-+` `div-inv` `rem-cube-cbrt` `sqr-pow`

Counts

4 → 145

Calls

4 calls:

39.0ms	(* (tan x) (- (tan x) (sqrt 1.0)))
211.0ms	(* (/ (+ (pow (sqrt 1.0) 3) (pow (tan x) 3)) (+ (* (tan x) (- (tan x) (sqrt 1.0))) 1.0)) (- (sqrt 1.0) (tan x)))
14.0ms	(* (tan x) (tan x))
4.0ms	(pow (tan x) 3)

series475.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(* (tan x) (- (tan x) (sqrt 1.0)))
324.0ms	(* (/ (+ (pow (sqrt 1.0) 3) (pow (tan x) 3)) (+ (* (tan x) (- (tan x) (sqrt 1.0))) 1.0)) (- (sqrt 1.0) (tan x)))
36.0ms	(* (tan x) (tan x))
47.0ms	(pow (tan x) 3)

simplify112.0ms

Counts

157 → 157

Iterations

Useful iterations: 2 (98.0ms)

Iter	Nodes	Cost
0	684	1761
1	3697	1615
2	5001	1603
done	5001	1603

prune397.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.1b

regimes164.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	12
1	13	12
done	13	12

end0.0ms

sample1.6s

Algorithm

intervals

Results

642.0ms	1436×	body	1280	valid
371.0ms	1280×	body	640	valid
242.0ms	4330×	body	80	valid
123.0ms	659×	body	320	valid
38.0ms	295×	body	160	valid