Details

sample141.0ms

Algorithm

intervals

Results

30.0ms	52×	body	1280	valid
13.0ms	35×	body	640	valid
12.0ms	132×	body	80	valid
9.0ms	25×	body	320	valid
2.0ms	12×	body	160	valid

simplify692.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	36
5	36
4	34
3	26
2	21
1	13
0	7

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize38.0ms

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))

rewrite88.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt`
21×	`*-un-lft-identity` `add-cube-cbrt`
18×	`pow1`
12×	`times-frac`
10×	`add-cbrt-cube` `add-exp-log`
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` `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 → 105

Calls

4 calls:

25.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
5.0ms	(- 1.0 (* (tan x) (tan x)))
24.0ms	(* (tan x) (tan x))
28.0ms	(* (tan x) (tan x))

series369.0ms

Counts

4 → 12

Calls

4 calls:

153.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
64.0ms	(- 1.0 (* (tan x) (tan x)))
71.0ms	(* (tan x) (tan x))
80.0ms	(* (tan x) (tan x))

simplify2.6s

Counts

117 → 117

Iterations

Iter	Nodes
done	5001
3	3710
2	997
1	349
0	138

prune700.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 0.0b

localize25.0ms

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

rewrite168.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 108

Calls

4 calls:

56.0ms	(/ (* (+ (sqrt 1.0) (tan x)) (- (sqrt 1.0) (tan x))) (+ 1.0 (* (tan x) (tan x))))
15.0ms	(- (sqrt 1.0) (tan x))
77.0ms	(* (+ (sqrt 1.0) (tan x)) (- (sqrt 1.0) (tan x)))
15.0ms	(* (tan x) (tan x))

series548.0ms

Counts

4 → 12

Calls

4 calls:

273.0ms	(/ (* (+ (sqrt 1.0) (tan x)) (- (sqrt 1.0) (tan x))) (+ 1.0 (* (tan x) (tan x))))
51.0ms	(- (sqrt 1.0) (tan x))
160.0ms	(* (+ (sqrt 1.0) (tan x)) (- (sqrt 1.0) (tan x)))
63.0ms	(* (tan x) (tan x))

simplify2.1s

Counts

120 → 120

Iterations

Iter	Nodes
done	5001
2	2250
1	573
0	191

prune751.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.0b

localize27.0ms

Local error

Found 4 expressions with local error:

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

rewrite173.0ms

Algorithm

rewrite-expression-head

Rules

69×	`add-sqr-sqrt`
48×	`*-un-lft-identity`
37×	`times-frac`
30×	`add-cube-cbrt`
27×	`associate-r`
16×	`difference-of-squares`
13×	`pow1` `add-cbrt-cube` `add-exp-log`
8×	`sqrt-prod` `distribute-lft-out--`
7×	`associate-l`
6×	`associate-/l*` `add-log-exp`
4×	`flip3-+` `tan-quot` `associate-/r/` `flip-+`
3×	`frac-times` `associate-/r` `swap-sqr` `associate-l/` `prod-exp` `cbrt-unprod` `unswap-sqr`
2×	`cbrt-undiv` `flip3--` `div-exp` `pow-prod-down` `associate-r/` `-commutative` `div-inv` `flip--` `associate-/l/`
1×	`pow2` `clear-num` `sub-neg` `frac-2neg` `pow-plus` `diff-log` `div-sub` `pow-sqr` `pow-prod-up` `distribute-lft-out`

Counts

4 → 135

Calls

4 calls:

42.0ms	(/ (- (sqrt 1.0) (tan x)) (+ 1.0 (* (tan x) (tan x))))
78.0ms	(* (+ (sqrt 1.0) (tan x)) (/ (- (sqrt 1.0) (tan x)) (+ 1.0 (* (tan x) (tan x)))))
14.0ms	(- (sqrt 1.0) (tan x))
30.0ms	(* (tan x) (tan x))

series492.0ms

Counts

4 → 12

Calls

4 calls:

135.0ms	(/ (- (sqrt 1.0) (tan x)) (+ 1.0 (* (tan x) (tan x))))
264.0ms	(* (+ (sqrt 1.0) (tan x)) (/ (- (sqrt 1.0) (tan x)) (+ 1.0 (* (tan x) (tan x)))))
53.0ms	(- (sqrt 1.0) (tan x))
40.0ms	(* (tan x) (tan x))

simplify2.0s

Counts

147 → 147

Iterations

Iter	Nodes
done	5001
2	2069
1	615
0	214

prune898.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize53.0ms

Local error

Found 4 expressions with local error:

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

rewrite121.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt`
30×	`*-un-lft-identity`
20×	`add-cube-cbrt`
15×	`times-frac`
13×	`pow1`
10×	`add-cbrt-cube` `add-exp-log`
6×	`associate-r` `associate-l` `add-log-exp`
5×	`tan-quot` `associate-/l*` `distribute-lft-out--` `difference-of-squares`
3×	`associate-/r*` `swap-sqr`
2×	`flip3--` `pow-prod-down` `associate-l/` `prod-exp` `associate-/r/` `-commutative` `cbrt-unprod` `flip--` `unswap-sqr` `associate-/l/`
1×	`pow2` `frac-times` `cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `flip3-+` `pow-plus` `diff-log` `div-sub` `div-exp` `associate-*r/` `pow-sqr` `pow-prod-up` `flip-+` `div-inv`

Counts

4 → 101

Calls

4 calls:

51.0ms	(/ (- 1.0 (/ (* (tan x) (sin x)) (cos x))) (+ 1.0 (* (tan x) (tan x))))
19.0ms	(- 1.0 (/ (* (tan x) (sin x)) (cos x)))
22.0ms	(* (tan x) (sin x))
24.0ms	(* (tan x) (tan x))

series397.0ms

Counts

4 → 12

Calls

4 calls:

164.0ms	(/ (- 1.0 (/ (* (tan x) (sin x)) (cos x))) (+ 1.0 (* (tan x) (tan x))))
93.0ms	(- 1.0 (/ (* (tan x) (sin x)) (cos x)))
74.0ms	(* (tan x) (sin x))
66.0ms	(* (tan x) (tan x))

simplify1.6s

Counts

113 → 113

Iterations

Iter	Nodes
done	5001
2	1335
1	436
0	172

prune737.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0b

regimes448.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
done	12
1	12
0	10

end0.0ms

sample4.6s

Algorithm

intervals

Results

2.5s	1554×	body	1280	valid
901.0ms	1207×	body	640	valid
699.0ms	4285×	body	80	valid
241.0ms	637×	body	320	valid
95.0ms	317×	body	160	valid