Details

sample209.0ms

Algorithm

intervals

Results

44.0ms	49×	body	1280	valid
26.0ms	44×	body	640	valid
17.0ms	124×	body	80	valid
11.0ms	26×	body	320	valid
4.0ms	13×	body	160	valid

simplify508.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	37
5	37
4	34
3	26
2	21
1	13
0	7

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize36.0ms

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))

rewrite90.0ms

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:

30.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
8.0ms	(- 1.0 (* (tan x) (tan x)))
23.0ms	(* (tan x) (tan x))
25.0ms	(* (tan x) (tan x))

series332.0ms

Counts

4 → 12

Calls

4 calls:

172.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
35.0ms	(- 1.0 (* (tan x) (tan x)))
57.0ms	(* (tan x) (tan x))
67.0ms	(* (tan x) (tan x))

simplify1.4s

Counts

117 → 117

Iterations

Iter	Nodes
done	5001
2	1540
1	350
0	138

prune712.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.1b

localize51.0ms

Local error

Found 4 expressions with local error:

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

rewrite112.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 175

Calls

4 calls:

7.0ms	(/ (sin x) (cos x))
6.0ms	(- 1.0 (* (/ (sin x) (cos x)) (/ (sin x) (cos x))))
48.0ms	(* (/ (sin x) (cos x)) (/ (sin x) (cos x)))
45.0ms	(* (/ (sin x) (cos x)) (/ (sin x) (cos x)))

series219.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(/ (sin x) (cos x))
73.0ms	(- 1.0 (* (/ (sin x) (cos x)) (/ (sin x) (cos x))))
62.0ms	(* (/ (sin x) (cos x)) (/ (sin x) (cos x)))
63.0ms	(* (/ (sin x) (cos x)) (/ (sin x) (cos x)))

simplify2.4s

Counts

187 → 187

Iterations

Iter	Nodes
done	5000
2	3421
1	522
0	166

prune1.1s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.1b

localize44.0ms

Local error

Found 4 expressions with local error:

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

rewrite81.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 83

Calls

4 calls:

24.0ms	(/ (* (tan x) (sin x)) (cos x))
21.0ms	(* (tan x) (sin x))
14.0ms	(- 1.0 (/ (* (tan x) (sin x)) (cos x)))
19.0ms	(* (tan x) (tan x))

series271.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(/ (* (tan x) (sin x)) (cos x))
67.0ms	(* (tan x) (sin x))
77.0ms	(- 1.0 (/ (* (tan x) (sin x)) (cos x)))
63.0ms	(* (tan x) (tan x))

simplify1.4s

Counts

95 → 95

Iterations

Iter	Nodes
done	5001
2	1766
1	326
0	134

prune665.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 0.1b

localize45.0ms

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

rewrite183.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 132

Calls

4 calls:

95.0ms	(* (+ (sqrt 1.0) (tan x)) (/ (- (sqrt 1.0) (tan x)) (+ 1.0 (* (tan x) (tan x)))))
43.0ms	(/ (- (sqrt 1.0) (tan x)) (+ 1.0 (* (tan x) (tan x))))
14.0ms	(+ (sqrt 1.0) (tan x))
28.0ms	(* (tan x) (tan x))

series521.0ms

Counts

4 → 12

Calls

4 calls:

287.0ms	(* (+ (sqrt 1.0) (tan x)) (/ (- (sqrt 1.0) (tan x)) (+ 1.0 (* (tan x) (tan x)))))
114.0ms	(/ (- (sqrt 1.0) (tan x)) (+ 1.0 (* (tan x) (tan x))))
66.0ms	(+ (sqrt 1.0) (tan x))
54.0ms	(* (tan x) (tan x))

simplify2.6s

Counts

144 → 144

Iterations

Iter	Nodes
done	5000
2	3835
1	617
0	213

prune749.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 0.1b

regimes442.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify5.0ms

Iterations

Iter	Nodes
done	13
1	13
0	10

end0.0ms

sample4.3s

Algorithm

intervals

Results

1.8s	1455×	body	1280	valid
1.3s	1236×	body	640	valid
535.0ms	4389×	body	80	valid
304.0ms	608×	body	320	valid
120.0ms	312×	body	160	valid