Details

sample275.0ms

Algorithm

intervals

Results

66.0ms	15×	body	320	valid
37.0ms	41×	body	1280	valid
26.0ms	40×	body	640	valid
20.0ms	154×	body	80	valid
2.0ms	6×	body	160	valid

simplify107.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	42
5	42
4	37
3	29
2	22
1	13
0	7

prune23.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize53.0ms

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)))
0.2b	(* (tan x) (tan x))
0.2b	(* (tan x) (tan x))

rewrite183.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt`
23×	`*-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×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `associate-/l*`
3×	`associate-/r*` `fma-neg` `prod-diff`
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 → 123

Calls

4 calls:

50.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
25.0ms	(- 1.0 (* (tan x) (tan x)))
45.0ms	(* (tan x) (tan x))
47.0ms	(* (tan x) (tan x))

series794.0ms

Counts

4 → 12

Calls

4 calls:

392.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
136.0ms	(- 1.0 (* (tan x) (tan x)))
106.0ms	(* (tan x) (tan x))
161.0ms	(* (tan x) (tan x))

simplify6.1s

Counts

135 → 135

Iterations

Iter	Nodes
done	5000
3	3560
2	1065
1	377
0	154

prune1.5s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize57.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (sqrt 1.0) (tan x))
0.1b	(/ (+ (sqrt 1.0) (tan x)) (/ (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)))

rewrite179.0ms

Algorithm

rewrite-expression-head

Rules

204×	`times-frac`
198×	`*-un-lft-identity`
186×	`add-sqr-sqrt`
106×	`add-cube-cbrt`
40×	`difference-of-squares`
35×	`sqrt-prod`
30×	`associate-/r*`
26×	`distribute-lft-out`
20×	`distribute-lft-out--`
18×	`prod-diff`
13×	`associate-/r/`
11×	`add-cbrt-cube` `add-exp-log`
8×	`add-log-exp`
7×	`flip3--` `div-inv` `flip--` `associate-/l*`
6×	`fma-def` `fma-neg`
4×	`expm1-log1p-u` `pow1` `cbrt-undiv` `div-exp` `insert-posit16` `log1p-expm1-u`
2×	`clear-num` `frac-2neg` `flip3-+` `flip-+` `associate-/l/`
1×	`+-commutative` `sum-log` `sub-neg` `diff-log`

Counts

4 → 251

Calls

4 calls:

25.0ms	(- (sqrt 1.0) (tan x))
70.0ms	(/ (+ (sqrt 1.0) (tan x)) (/ (fma (tan x) (tan x) 1.0) (- (sqrt 1.0) (tan x))))
19.0ms	(+ (sqrt 1.0) (tan x))
27.0ms	(/ (fma (tan x) (tan x) 1.0) (- (sqrt 1.0) (tan x)))

series1.0s

Counts

4 → 12

Calls

4 calls:

114.0ms	(- (sqrt 1.0) (tan x))
528.0ms	(/ (+ (sqrt 1.0) (tan x)) (/ (fma (tan x) (tan x) 1.0) (- (sqrt 1.0) (tan x))))
65.0ms	(+ (sqrt 1.0) (tan x))
317.0ms	(/ (fma (tan x) (tan x) 1.0) (- (sqrt 1.0) (tan x)))

simplify5.2s

Counts

263 → 263

Iterations

Iter	Nodes
done	5000
2	2683
1	807
0	322

prune2.4s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.0b

localize124.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (tan x) (tan x))
0.2b	(* (tan x) (tan x))
0.3b	(* (* (tan x) (tan x)) (* (tan x) (tan x)))
0.3b	(* (* (tan x) (tan x)) (* (tan x) (tan x)))

rewrite366.0ms

Algorithm

rewrite-expression-head

Rules

240×	`pow1`
74×	`pow-prod-up`
72×	`tan-quot`
48×	`pow-prod-down`
46×	`pow-sqr`
38×	`pow-plus`
36×	`frac-times`
32×	`add-cbrt-cube` `add-exp-log`
28×	`pow2`
24×	`associate-l/` `associate-r/`
18×	`prod-exp` `cbrt-unprod`
16×	`add-sqr-sqrt`
12×	`*-un-lft-identity` `add-cube-cbrt`
8×	`swap-sqr` `associate-r` `associate-l`
4×	`expm1-log1p-u` `*-commutative` `insert-posit16` `log1p-expm1-u` `add-log-exp` `unswap-sqr`

Counts

4 → 224

Calls

4 calls:

23.0ms	(* (tan x) (tan x))
42.0ms	(* (tan x) (tan x))
144.0ms	(* (* (tan x) (tan x)) (* (tan x) (tan x)))
125.0ms	(* (* (tan x) (tan x)) (* (tan x) (tan x)))

series449.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(* (tan x) (tan x))
93.0ms	(* (tan x) (tan x))
141.0ms	(* (* (tan x) (tan x)) (* (tan x) (tan x)))
147.0ms	(* (* (tan x) (tan x)) (* (tan x) (tan x)))

simplify5.3s

Counts

236 → 236

Iterations

Iter	Nodes
done	5001
3	2109
2	970
1	325
0	112

prune1.7s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

localize170.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (tan x) (tan x))
0.2b	(* (tan x) (tan x))
0.2b	(* (tan x) (tan x))
0.3b	(* (* (tan x) (tan x)) (* (tan x) (tan x)))

rewrite292.0ms

Algorithm

rewrite-expression-head

Rules

136×	`pow1`
44×	`tan-quot`
39×	`pow-prod-up`
26×	`pow-prod-down`
25×	`pow-sqr`
22×	`add-sqr-sqrt` `add-cbrt-cube` `add-exp-log`
21×	`pow-plus`
20×	`frac-times`
16×	`pow2` `*-un-lft-identity` `add-cube-cbrt`
14×	`associate-l/` `associate-r/`
11×	`prod-exp` `cbrt-unprod`
10×	`swap-sqr` `associate-r` `associate-l`
4×	`expm1-log1p-u` `*-commutative` `insert-posit16` `log1p-expm1-u` `add-log-exp` `unswap-sqr`

Counts

4 → 174

Calls

4 calls:

33.0ms	(* (tan x) (tan x))
27.0ms	(* (tan x) (tan x))
43.0ms	(* (tan x) (tan x))
162.0ms	(* (* (tan x) (tan x)) (* (tan x) (tan x)))

series411.0ms

Counts

4 → 12

Calls

4 calls:

112.0ms	(* (tan x) (tan x))
97.0ms	(* (tan x) (tan x))
77.0ms	(* (tan x) (tan x))
124.0ms	(* (* (tan x) (tan x)) (* (tan x) (tan x)))

simplify5.3s

Counts

186 → 186

Iterations

Iter	Nodes
done	5001
3	2109
2	970
1	325
0	112

prune1.6s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0.0b

regimes774.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify7.0ms

Iterations

Iter	Nodes
done	10
1	10
0	9

end0.0ms

sample4.2s

Algorithm

intervals

Results

1.6s	1501×	body	1280	valid
1.3s	1261×	body	640	valid
767.0ms	4281×	body	80	valid
241.0ms	629×	body	320	valid
82.0ms	328×	body	160	valid