Details

sample195.0ms

Algorithm

intervals

Results

40.0ms	51×	body	1280	valid
21.0ms	147×	body	80	valid
18.0ms	34×	body	640	valid
4.0ms	11×	body	320	valid
3.0ms	13×	body	160	valid

simplify36.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	44
5	44
4	39
3	31
2	24
1	15
0	7

prune103.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize84.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
0.1b	(- 1 (* (tan x) (tan x)))
0.3b	(* (tan x) (tan x))
0.3b	(* (tan x) (tan x))

rewrite147.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
29×	`*-un-lft-identity`
24×	`add-cube-cbrt`
18×	`pow1`
15×	`times-frac`
10×	`add-cbrt-cube` `add-exp-log` `difference-of-squares`
8×	`tan-quot`
6×	`swap-sqr` `associate-r` `associate-l` `add-log-exp`
5×	`associate-/l*`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
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 → 128

Calls

4 calls:

30.0ms	(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
6.0ms	(- 1 (* (tan x) (tan x)))
30.0ms	(* (tan x) (tan x))
76.0ms	(* (tan x) (tan x))

series262.0ms

Counts

4 → 12

Calls

4 calls:

124.0ms	(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
35.0ms	(- 1 (* (tan x) (tan x)))
40.0ms	(* (tan x) (tan x))
63.0ms	(* (tan x) (tan x))

simplify3.2s

Counts

140 → 140

Iterations

Iter	Nodes
done	5126
3	3513
2	1102
1	401
0	157

prune652.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b	(- 1 (tan x))
0.2b	(+ 1 (tan x))
0.2b	(* (+ 1 (tan x)) (- 1 (tan x)))
0.3b	(* (tan x) (tan x))

rewrite82.0ms

Algorithm

rewrite-expression-head

Rules

40×	`add-sqr-sqrt` `*-un-lft-identity`
30×	`add-cube-cbrt`
27×	`prod-diff`
13×	`pow1`
11×	`distribute-rgt-in` `distribute-lft-in`
9×	`associate-r`
8×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
7×	`associate-l`
5×	`frac-times`
4×	`expm1-log1p-u` `flip3-+` `flip3--` `tan-quot` `flip-+` `insert-posit16` `log1p-expm1-u` `flip--` `difference-of-squares`
3×	`sub-neg` `fma-def` `fma-neg` `swap-sqr` `associate-l/` `associate-r/`
2×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `distribute-lft-out` `distribute-lft-out--` `unswap-sqr`
1×	`pow2` `+-commutative` `sum-log` `pow-plus` `diff-log` `pow-sqr` `pow-prod-up`

Counts

4 → 134

Calls

4 calls:

6.0ms	(- 1 (tan x))
6.0ms	(+ 1 (tan x))
38.0ms	(* (+ 1 (tan x)) (- 1 (tan x)))
30.0ms	(* (tan x) (tan x))

series179.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(- 1 (tan x))
18.0ms	(+ 1 (tan x))
98.0ms	(* (+ 1 (tan x)) (- 1 (tan x)))
40.0ms	(* (tan x) (tan x))

simplify4.1s

Counts

146 → 146

Iterations

Iter	Nodes
done	5000
3	4855
2	1909
1	563
0	188

prune562.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize45.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (+ 1 (tan x)) (/ (fma (tan x) (tan x) 1) (- 1 (tan x))))
0.2b	(- 1 (tan x))
0.2b	(+ 1 (tan x))
0.2b	(/ (fma (tan x) (tan x) 1) (- 1 (tan x)))

rewrite100.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 236

Calls

4 calls:

52.0ms	(/ (+ 1 (tan x)) (/ (fma (tan x) (tan x) 1) (- 1 (tan x))))
11.0ms	(- 1 (tan x))
10.0ms	(+ 1 (tan x))
18.0ms	(/ (fma (tan x) (tan x) 1) (- 1 (tan x)))

series277.0ms

Counts

4 → 12

Calls

4 calls:

147.0ms	(/ (+ 1 (tan x)) (/ (fma (tan x) (tan x) 1) (- 1 (tan x))))
23.0ms	(- 1 (tan x))
19.0ms	(+ 1 (tan x))
89.0ms	(/ (fma (tan x) (tan x) 1) (- 1 (tan x)))

simplify2.1s

Counts

248 → 248

Iterations

Iter	Nodes
done	5038
2	2565
1	818
0	324

prune1.1s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.0b

localize38.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* (- 1 (* (tan x) (tan x))) (- 1 (* (tan x) (tan x)))) (* (- 1 (tan x)) (+ 1 (tan x))))
0.3b	(* (tan x) (tan x))
0.3b	(* (tan x) (tan x))
0.3b	(* (tan x) (tan x))

rewrite104.0ms

Algorithm

rewrite-expression-head

Rules

25×	`pow1`
22×	`add-sqr-sqrt` `add-cbrt-cube` `add-exp-log`
16×	`*-un-lft-identity` `add-cube-cbrt`
12×	`tan-quot`
11×	`frac-times`
9×	`flip3--` `swap-sqr` `associate-r` `associate-l` `flip--`
8×	`associate-/r/` `associate-/l/`
7×	`associate-l/` `prod-exp` `associate-r/` `cbrt-unprod`
4×	`expm1-log1p-u` `cbrt-undiv` `div-exp` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow2` `flip3-+` `pow-plus` `pow-prod-down` `pow-sqr` `*-commutative` `pow-prod-up` `flip-+` `unswap-sqr`
1×	`clear-num` `associate-/r` `frac-2neg` `times-frac` `div-inv` `associate-/l`

Counts

4 → 133

Calls

4 calls:

40.0ms	(/ (* (- 1 (* (tan x) (tan x))) (- 1 (* (tan x) (tan x)))) (* (- 1 (tan x)) (+ 1 (tan x))))
30.0ms	(* (tan x) (tan x))
15.0ms	(* (tan x) (tan x))
16.0ms	(* (tan x) (tan x))

series355.0ms

Counts

4 → 12

Calls

4 calls:

204.0ms	(/ (* (- 1 (* (tan x) (tan x))) (- 1 (* (tan x) (tan x)))) (* (- 1 (tan x)) (+ 1 (tan x))))
54.0ms	(* (tan x) (tan x))
56.0ms	(* (tan x) (tan x))
40.0ms	(* (tan x) (tan x))

simplify2.4s

Counts

145 → 145

Iterations

Iter	Nodes
done	5290
2	3116
1	547
0	147

prune655.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

regimes253.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	11
1	11
0	8

end0.0ms

sample4.6s

Algorithm

intervals

Results

1.9s	1533×	body	1280	valid
1.4s	1302×	body	640	valid
600.0ms	4271×	body	80	valid
336.0ms	582×	body	320	valid
146.0ms	312×	body	160	valid