Details

sample182.0ms

Algorithm

intervals

Results

45.0ms	46×	body	1280	valid
21.0ms	35×	body	640	valid
20.0ms	137×	body	80	valid
11.0ms	25×	body	320	valid
4.0ms	13×	body	160	valid

simplify88.0ms

Counts

1 → 1

Iterations

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

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize34.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
0.2b	(- 1 (* (tan x) (tan x)))
0.3b	(* (tan x) (tan x))
0.3b	(* (tan x) (tan x))

rewrite124.0ms

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:

28.0ms	(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
20.0ms	(- 1 (* (tan x) (tan x)))
33.0ms	(* (tan x) (tan x))
36.0ms	(* (tan x) (tan x))

series243.0ms

Counts

4 → 12

Calls

4 calls:

118.0ms	(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
35.0ms	(- 1 (* (tan x) (tan x)))
44.0ms	(* (tan x) (tan x))
45.0ms	(* (tan x) (tan x))

simplify3.2s

Counts

140 → 140

Iterations

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

prune610.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

localize43.0ms

Local error

Found 4 expressions with local error:

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

rewrite187.0ms

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:

31.0ms	(* (tan x) (tan x))
31.0ms	(* (tan x) (tan x))
23.0ms	(* (tan x) (tan x))
91.0ms	(* (* (tan x) (tan x)) (* (tan x) (tan x)))

series203.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(* (tan x) (tan x))
37.0ms	(* (tan x) (tan x))
44.0ms	(* (tan x) (tan x))
56.0ms	(* (* (tan x) (tan x)) (* (tan x) (tan x)))

simplify1.9s

Counts

186 → 186

Iterations

Iter	Nodes
done	5004
3	2022
2	901
1	324
0	112

prune732.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 0.1b

localize24.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- 1 (tan x)) (fma (tan x) (tan x) 1))
0.2b	(* (+ 1 (tan x)) (/ (- 1 (tan x)) (fma (tan x) (tan x) 1)))
0.2b	(+ 1 (tan x))
0.2b	(- 1 (tan x))

rewrite136.0ms

Algorithm

rewrite-expression-head

Rules

63×	`add-sqr-sqrt`
62×	`*-un-lft-identity`
37×	`times-frac`
34×	`add-cube-cbrt`
22×	`associate-r`
16×	`difference-of-squares`
11×	`add-cbrt-cube` `add-exp-log`
9×	`prod-diff`
8×	`distribute-lft-out--` `add-log-exp`
6×	`pow1` `associate-/l*`
4×	`expm1-log1p-u` `associate-l` `insert-posit16` `log1p-expm1-u`
3×	`associate-/r*` `fma-def` `flip3-+` `fma-neg` `flip-+`
2×	`frac-times` `cbrt-undiv` `flip3--` `div-exp` `associate-*l/` `prod-exp` `cbrt-unprod` `div-inv` `flip--` `distribute-lft-out` `unswap-sqr` `associate-/l/`
1×	`+-commutative` `clear-num` `sum-log` `sub-neg` `frac-2neg` `diff-log` `div-sub` `pow-prod-down` `associate-r/` `-commutative`

Counts

4 → 142

Calls

4 calls:

20.0ms	(/ (- 1 (tan x)) (fma (tan x) (tan x) 1))
81.0ms	(* (+ 1 (tan x)) (/ (- 1 (tan x)) (fma (tan x) (tan x) 1)))
12.0ms	(+ 1 (tan x))
19.0ms	(- 1 (tan x))

series339.0ms

Counts

4 → 12

Calls

4 calls:

125.0ms	(/ (- 1 (tan x)) (fma (tan x) (tan x) 1))
173.0ms	(* (+ 1 (tan x)) (/ (- 1 (tan x)) (fma (tan x) (tan x) 1)))
18.0ms	(+ 1 (tan x))
22.0ms	(- 1 (tan x))

simplify2.1s

Counts

154 → 154

Iterations

Iter	Nodes
done	5000
2	1706
1	523
0	208

prune794.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.1b

localize74.0ms

Local error

Found 4 expressions with local error:

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

rewrite176.0ms

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:

23.0ms	(* (tan x) (tan x))
24.0ms	(* (tan x) (tan x))
15.0ms	(* (tan x) (tan x))
108.0ms	(* (* (tan x) (tan x)) (* (tan x) (tan x)))

series200.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(* (tan x) (tan x))
42.0ms	(* (tan x) (tan x))
45.0ms	(* (tan x) (tan x))
64.0ms	(* (* (tan x) (tan x)) (* (tan x) (tan x)))

simplify2.4s

Counts

186 → 186

Iterations

Iter	Nodes
done	5004
3	2022
2	901
1	324
0	112

prune750.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 0.0b

regimes319.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
done	17
1	17
0	12

end0.0ms

sample4.2s

Algorithm

intervals

Results

2.0s	1468×	body	1280	valid
881.0ms	1206×	body	640	valid
610.0ms	4343×	body	80	valid
447.0ms	638×	body	320	valid
93.0ms	345×	body	160	valid