Details

sample141.0ms

Algorithm

intervals

Results

25.0ms	41×	body	1280	valid
16.0ms	40×	body	640	valid
14.0ms	154×	body	80	valid
5.0ms	15×	body	320	valid
1.0ms	6×	body	160	valid

simplify95.0ms

Counts

1 → 1

Iterations

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

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize38.0ms

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

rewrite116.0ms

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:

38.0ms	(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
7.0ms	(- 1 (* (tan x) (tan x)))
30.0ms	(* (tan x) (tan x))
36.0ms	(* (tan x) (tan x))

series256.0ms

Counts

4 → 12

Calls

4 calls:

116.0ms	(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
55.0ms	(- 1 (* (tan x) (tan x)))
39.0ms	(* (tan x) (tan x))
47.0ms	(* (tan x) (tan x))

simplify2.9s

Counts

140 → 140

Iterations

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

prune645.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize34.0ms

Local error

Found 4 expressions with local error:

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

rewrite126.0ms

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:

12.0ms	(- 1 (tan x))
65.0ms	(/ (+ 1 (tan x)) (/ (fma (tan x) (tan x) 1) (- 1 (tan x))))
11.0ms	(+ 1 (tan x))
22.0ms	(/ (fma (tan x) (tan x) 1) (- 1 (tan x)))

series345.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(- 1 (tan x))
211.0ms	(/ (+ 1 (tan x)) (/ (fma (tan x) (tan x) 1) (- 1 (tan x))))
22.0ms	(+ 1 (tan x))
82.0ms	(/ (fma (tan x) (tan x) 1) (- 1 (tan x)))

simplify2.8s

Counts

248 → 248

Iterations

Iter	Nodes
done	5001
2	2376
1	819
0	324

prune1.0s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize46.0ms

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)))

rewrite194.0ms

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:

18.0ms	(* (tan x) (tan x))
30.0ms	(* (tan x) (tan x))
17.0ms	(* (tan x) (tan x))
123.0ms	(* (* (tan x) (tan x)) (* (tan x) (tan x)))

series208.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(* (tan x) (tan x))
56.0ms	(* (tan x) (tan x))
42.0ms	(* (tan x) (tan x))
53.0ms	(* (* (tan x) (tan x)) (* (tan x) (tan x)))

simplify1.7s

Counts

186 → 186

Iterations

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

prune768.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

localize46.0ms

Local error

Found 4 expressions with local error:

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

rewrite156.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt` `pow1`
17×	`add-cbrt-cube` `add-exp-log`
16×	`*-un-lft-identity`
15×	`tan-quot`
14×	`add-cube-cbrt`
8×	`associate-*r/`
6×	`swap-sqr` `associate-r` `associate-l` `add-log-exp`
5×	`frac-times` `associate-/l/`
4×	`expm1-log1p-u` `cbrt-undiv` `associate-/r` `times-frac` `div-exp` `associate-l/` `prod-exp` `cbrt-unprod` `insert-posit16` `log1p-expm1-u`
3×	`frac-add`
2×	`pow2` `flip3-+` `pow-plus` `flip3--` `pow-prod-down` `associate-/r/` `pow-sqr` `*-commutative` `pow-prod-up` `flip-+` `flip--` `distribute-lft-out` `unswap-sqr`
1×	`+-commutative` `clear-num` `sum-log` `fma-def` `frac-2neg` `distribute-rgt-out` `div-inv` `associate-/l*`

Counts

4 → 116

Calls

4 calls:

73.0ms	(/ (* (/ (+ (tan x) 1) (fma (tan x) (tan x) 1)) (- 1 (* (tan x) (* (tan x) (tan x))))) (+ (* 1 1) (+ (* (tan x) (tan x)) (* 1 (tan x)))))
33.0ms	(+ (* (tan x) (tan x)) (* 1 (tan x)))
21.0ms	(* (tan x) (tan x))
26.0ms	(* (tan x) (tan x))

series461.0ms

Counts

4 → 12

Calls

4 calls:

332.0ms	(/ (* (/ (+ (tan x) 1) (fma (tan x) (tan x) 1)) (- 1 (* (tan x) (* (tan x) (tan x))))) (+ (* 1 1) (+ (* (tan x) (tan x)) (* 1 (tan x)))))
51.0ms	(+ (* (tan x) (tan x)) (* 1 (tan x)))
39.0ms	(* (tan x) (tan x))
39.0ms	(* (tan x) (tan x))

simplify2.4s

Counts

128 → 128

Iterations

Iter	Nodes
done	5004
2	2229
1	588
0	192

prune669.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

regimes326.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 0.5b

bsearch0.0ms

simplify6.0ms

Iterations

Iter	Nodes
done	21
1	21
0	14

end0.0ms

sample4.8s

Algorithm

intervals

Results

1.7s	1501×	body	1280	valid
1.4s	1261×	body	640	valid
802.0ms	629×	body	320	valid
613.0ms	4281×	body	80	valid
95.0ms	328×	body	160	valid