Details

sample306.0ms

Algorithm

intervals

Results

23.0ms	47×	body	1280	valid
16.0ms	51×	body	640	valid
9.0ms	126×	body	80	valid
5.0ms	22×	body	320	valid
1.0ms	10×	body	160	valid

simplify32.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (8.0ms)

Iter	Nodes	Cost
0	7	15
1	13	15
2	22	14
3	29	14
4	37	14
5	42	14
6	44	14
done	44	14

prune15.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.3b

localize11.0ms

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))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt`
23×	`add-cube-cbrt` `*-un-lft-identity`
18×	`pow1`
12×	`times-frac`
10×	`add-exp-log` `add-cbrt-cube`
8×	`tan-quot`
6×	`swap-sqr` `associate-r` `associate-l` `add-log-exp`
5×	`difference-of-squares`
4×	`expm1-log1p-u` `log1p-expm1-u` `associate-/l*`
3×	`fma-neg` `prod-diff` `associate-/r*`
2×	`pow2` `frac-times` `flip3--` `pow-plus` `associate-r/` `pow-prod-down` `associate-l/` `prod-exp` `associate-/r/` `pow-sqr` `*-commutative` `pow-prod-up` `flip--` `cbrt-unprod` `associate-/l/` `unswap-sqr`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `flip3-+` `diff-log` `div-sub` `div-exp` `clear-num` `flip-+` `div-inv`

Counts

4 → 119

Calls

4 calls:

9.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
3.0ms	(- 1.0 (* (tan x) (tan x)))
5.0ms	(* (tan x) (tan x))
7.0ms	(* (tan x) (tan x))

series209.0ms

Counts

4 → 12

Calls

4 calls:

94.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
34.0ms	(- 1.0 (* (tan x) (tan x)))
39.0ms	(* (tan x) (tan x))
42.0ms	(* (tan x) (tan x))

simplify1.7s

Counts

131 → 131

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	151	1789
1	336	1638
2	918	1453
3	3278	1419
done	5000	1418

prune297.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (cos x) 2)
0.2b	(pow (cos x) 2)
0.3b	(pow (sin x) 2)
0.3b	(pow (sin x) 2)

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `add-cube-cbrt` `unpow-prod-down` `pow-unpow` `*-un-lft-identity`
8×	`pow1` `add-exp-log`
4×	`expm1-log1p-u` `pow-to-exp` `pow-pow` `pow-exp` `add-cbrt-cube` `log1p-expm1-u` `unpow2` `add-log-exp` `sqr-pow`

Counts

4 → 80

Calls

4 calls:

1.0ms	(pow (cos x) 2)
1.0ms	(pow (cos x) 2)
1.0ms	(pow (sin x) 2)
2.0ms	(pow (sin x) 2)

series76.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(pow (cos x) 2)
17.0ms	(pow (cos x) 2)
19.0ms	(pow (sin x) 2)
23.0ms	(pow (sin x) 2)

simplify1.6s

Counts

92 → 92

Iterations

Useful iterations: 4 (530.0ms)

Iter	Nodes	Cost
0	68	616
1	143	530
2	318	466
3	825	466
4	3122	458
done	5000	458

prune255.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.1b

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(+ (sqrt 1.0) (tan x))
0.2b	(* (+ (sqrt 1.0) (tan x)) (/ (- (sqrt 1.0) (tan x)) (fma (tan x) (tan x) 1.0)))
0.2b	(- (sqrt 1.0) (tan x))
0.2b	(/ (- (sqrt 1.0) (tan x)) (fma (tan x) (tan x) 1.0))

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 153

Calls

4 calls:

5.0ms	(+ (sqrt 1.0) (tan x))
35.0ms	(* (+ (sqrt 1.0) (tan x)) (/ (- (sqrt 1.0) (tan x)) (fma (tan x) (tan x) 1.0)))
6.0ms	(- (sqrt 1.0) (tan x))
15.0ms	(/ (- (sqrt 1.0) (tan x)) (fma (tan x) (tan x) 1.0))

series382.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(+ (sqrt 1.0) (tan x))
208.0ms	(* (+ (sqrt 1.0) (tan x)) (/ (- (sqrt 1.0) (tan x)) (fma (tan x) (tan x) 1.0)))
36.0ms	(- (sqrt 1.0) (tan x))
103.0ms	(/ (- (sqrt 1.0) (tan x)) (fma (tan x) (tan x) 1.0))

simplify907.0ms

Counts

165 → 165

Iterations

Useful iterations: 2 (352.0ms)

Iter	Nodes	Cost
0	220	3115
1	531	2704
2	1815	2386
done	5000	2386

prune396.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(+ (sqrt 1.0) (tan x))
0.2b	(/ (tan x) (fma (tan x) (tan x) 1.0))
0.2b	(* (+ (sqrt 1.0) (tan x)) (- (/ (sqrt 1.0) (fma (tan x) (tan x) 1.0)) (/ (tan x) (fma (tan x) (tan x) 1.0))))
0.3b	(- (/ (sqrt 1.0) (fma (tan x) (tan x) 1.0)) (/ (tan x) (fma (tan x) (tan x) 1.0)))

rewrite293.0ms

Algorithm

rewrite-expression-head

Rules

1349×	`times-frac`
1042×	`add-sqr-sqrt`
1022×	`*-un-lft-identity`
1002×	`add-cube-cbrt`
858×	`prod-diff`
367×	`sqrt-prod`
288×	`distribute-rgt-in` `distribute-lft-in`
111×	`div-inv`
22×	`fma-neg`
14×	`associate-r`
12×	`difference-of-squares`
8×	`add-exp-log` `frac-times` `add-cbrt-cube` `distribute-lft-out--` `add-log-exp`
6×	`pow1` `fma-def` `flip3-+` `flip-+`
4×	`expm1-log1p-u` `flip3--` `associate-r/` `associate-l*` `frac-sub` `flip--` `log1p-expm1-u` `sub-div`
3×	`sub-neg` `associate-/r` `associate-/l`
2×	`distribute-rgt-out--` `associate-*l/` `distribute-lft-out`
1×	`tan-quot` `cbrt-undiv` `+-commutative` `frac-2neg` `diff-log` `div-exp` `pow-prod-down` `prod-exp` `clear-num` `sum-log` `*-commutative` `cbrt-unprod` `associate-/l/` `unswap-sqr`

Counts

4 → 1007

Calls

4 calls:

5.0ms	(+ (sqrt 1.0) (tan x))
3.0ms	(/ (tan x) (fma (tan x) (tan x) 1.0))
146.0ms	(* (+ (sqrt 1.0) (tan x)) (- (/ (sqrt 1.0) (fma (tan x) (tan x) 1.0)) (/ (tan x) (fma (tan x) (tan x) 1.0))))
39.0ms	(- (/ (sqrt 1.0) (fma (tan x) (tan x) 1.0)) (/ (tan x) (fma (tan x) (tan x) 1.0)))

series550.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(+ (sqrt 1.0) (tan x))
88.0ms	(/ (tan x) (fma (tan x) (tan x) 1.0))
269.0ms	(* (+ (sqrt 1.0) (tan x)) (- (/ (sqrt 1.0) (fma (tan x) (tan x) 1.0)) (/ (tan x) (fma (tan x) (tan x) 1.0))))
160.0ms	(- (/ (sqrt 1.0) (fma (tan x) (tan x) 1.0)) (/ (tan x) (fma (tan x) (tan x) 1.0)))

simplify1.7s

Counts

1019 → 1019

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	1066	88795
1	3287	79514
done	5000	79277

prune2.0s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

regimes106.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	27
1	17	27
done	17	27

end0.0ms

sample1.7s

Algorithm

intervals

Results

734.0ms	1521×	body	1280	valid
396.0ms	1285×	body	640	valid
269.0ms	4286×	body	80	valid
125.0ms	606×	body	320	valid
43.0ms	302×	body	160	valid