Details

sample252.0ms

Algorithm

intervals

Results

62.0ms	9×	body	160	valid
60.0ms	54×	body	1280	valid
25.0ms	35×	body	640	valid
23.0ms	143×	body	80	valid
10.0ms	15×	body	320	valid

simplify176.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (54.0ms)

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

prune53.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize33.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma (tan x) (tan x) 1.0)
0.1b	(- 1.0 (* (tan x) (tan x)))
0.1b	(/ (- 1.0 (* (tan x) (tan x))) (fma (tan x) (tan x) 1.0))
0.2b	(* (tan x) (tan x))

rewrite85.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 97

Calls

4 calls:

1.0ms	(fma (tan x) (tan x) 1.0)
10.0ms	(- 1.0 (* (tan x) (tan x)))
18.0ms	(/ (- 1.0 (* (tan x) (tan x))) (fma (tan x) (tan x) 1.0))
49.0ms	(* (tan x) (tan x))

series377.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(fma (tan x) (tan x) 1.0)
37.0ms	(- 1.0 (* (tan x) (tan x)))
196.0ms	(/ (- 1.0 (* (tan x) (tan x))) (fma (tan x) (tan x) 1.0))
90.0ms	(* (tan x) (tan x))

simplify2.4s

Counts

109 → 109

Iterations

Useful iterations: done (2.4s)

Iter	Nodes	Cost
0	155	1557
1	330	1462
2	893	1345
3	2809	1320
done	5000	1314

prune416.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 3 expressions with local error:

0.1b	(fma (tan x) (tan x) 1.0)
0.1b	(/ (fma (- (tan x)) (tan x) 1.0) (fma (tan x) (tan x) 1.0))
0.2b	(fma (- (tan x)) (tan x) 1.0)

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
5×	`add-exp-log` `add-cbrt-cube`
3×	`pow1` `expm1-log1p-u` `associate-/r` `log1p-expm1-u` `associate-/l` `add-log-exp`
2×	`fma-udef`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `div-inv`

Counts

3 → 49

Calls

3 calls:

0.0ms	(fma (tan x) (tan x) 1.0)
5.0ms	(/ (fma (- (tan x)) (tan x) 1.0) (fma (tan x) (tan x) 1.0))
0.0ms	(fma (- (tan x)) (tan x) 1.0)

series323.0ms

Counts

3 → 9

Calls

3 calls:

55.0ms	(fma (tan x) (tan x) 1.0)
176.0ms	(/ (fma (- (tan x)) (tan x) 1.0) (fma (tan x) (tan x) 1.0))
91.0ms	(fma (- (tan x)) (tan x) 1.0)

simplify2.2s

Counts

58 → 58

Iterations

Useful iterations: 3 (214.0ms)

Iter	Nodes	Cost
0	87	978
1	160	967
2	377	883
3	984	882
4	3063	882
done	5001	882

prune302.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize25.0ms

Local error

Found 4 expressions with local error:

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

rewrite23.0ms

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:

4.0ms	(pow (sin x) 2)
4.0ms	(pow (sin x) 2)
3.0ms	(pow (cos x) 2)
4.0ms	(pow (cos x) 2)

series115.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(pow (sin x) 2)
37.0ms	(pow (sin x) 2)
19.0ms	(pow (cos x) 2)
23.0ms	(pow (cos x) 2)

simplify3.2s

Counts

92 → 92

Iterations

Useful iterations: 4 (1.3s)

Iter	Nodes	Cost
0	68	616
1	138	530
2	293	466
3	808	466
4	3771	458
done	5000	458

prune358.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.1b	(- 1.0 (/ (* (sin x) (tan x)) (cos x)))
0.1b	(/ (* (sin x) (tan x)) (cos x))
0.1b	(/ (- 1.0 (/ (* (sin x) (tan x)) (cos x))) (fma (tan x) (tan x) 1.0))
0.2b	(* (sin x) (tan x))

rewrite140.0ms

Algorithm

rewrite-expression-head

Rules

44×	`add-sqr-sqrt`
42×	`*-un-lft-identity`
32×	`add-cube-cbrt`
27×	`times-frac`
21×	`prod-diff`
13×	`add-exp-log` `add-cbrt-cube`
6×	`pow1` `associate-/r` `associate-/l` `add-log-exp`
5×	`div-inv` `distribute-lft-out--` `difference-of-squares`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`cbrt-undiv` `fma-neg` `div-exp` `associate-r` `associate-l` `associate-/l/`
2×	`tan-quot` `flip3--` `frac-2neg` `associate-*r/` `prod-exp` `clear-num` `flip--` `cbrt-unprod`
1×	`sub-neg` `diff-log` `div-sub` `pow-prod-down` `*-commutative` `unswap-sqr`

Counts

4 → 125

Calls

4 calls:

24.0ms	(- 1.0 (/ (* (sin x) (tan x)) (cos x)))
31.0ms	(/ (* (sin x) (tan x)) (cos x))
62.0ms	(/ (- 1.0 (/ (* (sin x) (tan x)) (cos x))) (fma (tan x) (tan x) 1.0))
13.0ms	(* (sin x) (tan x))

series464.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(- 1.0 (/ (* (sin x) (tan x)) (cos x)))
97.0ms	(/ (* (sin x) (tan x)) (cos x))
217.0ms	(/ (- 1.0 (/ (* (sin x) (tan x)) (cos x))) (fma (tan x) (tan x) 1.0))
57.0ms	(* (sin x) (tan x))

simplify1.8s

Counts

137 → 137

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	232	3121
1	531	2750
2	1713	2370
done	5000	2128

prune560.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 0.0b

regimes162.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	23
1	12	23
done	12	23

end0.0ms

sample4.7s

Algorithm

intervals

Results

1.9s	1468×	body	1280	valid
1.5s	1253×	body	640	valid
558.0ms	4342×	body	80	valid
341.0ms	616×	body	320	valid
89.0ms	321×	body	160	valid