Details

sample312.0ms

Algorithm

intervals

Results

21.0ms	47×	body	1280	valid
14.0ms	51×	body	640	valid
9.0ms	126×	body	80	valid
4.0ms	22×	body	320	valid
1.0ms	10×	body	160	valid

simplify30.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (7.0ms)

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

prune8.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.3b

localize19.0ms

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))))
2.0ms	(- 1.0 (* (tan x) (tan x)))
5.0ms	(* (tan x) (tan x))
8.0ms	(* (tan x) (tan x))

series211.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(/ (- 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))
44.0ms	(* (tan x) (tan x))

simplify746.0ms

Counts

131 → 131

Iterations

Useful iterations: 2 (125.0ms)

Iter	Nodes	Cost
0	151	1789
1	336	1638
2	1011	1453
done	5000	1453

prune291.0ms

Pruning

12 alts after pruning (12 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)

rewrite10.0ms

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

series73.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(pow (cos x) 2)
17.0ms	(pow (cos x) 2)
19.0ms	(pow (sin x) 2)
20.0ms	(pow (sin x) 2)

simplify762.0ms

Counts

92 → 92

Iterations

Useful iterations: 2 (55.0ms)

Iter	Nodes	Cost
0	68	616
1	143	530
2	390	466
3	1227	466
done	5001	466

prune257.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma (tan x) (tan x) 1.0)
0.2b	(- 1.0 (* (tan x) (tan x)))
0.2b	(/ 1 (/ (fma (tan x) (tan x) 1.0) (- 1.0 (* (tan x) (tan x)))))
0.3b	(* (tan x) (tan x))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 159

Calls

4 calls:

0.0ms	(fma (tan x) (tan x) 1.0)
2.0ms	(- 1.0 (* (tan x) (tan x)))
8.0ms	(/ 1 (/ (fma (tan x) (tan x) 1.0) (- 1.0 (* (tan x) (tan x)))))
5.0ms	(* (tan x) (tan x))

series218.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(fma (tan x) (tan x) 1.0)
33.0ms	(- 1.0 (* (tan x) (tan x)))
106.0ms	(/ 1 (/ (fma (tan x) (tan x) 1.0) (- 1.0 (* (tan x) (tan x)))))
33.0ms	(* (tan x) (tan x))

simplify793.0ms

Counts

171 → 171

Iterations

Useful iterations: 2 (229.0ms)

Iter	Nodes	Cost
0	270	3573
1	571	3211
2	1694	2917
done	5000	2917

prune332.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize10.0ms

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))

rewrite71.0ms

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))
38.0ms	(* (+ (sqrt 1.0) (tan x)) (/ (- (sqrt 1.0) (tan x)) (fma (tan x) (tan x) 1.0)))
6.0ms	(- (sqrt 1.0) (tan x))
16.0ms	(/ (- (sqrt 1.0) (tan x)) (fma (tan x) (tan x) 1.0))

series381.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(+ (sqrt 1.0) (tan x))
206.0ms	(* (+ (sqrt 1.0) (tan x)) (/ (- (sqrt 1.0) (tan x)) (fma (tan x) (tan x) 1.0)))
36.0ms	(- (sqrt 1.0) (tan x))
105.0ms	(/ (- (sqrt 1.0) (tan x)) (fma (tan x) (tan x) 1.0))

simplify716.0ms

Counts

165 → 165

Iterations

Useful iterations: 2 (212.0ms)

Iter	Nodes	Cost
0	220	3115
1	531	2704
2	1966	2342
done	5000	2342

prune366.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

regimes92.0ms

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	11	26
1	13	26
done	13	26

end0.0ms

sample1.6s

Algorithm

intervals

Results

694.0ms	1521×	body	1280	valid
365.0ms	1285×	body	640	valid
240.0ms	4286×	body	80	valid
120.0ms	606×	body	320	valid
40.0ms	302×	body	160	valid