Details

sample346.0ms

Algorithm

intervals

Results

20.0ms	43×	body	1280	valid
12.0ms	42×	body	640	valid
8.0ms	141×	body	80	valid
7.0ms	25×	body	320	valid
1.0ms	5×	body	160	valid

simplify62.0ms

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

prune7.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.3b

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(- 1.0 (* (tan x) (tan x)))
0.1b	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
0.3b	(* (tan x) (tan x))
0.3b	(* (tan x) (tan x))

rewrite65.0ms

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:

6.0ms	(- 1.0 (* (tan x) (tan x)))
18.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
20.0ms	(* (tan x) (tan x))
17.0ms	(* (tan x) (tan x))

series209.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(- 1.0 (* (tan x) (tan x)))
96.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
37.0ms	(* (tan x) (tan x))
44.0ms	(* (tan x) (tan x))

simplify1.6s

Counts

131 → 131

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	151	1789
1	338	1638
2	941	1453
3	2995	1419
done	5000	1411

prune275.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 4 expressions with local error:

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

rewrite99.0ms

Algorithm

rewrite-expression-head

Rules

62×	`add-sqr-sqrt`
58×	`*-un-lft-identity`
54×	`prod-diff`
50×	`add-cube-cbrt`
35×	`sqrt-prod`
20×	`distribute-rgt-in` `distribute-lft-in`
13×	`pow1`
9×	`associate-r`
8×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
7×	`associate-l`
6×	`fma-def` `fma-neg`
5×	`frac-times`
4×	`tan-quot` `expm1-log1p-u` `flip3--` `flip3-+` `flip--` `flip-+` `log1p-expm1-u` `difference-of-squares`
3×	`sub-neg` `associate-r/` `swap-sqr` `associate-l/`
2×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `distribute-lft-out` `distribute-lft-out--` `unswap-sqr`
1×	`+-commutative` `pow2` `pow-plus` `diff-log` `sum-log` `pow-sqr` `pow-prod-up`

Counts

4 → 163

Calls

4 calls:

9.0ms	(+ (sqrt 1.0) (tan x))
11.0ms	(- (sqrt 1.0) (tan x))
57.0ms	(* (+ (sqrt 1.0) (tan x)) (- (sqrt 1.0) (tan x)))
15.0ms	(* (tan x) (tan x))

series213.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(+ (sqrt 1.0) (tan x))
37.0ms	(- (sqrt 1.0) (tan x))
104.0ms	(* (+ (sqrt 1.0) (tan x)) (- (sqrt 1.0) (tan x)))
36.0ms	(* (tan x) (tan x))

simplify838.0ms

Counts

175 → 175

Iterations

Useful iterations: done (833.0ms)

Iter	Nodes	Cost
0	210	3440
1	509	2534
2	1589	1952
done	5000	1658

prune301.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

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

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-sqr-sqrt` `*-un-lft-identity`
15×	`add-cube-cbrt`
13×	`pow1` `associate-l`
9×	`fma-def`
8×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
7×	`tan-quot` `associate-r`
4×	`expm1-log1p-u` `flip3-+` `flip-+` `log1p-expm1-u`
3×	`distribute-lft-neg-out` `distribute-lft-neg-in` `frac-times` `distribute-rgt-neg-in` `associate-*r/` `swap-sqr` `sqrt-prod` `distribute-neg-frac`
2×	`+-commutative` `distribute-rgt-in` `associate-+r+` `distribute-lft-in` `pow-prod-down` `associate-l/` `prod-exp` `sum-log` `-commutative` `cbrt-unprod` `distribute-lft-out` `unswap-sqr`
1×	`pow2` `neg-mul-1` `associate-+l+` `pow-plus` `unsub-neg` `pow-sqr` `pow-prod-up` `fma-udef`

Counts

4 → 107

Calls

4 calls:

9.0ms	(+ (sqrt 1.0) (tan x))
38.0ms	(* (- (tan x)) (+ (sqrt 1.0) (tan x)))
7.0ms	(+ (fma (tan x) (sqrt 1.0) 1.0) (* (- (tan x)) (+ (sqrt 1.0) (tan x))))
15.0ms	(* (tan x) (tan x))

series285.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(+ (sqrt 1.0) (tan x))
79.0ms	(* (- (tan x)) (+ (sqrt 1.0) (tan x)))
137.0ms	(+ (fma (tan x) (sqrt 1.0) 1.0) (* (- (tan x)) (+ (sqrt 1.0) (tan x))))
33.0ms	(* (tan x) (tan x))

simplify1.0s

Counts

119 → 119

Iterations

Useful iterations: done (1.0s)

Iter	Nodes	Cost
0	164	1316
1	448	1183
2	1618	983
done	5001	959

prune317.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0.0b

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)

rewrite15.0ms

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:

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

series74.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(pow (cos x) 2)
16.0ms	(pow (cos x) 2)
18.0ms	(pow (sin x) 2)
22.0ms	(pow (sin x) 2)

simplify1.9s

Counts

92 → 92

Iterations

Useful iterations: 4 (740.0ms)

Iter	Nodes	Cost
0	68	616
1	138	530
2	293	466
3	807	466
4	3813	458
done	5000	458

prune218.0ms

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 0.0b

regimes82.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify5.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	24
1	18	24
2	22	24
3	26	24
done	26	24

end0.0ms

sample1.6s

Algorithm

intervals

Results

657.0ms	1467×	body	1280	valid
352.0ms	1238×	body	640	valid
245.0ms	4342×	body	80	valid
120.0ms	635×	body	320	valid
46.0ms	318×	body	160	valid