Details

sample298.0ms

Algorithm

intervals

Results

19.0ms	42×	body	1280	valid
15.0ms	52×	body	640	valid
10.0ms	140×	body	80	valid
3.0ms	15×	body	320	valid
1.0ms	7×	body	160	valid

simplify29.0ms

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

prune15.0ms

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))

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:

2.0ms	(- 1.0 (* (tan x) (tan x)))
8.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
5.0ms	(* (tan x) (tan x))
7.0ms	(* (tan x) (tan x))

series204.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(- 1.0 (* (tan x) (tan x)))
93.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
37.0ms	(* (tan x) (tan x))
42.0ms	(* (tan x) (tan x))

simplify495.0ms

Counts

131 → 131

Iterations

Useful iterations: 2 (105.0ms)

Iter	Nodes	Cost
0	151	1789
1	339	1638
2	1140	1453
done	5001	1453

prune291.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 4 expressions with local error:

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

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 143

Calls

4 calls:

0.0ms	(fma (tan x) (tan x) 1.0)
35.0ms	(* (+ (tan x) (sqrt 1.0)) (/ (- (sqrt 1.0) (tan x)) (fma (tan x) (tan x) 1.0)))
14.0ms	(/ (- (sqrt 1.0) (tan x)) (fma (tan x) (tan x) 1.0))
6.0ms	(- (sqrt 1.0) (tan x))

series380.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(fma (tan x) (tan x) 1.0)
203.0ms	(* (+ (tan x) (sqrt 1.0)) (/ (- (sqrt 1.0) (tan x)) (fma (tan x) (tan x) 1.0)))
100.0ms	(/ (- (sqrt 1.0) (tan x)) (fma (tan x) (tan x) 1.0))
36.0ms	(- (sqrt 1.0) (tan x))

simplify858.0ms

Counts

155 → 155

Iterations

Useful iterations: 2 (183.0ms)

Iter	Nodes	Cost
0	224	3085
1	562	2688
2	2315	2322
done	5000	2322

prune371.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize14.0ms

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)

rewrite8.0ms

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

series69.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify1.2s

Counts

92 → 92

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	68	616
1	149	530
2	472	466
3	1504	466
done	5000	466

prune249.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- 1.0 (/ (* (tan x) (sin x)) (cos x))) (+ 1.0 (* (tan x) (tan x))))
0.1b	(/ (* (tan x) (sin x)) (cos x))
0.2b	(* (tan x) (sin x))
0.3b	(* (tan x) (tan x))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt`
30×	`*-un-lft-identity`
22×	`add-cube-cbrt`
18×	`times-frac`
15×	`add-exp-log` `add-cbrt-cube`
13×	`pow1`
6×	`tan-quot` `associate-r` `associate-l` `associate-/r` `associate-/l`
4×	`expm1-log1p-u` `log1p-expm1-u` `distribute-lft-out--` `add-log-exp` `difference-of-squares`
3×	`cbrt-undiv` `swap-sqr` `div-exp` `associate-*l/` `prod-exp` `cbrt-unprod` `associate-/l/`
2×	`frac-2neg` `pow-prod-down` `clear-num` `associate-/r/` `*-commutative` `div-inv` `unswap-sqr`
1×	`pow2` `frac-times` `flip3--` `flip3-+` `pow-plus` `div-sub` `associate-*r/` `pow-sqr` `pow-prod-up` `flip--` `flip-+`

Counts

4 → 117

Calls

4 calls:

19.0ms	(/ (- 1.0 (/ (* (tan x) (sin x)) (cos x))) (+ 1.0 (* (tan x) (tan x))))
5.0ms	(/ (* (tan x) (sin x)) (cos x))
5.0ms	(* (tan x) (sin x))
5.0ms	(* (tan x) (tan x))

series239.0ms

Counts

4 → 12

Calls

4 calls:

107.0ms	(/ (- 1.0 (/ (* (tan x) (sin x)) (cos x))) (+ 1.0 (* (tan x) (tan x))))
59.0ms	(/ (* (tan x) (sin x)) (cos x))
41.0ms	(* (tan x) (sin x))
31.0ms	(* (tan x) (tan x))

simplify586.0ms

Counts

129 → 129

Iterations

Useful iterations: 2 (143.0ms)

Iter	Nodes	Cost
0	198	2029
1	461	1923
2	1781	1708
done	5000	1708

prune328.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

regimes143.0ms

Accuracy

0% (0.4b 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	19
1	15	19
done	15	19

end0.0ms

sample1.6s

Algorithm

intervals

Results

682.0ms	1515×	body	1280	valid
368.0ms	1230×	body	640	valid
255.0ms	4337×	body	80	valid
126.0ms	624×	body	320	valid
41.0ms	294×	body	160	valid