Details

sample549.0ms

Algorithm

intervals

Results

111.0ms	49×	body	2560	valid
90.0ms	92×	body	1280	valid
18.0ms	53×	body	640	valid
7.0ms	33×	body	320	valid
3.0ms	16×	body	160	valid
1.0ms	13×	body	80	valid

simplify10.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	13	5
1	17	5
2	19	5
3	19	5
done	19	5

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.4b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
2.1b	(- x (tan x))
2.1b	(- x (sin x))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

57×	`add-sqr-sqrt` `*-un-lft-identity`
29×	`add-cube-cbrt`
25×	`times-frac`
18×	`prod-diff`
14×	`distribute-lft-out--` `difference-of-squares`
7×	`add-log-exp`
6×	`fma-neg`
5×	`add-exp-log` `associate-/r` `add-cbrt-cube` `associate-/l`
4×	`flip3--` `flip--`
3×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
2×	`sub-neg` `diff-log` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

3 → 110

Calls

3 calls:

25.0ms	(/ (- x (sin x)) (- x (tan x)))
6.0ms	(- x (tan x))
10.0ms	(- x (sin x))

series178.0ms

Counts

3 → 9

Calls

3 calls:

76.0ms	(/ (- x (sin x)) (- x (tan x)))
59.0ms	(- x (tan x))
43.0ms	(- x (sin x))

simplify57.0ms

Counts

119 → 119

Iterations

Useful iterations: 1 (11.0ms)

Iter	Nodes	Cost
0	472	1059
1	1737	854
2	5001	854
done	5001	854

prune230.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b	(fma 27/2800 (pow x 4) 1/2)
15.3b	(fma 9/40 (pow x 2) (- (fma 27/2800 (pow x 4) 1/2)))

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

2×	`pow1` `add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `fma-udef` `log1p-expm1-u` `add-log-exp`

Counts

2 → 20

Calls

2 calls:

0.0ms	(fma 27/2800 (pow x 4) 1/2)
0.0ms	(fma 9/40 (pow x 2) (- (fma 27/2800 (pow x 4) 1/2)))

series130.0ms

Counts

2 → 6

Calls

2 calls:

84.0ms	(fma 27/2800 (pow x 4) 1/2)
46.0ms	(fma 9/40 (pow x 2) (- (fma 27/2800 (pow x 4) 1/2)))

simplify142.0ms

Counts

26 → 26

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	51	133
1	162	117
2	626	117
3	3552	117
4	5001	117
done	5001	117

prune70.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize16.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma 27/2800 (pow x 4) 1/2)
0.5b	(log (exp (fma 9/40 (pow x 2) (- (fma 27/2800 (pow x 4) 1/2)))))
15.3b	(fma 9/40 (pow x 2) (- (fma 27/2800 (pow x 4) 1/2)))

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

5×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `log-prod` `log-pow`
3×	`add-exp-log` `expm1-log1p-u` `exp-prod` `add-cbrt-cube` `fma-udef` `log1p-expm1-u` `add-log-exp`
1×	`rem-log-exp` `exp-sum`

Counts

3 → 38

Calls

3 calls:

0.0ms	(fma 27/2800 (pow x 4) 1/2)
3.0ms	(log (exp (fma 9/40 (pow x 2) (- (fma 27/2800 (pow x 4) 1/2)))))
0.0ms	(fma 9/40 (pow x 2) (- (fma 27/2800 (pow x 4) 1/2)))

series176.0ms

Counts

3 → 9

Calls

3 calls:

83.0ms	(fma 27/2800 (pow x 4) 1/2)
48.0ms	(log (exp (fma 9/40 (pow x 2) (- (fma 27/2800 (pow x 4) 1/2)))))
45.0ms	(fma 9/40 (pow x 2) (- (fma 27/2800 (pow x 4) 1/2)))

simplify32.0ms

Counts

47 → 47

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	89	295
1	229	260
2	853	260
3	5002	260
done	5002	260

prune128.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

localize19.0ms

Local error

Found 4 expressions with local error:

2.1b	(- (pow x 3) (pow (tan x) 3))
2.1b	(- x (sin x))
5.2b	(/ (- x (sin x)) (- (pow x 3) (pow (tan x) 3)))
14.9b	(* (/ (- x (sin x)) (- (pow x 3) (pow (tan x) 3))) (+ (* x x) (+ (* (tan x) (tan x)) (* x (tan x)))))

rewrite301.0ms

Algorithm

rewrite-expression-head

Rules

547×	`add-sqr-sqrt`
374×	`*-un-lft-identity`
251×	`times-frac`
244×	`difference-of-squares`
219×	`unpow-prod-down` `cube-prod`
153×	`prod-diff`
150×	`add-cube-cbrt`
131×	`associate-l`
121×	`sqr-pow`
112×	`distribute-lft-out--`
25×	`cube-mult` `unpow3` `associate-/r*`
15×	`fma-neg`
12×	`difference-cubes`
11×	`add-exp-log` `add-cbrt-cube`
8×	`add-log-exp`
6×	`pow1`
5×	`flip3--` `flip--` `associate-/l*`
4×	`expm1-log1p-u` `associate-/r/` `log1p-expm1-u`
3×	`associate-r`
2×	`cbrt-undiv` `frac-times` `sub-neg` `flip3-+` `diff-log` `associate-*r/` `div-exp` `prod-exp` `cbrt-unprod` `flip-+` `div-inv` `associate-/l/` `unswap-sqr`
1×	`distribute-rgt-in` `frac-2neg` `distribute-lft-in` `div-sub` `pow-prod-down` `associate-l/` `clear-num` `-commutative`

Counts

4 → 552

Calls

4 calls:

30.0ms	(- (pow x 3) (pow (tan x) 3))
8.0ms	(- x (sin x))
52.0ms	(/ (- x (sin x)) (- (pow x 3) (pow (tan x) 3)))
176.0ms	(* (/ (- x (sin x)) (- (pow x 3) (pow (tan x) 3))) (+ (* x x) (+ (* (tan x) (tan x)) (* x (tan x)))))

series566.0ms

Counts

4 → 12

Calls

4 calls:

131.0ms	(- (pow x 3) (pow (tan x) 3))
31.0ms	(- x (sin x))
115.0ms	(/ (- x (sin x)) (- (pow x 3) (pow (tan x) 3)))
288.0ms	(* (/ (- x (sin x)) (- (pow x 3) (pow (tan x) 3))) (+ (* x x) (+ (* (tan x) (tan x)) (* x (tan x)))))

simplify102.0ms

Counts

564 → 564

Iterations

Useful iterations: 1 (34.0ms)

Iter	Nodes	Cost
0	1707	8155
1	5001	7080
done	5001	7080

prune939.0ms

Pruning

4 alts after pruning (0 fresh and 4 done)

Merged error: 0b

regimes58.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 30.9b

bsearch75.0ms

Steps

Iters	Range		Point
9	0.00021078761332869983	22.544919195950573	0.02833570517365807
8	-1.6220908197114983	-0.002799490342594777	-0.02627666216149913

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

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

end0.0ms

sample6.5s

Algorithm

intervals

Results

3.5s	1578×	body	2560	valid
1.9s	2771×	body	1280	valid
679.0ms	1866×	body	640	valid
218.0ms	948×	body	320	valid
79.0ms	462×	body	160	valid
34.0ms	375×	body	80	valid