Details

sample542.0ms

Algorithm

intervals

Results

102.0ms	47×	body	2560	valid
86.0ms	87×	body	1280	valid
21.0ms	61×	body	640	valid
11.0ms	40×	body	320	valid
2.0ms	10×	body	160	valid
1.0ms	11×	body	80	valid

simplify16.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	6	9
1	13	9
2	17	9
3	19	9
done	19	9

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.3b

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))

rewrite56.0ms

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:

34.0ms	(/ (- x (sin x)) (- x (tan x)))
6.0ms	(- x (tan x))
10.0ms	(- x (sin x))

series181.0ms

Counts

3 → 9

Calls

3 calls:

79.0ms	(/ (- x (sin x)) (- x (tan x)))
59.0ms	(- x (tan x))
42.0ms	(- x (sin x))

simplify797.0ms

Counts

119 → 119

Iterations

Useful iterations: done (793.0ms)

Iter	Nodes	Cost
0	209	1823
1	476	1563
2	1343	1384
done	5000	1306

prune244.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize11.0ms

Local error

Found 3 expressions with local error:

0.3b	(fma 27/2800 (pow x 4) 1/2)
0.3b	(* 9/40 (pow x 2))
15.8b	(- (* 9/40 (pow x 2)) (fma 27/2800 (pow x 4) 1/2))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt`
8×	`add-exp-log` `associate-r`
7×	`add-cube-cbrt` `*-un-lft-identity`
5×	`add-cbrt-cube` `add-log-exp`
4×	`unpow-prod-down` `unswap-sqr`
3×	`pow1` `expm1-log1p-u` `associate-l` `prod-diff` `prod-exp` `log1p-expm1-u`
2×	`fma-udef` `unpow2` `sqr-pow`
1×	`pow-to-exp` `sub-neg` `flip3--` `fma-neg` `diff-log` `pow-exp` `*-commutative` `flip--` `cbrt-unprod` `associate--r+`

Counts

3 → 58

Calls

3 calls:

0.0ms	(fma 27/2800 (pow x 4) 1/2)
12.0ms	(* 9/40 (pow x 2))
14.0ms	(- (* 9/40 (pow x 2)) (fma 27/2800 (pow x 4) 1/2))

series161.0ms

Counts

3 → 9

Calls

3 calls:

85.0ms	(fma 27/2800 (pow x 4) 1/2)
30.0ms	(* 9/40 (pow x 2))
47.0ms	(- (* 9/40 (pow x 2)) (fma 27/2800 (pow x 4) 1/2))

simplify1.8s

Counts

67 → 67

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	106	845
1	219	700
2	588	624
3	2787	573
done	5000	572

prune148.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (/ (sin x) (cos x))))
0.1b	(/ (sin x) (cos x))
2.1b	(- x (/ (sin x) (cos x)))
2.1b	(- x (sin x))

rewrite82.0ms

Algorithm

rewrite-expression-head

Rules

118×	`add-sqr-sqrt`
97×	`*-un-lft-identity`
73×	`times-frac`
67×	`add-cube-cbrt`
48×	`prod-diff`
22×	`difference-of-squares`
15×	`distribute-lft-out--`
9×	`associate-/r*`
8×	`add-exp-log` `add-cbrt-cube` `associate-/l*` `add-log-exp`
6×	`fma-neg`
5×	`div-inv`
4×	`pow1` `expm1-log1p-u` `flip3--` `flip--` `log1p-expm1-u`
2×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-exp` `clear-num` `associate-/r/` `associate-/l/`
1×	`quot-tan` `div-sub`

Counts

4 → 177

Calls

4 calls:

41.0ms	(/ (- x (sin x)) (- x (/ (sin x) (cos x))))
9.0ms	(/ (sin x) (cos x))
16.0ms	(- x (/ (sin x) (cos x)))
8.0ms	(- x (sin x))

series187.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(/ (- x (sin x)) (- x (/ (sin x) (cos x))))
20.0ms	(/ (sin x) (cos x))
51.0ms	(- x (/ (sin x) (cos x)))
37.0ms	(- x (sin x))

simplify1.4s

Counts

189 → 189

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	325	4357
1	746	3810
2	2271	3031
done	5000	2697

prune319.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sin x) (cos x))
2.0b	(- (/ x (- x (/ (sin x) (cos x)))) (/ (sin x) (- x (/ (sin x) (cos x)))))
2.1b	(- x (/ (sin x) (cos x)))
2.1b	(- x (/ (sin x) (cos x)))

rewrite344.0ms

Algorithm

rewrite-expression-head

Rules

1341×	`add-sqr-sqrt`
1116×	`times-frac`
900×	`*-un-lft-identity`
654×	`prod-diff`
574×	`add-cube-cbrt`
306×	`difference-of-squares`
162×	`distribute-lft-out--`
102×	`associate-/r/`
58×	`div-inv`
54×	`flip3--` `flip--`
30×	`fma-neg`
10×	`add-log-exp`
6×	`add-exp-log` `add-cbrt-cube`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
3×	`sub-neg` `distribute-rgt-out--` `diff-log` `associate-/r` `associate-/l`
1×	`cbrt-undiv` `quot-tan` `frac-2neg` `div-exp` `clear-num` `frac-sub` `sub-div`

Counts

4 → 780

Calls

4 calls:

9.0ms	(/ (sin x) (cos x))
216.0ms	(- (/ x (- x (/ (sin x) (cos x)))) (/ (sin x) (- x (/ (sin x) (cos x)))))
15.0ms	(- x (/ (sin x) (cos x)))
16.0ms	(- x (/ (sin x) (cos x)))

series313.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(/ (sin x) (cos x))
183.0ms	(- (/ x (- x (/ (sin x) (cos x)))) (/ (sin x) (- x (/ (sin x) (cos x)))))
51.0ms	(- x (/ (sin x) (cos x)))
59.0ms	(- x (/ (sin x) (cos x)))

simplify1.6s

Counts

792 → 792

Iterations

Useful iterations: 2 (836.0ms)

Iter	Nodes	Cost
0	836	63656
1	1836	58367
2	4020	44264
done	5000	44264

prune1.5s

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes25.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 31.7b

bsearch91.0ms

Steps

Iters	Range		Point
11	6.1632953816490534e-12	2923699147.8271213	0.02652408205241486
10	-21283307590.397102	-3.152803306627408e-07	-0.02620088919165833

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	26	52
1	27	52
done	27	52

end0.0ms

sample6.7s

Algorithm

intervals

Results

3.6s	1608×	body	2560	valid
1.8s	2725×	body	1280	valid
778.0ms	1853×	body	640	valid
226.0ms	954×	body	320	valid
78.0ms	502×	body	160	valid
32.0ms	358×	body	80	valid