Details

sample446.0ms

Algorithm

intervals

Results

226.0ms	58×	body	2560	valid
81.0ms	75×	body	1280	valid
41.0ms	65×	body	640	valid
11.0ms	32×	body	320	valid
5.0ms	15×	body	160	valid
2.0ms	11×	body	80	valid

simplify29.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.0b

localize23.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
1.6b	(- x (tan x))
1.6b	(- x (sin x))

rewrite144.0ms

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:

53.0ms	(/ (- x (sin x)) (- x (tan x)))
21.0ms	(- x (tan x))
60.0ms	(- x (sin x))

series285.0ms

Counts

3 → 9

Calls

3 calls:

122.0ms	(/ (- x (sin x)) (- x (tan x)))
71.0ms	(- x (tan x))
92.0ms	(- x (sin x))

simplify1.8s

Counts

119 → 119

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	209	1823
1	501	1569
2	2266	1386
done	5002	1362

prune342.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma 27/2800 (pow x 4) 1/2)
0.1b	(* 9/40 (pow x 2))
14.1b	(- (* 9/40 (pow x 2)) (fma 27/2800 (pow x 4) 1/2))

rewrite56.0ms

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:

1.0ms	(fma 27/2800 (pow x 4) 1/2)
33.0ms	(* 9/40 (pow x 2))
19.0ms	(- (* 9/40 (pow x 2)) (fma 27/2800 (pow x 4) 1/2))

series219.0ms

Counts

3 → 9

Calls

3 calls:

120.0ms	(fma 27/2800 (pow x 4) 1/2)
30.0ms	(* 9/40 (pow x 2))
69.0ms	(- (* 9/40 (pow x 2)) (fma 27/2800 (pow x 4) 1/2))

simplify1.6s

Counts

67 → 67

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	106	845
1	250	714
2	1251	624
done	5001	581

prune275.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sin x) (- x (tan x)))
1.4b	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
1.6b	(- x (tan x))
1.6b	(- x (tan x))

rewrite308.0ms

Algorithm

rewrite-expression-head

Rules

713×	`*-un-lft-identity`
703×	`add-sqr-sqrt`
678×	`times-frac`
459×	`prod-diff`
417×	`add-cube-cbrt`
147×	`distribute-lft-out--`
141×	`difference-of-squares`
92×	`associate-/r/`
49×	`flip3--` `flip--`
46×	`div-inv`
27×	`fma-neg`
10×	`add-log-exp`
6×	`add-exp-log` `add-cbrt-cube`
5×	`associate-/r*`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
3×	`sub-neg` `distribute-rgt-out--` `diff-log` `associate-/l*`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `frac-sub` `sub-div`

Counts

4 → 588

Calls

4 calls:

34.0ms	(/ (sin x) (- x (tan x)))
163.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
15.0ms	(- x (tan x))
13.0ms	(- x (tan x))

series570.0ms

Counts

4 → 12

Calls

4 calls:

105.0ms	(/ (sin x) (- x (tan x)))
287.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
90.0ms	(- x (tan x))
87.0ms	(- x (tan x))

simplify2.9s

Counts

600 → 600

Iterations

Useful iterations: 2 (1.0s)

Iter	Nodes	Cost
0	617	35000
1	1404	31493
2	4797	24519
done	5000	24519

prune2.0s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

localize47.0ms

Local error

Found 4 expressions with local error:

1.6b	(- x (tan x))
1.6b	(- x (tan x))
1.6b	(- x (tan x))
1.8b	(fma (/ 1 (* (cbrt (- x (tan x))) (cbrt (- x (tan x))))) (/ x (cbrt (- x (tan x)))) (/ (- (/ (sin x) (cbrt (- x (tan x))))) (* (cbrt (- x (tan x))) (cbrt (- x (tan x))))))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-sqr-sqrt` `*-un-lft-identity`
27×	`prod-diff`
25×	`add-cube-cbrt`
10×	`add-log-exp`
9×	`fma-neg`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--` `difference-of-squares`
1×	`fma-udef`

Counts

4 → 94

Calls

4 calls:

13.0ms	(- x (tan x))
13.0ms	(- x (tan x))
24.0ms	(- x (tan x))
1.0ms	(fma (/ 1 (* (cbrt (- x (tan x))) (cbrt (- x (tan x))))) (/ x (cbrt (- x (tan x)))) (/ (- (/ (sin x) (cbrt (- x (tan x))))) (* (cbrt (- x (tan x))) (cbrt (- x (tan x))))))

series586.0ms

Counts

4 → 12

Calls

4 calls:

99.0ms	(- x (tan x))
72.0ms	(- x (tan x))
104.0ms	(- x (tan x))
311.0ms	(fma (/ 1 (* (cbrt (- x (tan x))) (cbrt (- x (tan x))))) (/ x (cbrt (- x (tan x)))) (/ (- (/ (sin x) (cbrt (- x (tan x))))) (* (cbrt (- x (tan x))) (cbrt (- x (tan x))))))

simplify1.0s

Counts

106 → 106

Iterations

Useful iterations: done (1.0s)

Iter	Nodes	Cost
0	122	1910
1	274	1570
2	994	1240
done	5001	1121

prune564.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0.0b

regimes33.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 32.3b

bsearch153.0ms

Steps

Iters	Range		Point
8	0.0004268116563047139	15.006088268796836	0.029128717039290496
8	-101.50163225226844	-0.031678663534995	-0.03379760502135155

simplify6.0ms

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	23	48
1	27	35
done	27	35

end0.0ms

sample13.2s

Algorithm

intervals

Results

6.8s	1549×	body	2560	valid
4.0s	2796×	body	1280	valid
1.3s	1891×	body	640	valid
619.0ms	934×	body	320	valid
129.0ms	461×	body	160	valid
58.0ms	369×	body	80	valid