Details

sample722.0ms

Algorithm

intervals

Results

216.0ms	63×	body	640	valid
202.0ms	51×	body	2560	valid
178.0ms	88×	body	1280	valid
15.0ms	27×	body	320	valid
6.0ms	18×	body	160	valid
1.0ms	9×	body	80	valid

simplify31.0ms

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

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.7b

localize25.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
1.0b	(- x (tan x))
1.0b	(- x (sin x))

rewrite149.0ms

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:

56.0ms	(/ (- x (sin x)) (- x (tan x)))
19.0ms	(- x (tan x))
63.0ms	(- x (sin x))

series320.0ms

Counts

3 → 9

Calls

3 calls:

122.0ms	(/ (- x (sin x)) (- x (tan x)))
107.0ms	(- x (tan x))
91.0ms	(- x (sin x))

simplify1.4s

Counts

119 → 119

Iterations

Useful iterations: done (1.3s)

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

prune432.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize32.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (sin x) 2)
0.3b	(pow (sin x) 2)
15.5b	(/ (pow (sin x) 2) (* (pow x 2) (pow (cos x) 2)))
15.5b	(/ (pow (sin x) 2) (* (pow x 2) (cos x)))

rewrite84.0ms

Algorithm

rewrite-expression-head

Rules

91×	`add-exp-log`
42×	`div-exp`
37×	`pow-to-exp` `pow-exp`
36×	`prod-exp`
18×	`unpow-prod-down`
16×	`add-sqr-sqrt` `add-cube-cbrt` `-un-lft-identity` `times-frac` `associate-/l`
14×	`add-cbrt-cube`
6×	`pow1` `pow-unpow` `unpow2` `sqr-pow`
4×	`cbrt-undiv` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`pow-pow` `frac-2neg` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

4 → 144

Calls

4 calls:

7.0ms	(pow (sin x) 2)
7.0ms	(pow (sin x) 2)
32.0ms	(/ (pow (sin x) 2) (* (pow x 2) (pow (cos x) 2)))
30.0ms	(/ (pow (sin x) 2) (* (pow x 2) (cos x)))

series251.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(pow (sin x) 2)
21.0ms	(pow (sin x) 2)
104.0ms	(/ (pow (sin x) 2) (* (pow x 2) (pow (cos x) 2)))
100.0ms	(/ (pow (sin x) 2) (* (pow x 2) (cos x)))

simplify993.0ms

Counts

156 → 156

Iterations

Useful iterations: 2 (244.0ms)

Iter	Nodes	Cost
0	167	2060
1	384	1856
2	1153	1661
done	5001	1661

prune629.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sin x) (- x (tan x)))
1.0b	(- x (tan x))
1.0b	(- x (tan x))
1.0b	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))

rewrite369.0ms

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)))
13.0ms	(- x (tan x))
14.0ms	(- x (tan x))
190.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))

series671.0ms

Counts

4 → 12

Calls

4 calls:

131.0ms	(/ (sin x) (- x (tan x)))
110.0ms	(- x (tan x))
104.0ms	(- x (tan x))
326.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))

simplify2.1s

Counts

600 → 600

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	617	35000
1	1353	31424
2	3026	23405
done	5000	20458

prune1.1s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 3 expressions with local error:

0.1b	(fma 27/2800 (pow x 4) 1/2)
0.1b	(* 9/40 (pow x 2))
14.8b	(- (* 9/40 (pow x 2)) (fma 27/2800 (pow x 4) 1/2))

rewrite49.0ms

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)
23.0ms	(* 9/40 (pow x 2))
23.0ms	(- (* 9/40 (pow x 2)) (fma 27/2800 (pow x 4) 1/2))

series243.0ms

Counts

3 → 9

Calls

3 calls:

129.0ms	(fma 27/2800 (pow x 4) 1/2)
38.0ms	(* 9/40 (pow x 2))
76.0ms	(- (* 9/40 (pow x 2)) (fma 27/2800 (pow x 4) 1/2))

simplify2.7s

Counts

67 → 67

Iterations

Useful iterations: done (2.7s)

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

prune227.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

regimes45.0ms

Accuracy

99% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 31.7b

bsearch181.0ms

Steps

Iters	Range		Point
9	0.21963308938311268	137362616.0762091	2.4305949570220666
11	-2445851338.3862987	-4.2674702477225e-16	-2.421622929505549

simplify5.0ms

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	33	100
1	45	61
done	45	61

end0.0ms

sample14.4s

Algorithm

intervals

Results

6.0s	1598×	body	2560	valid
5.3s	2730×	body	1280	valid
1.9s	1873×	body	640	valid
544.0ms	943×	body	320	valid
148.0ms	479×	body	160	valid
69.0ms	377×	body	80	valid