Details

sample454.0ms

Algorithm

intervals

Results

197.0ms	45×	body	2560	valid
106.0ms	86×	body	1280	valid
39.0ms	56×	body	640	valid
17.0ms	34×	body	320	valid
6.0ms	20×	body	160	valid
3.0ms	15×	body	80	valid

simplify23.0ms

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

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.3b

localize22.0ms

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))

rewrite115.0ms

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:

76.0ms	(/ (- x (sin x)) (- x (tan x)))
14.0ms	(- x (tan x))
19.0ms	(- x (sin x))

series217.0ms

Counts

3 → 9

Calls

3 calls:

84.0ms	(/ (- x (sin x)) (- x (tan x)))
75.0ms	(- x (tan x))
58.0ms	(- x (sin x))

simplify1.3s

Counts

119 → 119

Iterations

Useful iterations: done (1.3s)

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

prune332.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sin x) (- x (tan x)))
2.0b	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
2.1b	(- x (tan x))
2.1b	(- x (tan x))

rewrite275.0ms

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:

33.0ms	(/ (sin x) (- x (tan x)))
158.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
12.0ms	(- x (tan x))
13.0ms	(- x (tan x))

series566.0ms

Counts

4 → 12

Calls

4 calls:

111.0ms	(/ (sin x) (- x (tan x)))
312.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
69.0ms	(- x (tan x))
74.0ms	(- x (tan x))

simplify2.1s

Counts

600 → 600

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	617	35000
1	1353	31424
2	3023	23405
done	5001	20458

prune1.0s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize71.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (sin x) 2)
0.3b	(pow (sin x) 2)
13.0b	(/ (pow (sin x) 2) (* (pow x 2) (pow (cos x) 2)))
13.0b	(/ (pow (sin x) 2) (* (pow x 2) (cos x)))

rewrite91.0ms

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)
8.0ms	(pow (sin x) 2)
38.0ms	(/ (pow (sin x) 2) (* (pow x 2) (pow (cos x) 2)))
34.0ms	(/ (pow (sin x) 2) (* (pow x 2) (cos x)))

series222.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(pow (sin x) 2)
26.0ms	(pow (sin x) 2)
93.0ms	(/ (pow (sin x) 2) (* (pow x 2) (pow (cos x) 2)))
81.0ms	(/ (pow (sin x) 2) (* (pow x 2) (cos x)))

simplify912.0ms

Counts

156 → 156

Iterations

Useful iterations: 2 (256.0ms)

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

prune697.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize20.0ms

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))
13.8b	(- (* 9/40 (pow x 2)) (fma 27/2800 (pow x 4) 1/2))

rewrite38.0ms

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)
13.0ms	(* 9/40 (pow x 2))
23.0ms	(- (* 9/40 (pow x 2)) (fma 27/2800 (pow x 4) 1/2))

series291.0ms

Counts

3 → 9

Calls

3 calls:

168.0ms	(fma 27/2800 (pow x 4) 1/2)
39.0ms	(* 9/40 (pow x 2))
84.0ms	(- (* 9/40 (pow x 2)) (fma 27/2800 (pow x 4) 1/2))

simplify2.6s

Counts

67 → 67

Iterations

Useful iterations: done (2.6s)

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

prune199.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

regimes54.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 31.4b

bsearch129.0ms

Steps

Iters	Range		Point
10	1.5244367550608482e-07	9556.682540875734	0.03007487465186483
9	-1501.2167507114543	-0.006495210018506858	-0.027057923325783554

simplify3.0ms

Iterations

Useful iterations: 1 (2.0ms)

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

end0.0ms

sample14.2s

Algorithm

intervals

Results

6.2s	1545×	body	2560	valid
5.3s	2810×	body	1280	valid
1.5s	1867×	body	640	valid
491.0ms	952×	body	320	valid
222.0ms	463×	body	160	valid
109.0ms	363×	body	80	valid